Florent Patrice

Aymeric, Manuel Nicolas Angélique

ATLAS Danish Tel

Keywords: LIGO, Virgo Fermi, INTEGRAL, Astrosat, IPN, Insight-HXMT, Swift, AGILE, CALET, H

tout au long de ce périple, que ce soit dans mon travail ou sur le plan personnel.

Résumé: L'événement GW170817 a permis d'observer pour la première fois des ondes gravitationnelles (OG) provenant d'une fusion de binaire d'étoiles à neutrons (BNS) avec des contreparties associées sur l'ensemble du spectre électromagnétique. Cette découverte a permis de répondre à d'importantes questions ouvertes en astrophysique moderne, notamment en démontrant l'association longtemps hypothétique des sursauts gamma (GRB) courts et des fusions d'étoiles à neutrons. Malgré les nombreux résultats qui ont découlé de GW170817, notre compréhension des sources de ces processus physiques complexes et violents demeure incomplète. Nous ignorons également si les propriétés de GW170817 sont communes à toutes les fusions d'étoiles à neutrons ou si elles représentent un cas exceptionnel. D'autres détections conjointes sont nécessaires pour explorer la relation entre les paramètres déduits de l'OG et les propriétés du signal GRB, ce qui pourrait permettre d'invalider certains des modèles existants des processus physiques responsables de ces événements. A cet effet, nous avons développé une analyse multi-messager conjointe des données de LIGO, Virgo (détecteurs deuxième génération (2G)) et Fermi/GBM, conçue pour détecter les événements transitoires OG sous le seuil associé à des GRB sous le seuil. Nous considérons la liste complète des candidats générés par les recherches produites par des systèmes binaires d'objets compactes et nous réanalysons l'ensemble des données publiques Fermi/GBM couvrant le même cycle d'observations pour générer un ensemble compatible de candidats aux GRB, dans l'espoir de trouver davantage de détections conjointes. Au sein de l'équipe, j'ai également appliqué l'une des méthodes de recherche qui a produit les événements rapportés dans le catalogue GWTC et j'ai travaillé sur divers projets visant à améliorer la sensibilité de la recherche OG. Nous avons ainsi mis en place une nouvelle méthode visant à distinguer le bruit des détecteurs des signaux astrophysiques. Ces activités impliquent des techniques telles que la détection de signaux avec filtrage adapté, l'inférence Bayésienne des paramètres, la génération d'une banque de modèles de formes d'ondes et le calcul scientifique sur de grandes grappes d'ordinateurs. Enfin, je me suis intéressée à la prochaine génération de détecteurs OG, en particulier Einstein Telescope (ET) qui devrait détecter annuellement plus de 10 000 BNS. Nous avons commencé à réfléchir à la manière d'analyser ses données car des différences importantes par rapport aux détecteurs 2G devront être prises en compte et avons décidé de nous concentrer sur la différence de durée des signaux BNS dans le détecteur. Abstract: The GW170817 event provided the first observation of gravitational waves (GW) from a neutron star (NS) merger with associated transient counterparts across the entire electromagnetic spectrum. This discovery answered important open questions in modern astrophysics, notably demonstrating the longhypothesized association between short gammaray bursts (GRB) and NS mergers. Despite the number of scientific results arisen from GW170817, we do not yet have a complete understanding of the complicated and violent physical processes that developed at the source. We also do not know if the properties of GW170817 are common to all NS mergers or do they represent an exceptional case. More joint detections are needed to explore the relation between the parameters inferred from the GW and the properties of the GRB signal, potentially ruling out some of the existing models of the physical processes responsible for these events. For this purpose, we developed a joint multi-messenger analysis of LIGO, Virgo (the 2G detectors), and Fermi/GBM data designed for detecting weak GW transients associated with weak GRB. We take the full list of exist-ing compact binary coalescence (CBC) triggers generated with the GW searches and reanalyze the entire set of public Fermi/GBM data covering the same observing run to generate a corresponding set of GRB candidate triggers in the hope to find more joint detections. I also applied one of the search methods that produced the events reported in the GWTC catalog and worked on various projects aimed at improving the GW search's sensitivity. We set up, for instance, a new method aimed at discriminating between glitches from astrophysical signals. These activities involved techniques such as signal detection with matched filtering, Bayesian parameter inference, template bank of waveform model generation, and scientific calculation on large computer clusters. Finally, I have been interested in the next generation of GW detectors, in particular Einstein Telescope (ET) which expects to detect more than 10 000 binary neutron star (BNS) signals per year. We have started to think about how to analyze its data now, important differences with respect to 2G detectors will need to be considered, and we have decided to focus on the difference in the duration of BNS signals in the detector. Depuis leur première détection en 2015, les ondes gravitationnelles (OG) sont devenues un vecteur d'information majeur pour l'astrophysique. Elles ouvrent la voie à de nouveaux outils d'observation et donc de compréhension de notre Univers. Tout objet massif est potentiellement une source d'OG, et l'Univers en regorge. Parmi toutes les sources possibles d'OG, les systèmes binaires de trous noirs ou d'étoiles à neutrons (NS) qui fusionnent (BBH, NSBH, BNS), les CBC, sont les sources les plus lumineuses et les seules détectées actuellement par nos détecteurs d'OG au sol (détecteurs deuxième génération, 2G) LIGO [START_REF] Aasi | Advanced ligo. Classical and Quantum Gravity[END_REF] et Virgo [START_REF] Acernese | Advanced virgo: a second-generation interferometric gravitational wave detector[END_REF]. Ces sources peuvent être étudiées directement par le biais des OG qu'elles émettent et de nombreuses propriétés des sources sont encodées dans la forme d'OG détectée. Cependant, les signal OG n'est pas le seul signal qui peut être détecté lors de tels événements. Les fusions d'étoiles à neutrons sont des sources multi-messagers qui peuvent produire des sursauts gamma (GRB) courts (ainsi que leur émission rémanente et leurs contreparties kilonova peuvent également être observées par des télescopes observant dans le domaine électroamgnétique), et éventuellement des neutrinos et des rayons cosmiques, en plus des OG. L'observation des GRBs provenant d'une fusion d'étoiles à neutrons apporte des informations complémentaires sur les éjectas de la fusion, leurs géometries (par exemple, l'orientation du jet), et permet de déterminer avec précision l'emplacement de la source dans le ciel.

La première et seule observation complète multi-messagers d'une fusion d'étoiles à neutrons a eu lieu pendant la deuxième prise de données d'OG, le 17 août 2017, avec la détection conjointe d'une OG et d'un GRB court : GW170817 -GRB 170817A, qui a démontré l'association longtemps hypothétique entre les sGRBs et les fusions d'étoiles à neutrons. Cette détection conjointe a donné naissance à l'ère de l'astronomie multi-messagers avec les ondes gravitationnelles qui consiste à combiner les observations de différents signaux ("messagers") de la source astrophysique commune.

La deuxième prise de données (O2) a commencé le 30 novembre 2016 avec les deux détecteurs LIGO Hanford (H1) et Livingston (L1), qui ont été rejoints par Virgo (V1) le 1 er août 2017. À cette date, deux détections de BBH avaient déjà été annoncées dans le cadre de la campagne O2. Vers la fin de O2, le 17 août 2017 à 12:41:04 UTC, le premier signal OG provenant d'une fusion BNS a été observé. Le réseau de détecteurs a détecté la partie inspiralante de l'OG d'une durée "100 s (calculée avec une fréquence de départ de 24 Hz), avec une évolution de la forme d'onde plus lente que tous les systèmes BBH observés à cette époque, ce qui implique une "chirp mass" beaucoup plus faible. Les masses (m 1 P 1.36 -2.26 M d and m 2 P 0.86 -1.36 M d ) et les spins (ď 0.1) des deux objets se situent dans les gammes attendue pour les étoiles à neutrons.

12 GW170817 a été localisée près de l'extrémité sud de la constellation de l'Hydre. Virgo a joué un rôle essentiel dans la réduction de la localisation à une seule région du ciel. De plus, GW170817 était la source OG la plus proche jamais observée avec une distance de luminosité à la source de D L " 40 `8 ´14 Mpc. Les observations complémentaires détaillées ci-dessous ont conduit à l'identification de NGC4993 comme la galaxie hôte de GW170817.

• Des études théoriques [START_REF] Metzger | What is the Most Promising Electromagnetic Counterpart of a Neutron Star Binary Merger[END_REF][START_REF] Piran | The electromagnetic signals of compact binary mergers[END_REF] prédisent que les fusions BNS sont des événements multi-messagers donnant des signatures à travers le spectre électromagnétique, y compris l'émission de rayons gamma. Environ 1.7 secondes après GW170817, le Fermi Gamma-ray Burst Monitor (Fermi/GBM) [START_REF] Charles | The Fermi Gamma-ray Burst Monitor[END_REF] et le Anti-Coincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory (INTEGRAL) [START_REF] Rau | The 1st integral spi-acs gamma-ray burst catalogue[END_REF], deux instruments utilisés pour observer la forme de lumière la plus énergétique de l'univers, les GRB, ont détecté indépendamment un GRB court appelé GRB 170817A [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF]. Cette association sans ambiguïté a confirmé que les fusions BNS sont les progéniteurs des (au moins certains) GRB courts et a marqué le début de la recherche des contreparties électromagnétiques des BNS sur l'ensemble du spectre.

• Des prédictions théoriques affirment que la fusion de deux étoiles à neutrons produirait un transitoire optique + proche infrarouge (NIR) (d'une durée de quelques jours) connu sous le nom de "kilonova". Environ 11 heures après la fusion, la détection d'une contrepartie optique de GW710817, initialement appelée "AT 2017gfo" (et plus tard KN170817), a été signalée pour la première fois [START_REF] Valenti | The discovery of the electromagnetic counterpart of GW170817: Kilonova AT 2017gfo/DLT17ck[END_REF][START_REF] Daniel | GW170817 -the first observed neutron star merger and its kilonova: Implications for the astrophysical site of the r-process[END_REF]. Cette contrepartie a ensuite été identifiée comme une kilonova. Cette source optique transitoire et évanescente, appelée SSS17a (Swope Supernova Survey 2017a), a été localisée dans NGC 4993, une galaxie située à une distance de 40 Mpc, ce qui nous a permis d'identifier la galaxie hôte de GW170817 -GRB 170817A. Cette détection a confirmé que les fusions BNS produisent des kilonovae dont les propriétés d'émission sont en accord avec les prédictions théoriques [START_REF] Arcavi | Optical emission from a kilonova following a gravitational-wave-detected neutron-star merger[END_REF].

• L'émission des GRB se déroule en deux phases : la phase d'émission initiale, l'émission rapide, et la seconde, la rémanence, qui se produit lorsque le jet entre en collision avec le milieu interstellaire environnant et qui peut être détectée dans une large gamme de fréquences, y compris dans les rayons X. Le 26 août 2017, 9 jours après l'émission de l'OG et du GRB, le Chandra X-ray Observatory (CX0) [START_REF] Weisskopf | Chandra X-ray Observatory (CXO): overview[END_REF] a détecté une émission de rayons X avec une exposition de 50ks à la position de SSS17a [START_REF] Troja | The x-ray counterpart to the gravitational-wave event GW170817[END_REF]. Les observations de la rémanence des rayons X ont également révélé le comportement d'un jet de GRB vu hors axe par rapport à la ligne de visée des observateurs (c'est-àdire l'observateur qui n'est pas situé sur l'axe du jet) [START_REF] Van Eerten | OFF-AXIS GAMMA-RAY BURST AFTERGLOW MODELING BASED ON a TWO-DIMENSIONAL AXISYMMETRIC HYDRODYNAMICS SIMULATION[END_REF]. La rémanence des GRB peut également être observée dans les fréquences radio. L'étude de la contrepartie radio fournit des informations sur la trace de l'éjecta en mouvement rapide d'une coalescence NS, ce qui donne des connaissances sur l'énergétique de l'explosion, la géométrie de l'éjecta et l'environnement de 0.2. Amélioration de la sensibilité de la recherche d'ondes gravitationnelles la fusion. La première contrepartie radio compatible avec l'emplacement de SSS17a/AT 2017gfo a été détectée avec le Very Large Array (VLA) [START_REF] Thompson | The Very Large Array[END_REF] les 2 et 3 septembre 2017. Plusieurs années après cette détection conjointe unique, de nombreux observatoires mesurent encore une rémanence tardive radio et rayons X associées au GRB 170718A [START_REF] Balasubramanian | Continued radio observations of GW170817 3.5 yr post-merger[END_REF][START_REF] Wang | GRB 190829a-a showcase of binary late evolution[END_REF].

• La coalescence de deux étoiles à neutrons est possiblement une source de neutrinos émis dans le flux relativiste produit par la fusion [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF][START_REF] Eichler | Nucleosynthesis, Neutrino Bursts and Gamma-Rays from Coalescing Neutron Stars[END_REF]. La détection de GW170817 a conduit à la recherche de neutrinos coïncidents de haute énergie (GeV-EeV) par IceCube [START_REF] Aartsen | The IceCube neutrino observatory: instrumentation and online systems[END_REF], ANTARES [START_REF] Ageron | ANTARES: The first undersea neutrino telescope[END_REF] et l'Observatoire Pierre Auger [START_REF] Pierre | The pierre auger cosmic ray observatory[END_REF]. Aucun candidat significatif n'a été trouvé avec l'une ou l'autre de ces recherches.

La détection conjointe de GW170817 et de GRB 170817A a marqué une étape importante pour l'astronomie multi-messagers. Elle a confirmé qu'au moins une fraction des GRB courts provient de fusions d'étoiles à neutrons. Cette détection conjointe a également eu des implications en physique des GRBs (formation des jets, éjecta de la fusion...), en astrophysique/physique plus généralement (contraindre la célérité des ondes gravitationnelles, tester différentes équations d'état des étoiles à neutrons, estimer le taux de fusion des BNS...), et en cosmologie (mesurer la constante de Hubble H 0 ). Cependant, de nombreuses questions restent ouvertes par exemple les propriétés de GW170817 sont-elles communes à toutes les fusions d'étoiles à neutrons ou représentent-elles un cas exceptionnel ? Nous avons également été confrontés à un cas intéressant au cours des dernières années, remettant en cause la classification GRB courts -GRB long, où une kilonova pourrait avoir été associée à un GRB long [START_REF] Rastinejad | A kilonova following a long-duration gamma-ray burst at 350 mpc[END_REF]. Cela soulève la question de la fraction de GRB courts et longs associés à des fusions d'étoiles à neutrons.

Un plus grand nombre de détections conjointes sont nécessaires afin d'apporter des éléments de réponse à ces questions. C'est pourquoi, dans le cadre de mon doctorat, nous nous sommes concentrés sur la recherche de coïncidences dans les données LIGO/Virgo et Fermi/GBM dans l'espoir de trouver davantage de détections conjointes de OG/GRB.

. Amélioration de la sensibilité de la recherche d'ondes gravitationnelles

Dans un premier temps, j'ai effectué un travail sur l'analyse des données OG afin d'explorer l'amélioration la sensibilité de la recherche dans le cadre de l'analyse PyCBC. Les techniques d'analyses de données OG ainsi que mon travail sur la sensibilité de l'analyse sont présentés dans les Chapitres 2 et 3.

PyCBC [START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF] est un algorithme qui utilise des techniques de filtrage adapté [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF] afin de trouver des signaux OG provenant de systèmes binaires compactes dans les données fortement bruitées des détecteurs LIGO/Virgo. PyCBC travaille avec des banques de modèles de formes d'onde gravitationnelle et filtre les données des détecteurs en les corrélant avec les modèles de la banque. PyCBC calcule un rapport signal sur bruit (SNR) et génére des candidats OG soumis à des tests afin de vérifier leur significance, tels que le test du χ 2 : une signal OG a une forme très specifique, appelée un chirp , dans le plan temps-fréquence (i.e spectrogramme) dissociable des bruits que l'on peut trouver dans le détecteurs (bruits Gaussien ou transitoires d'origine instrumentale ou environnementale); le test du χ 2 détermine si le SNR du candidat dans le plan temps-fréquence est bien réparti le long de celle attendue de la forme d'onde du modèle correspondant. Cependant, le χ 2 ne prend en compte que le SNR distribué du modèle correspondant. Pour mieux rejeter les bruits transitoires, nous voulons aussi prendre en compte le SNR en dehors du modèle, car nous nous attendons à ce que l'excès de puissance déclenché par un bruit transitoire ne soit pas bien distribué du chirp. Cette méthode viendrait compléter le test du χ 2 déjà mis en place dans PyCBC.

Pour ce faire, nous utilisons l'algorithme Omicron [START_REF] Robinet | Omicron: A tool to characterize transient noise in gravitational-wave detectors[END_REF] qui a été développé pour comprendre et distinguer les signaux OG des bruits transitoires. Omicron permet de visualiser les bruit transitoires des détecteurs et les événements OG à l'aide de spectrogrammes (donnant une représentation de la variation tempsfréquence du signal). Nous définissons une métrique qui calcule l'écart-type de la distance (en temps) entre le modèle généré avec PyCBC et les tuiles Omicron associées. Nous nous attendons à avoir une métrique proche de 0 dans le cas d'un signal astrophysiqueet une métrique qui dévie de 0 pour un bruit transitoire. Nous calculons cette métrique pour chaque candidat provenant d'un segment de données de la prise de données O3 et nous repondérons le SNR des candidats en fonction de leur valeur de métrique et de durée et réanalysons le segment afin d'explorer l'amélioration de la sensibilité de PyCBC grâce à la métrique. Le rapport de sensibilité avant/après l'application de la métrique est présenté sur la Figure 1. Pour vérifier les performances de la recherche, PyCBC injecte des signaux simulés (injections) et j'ai comparé la capacité de PyCBC à les retrouver avec et sans l'application de la métrique. Nous pouvons voir qu'il y a une amélioration de l'ordre de " 20% pour les signaux dans la gamme de masse élevée (BBH). Cela pourrait être utile pour les recherches de CBC, car la forme temps-fréquence de certains bruit transitoires courts ressemble à l'empreinte OG des CBC avec une grande masse totale [START_REF] Cabero | Blip glitches in advanced LIGO data[END_REF]. Au contraire, pour les signaux de faible masse, un bruit transitoire chevauchant le chirp de longue durée est plus facile à détecter. En revanche, l'impact sur les signaux de faible masse (BNS, NSBH) semble négligeable, principalement en raison de bruits transitoires chevauchant les injections de longue durée.

Pour résoudre ce problème, nous envisageons de calculer la métrique en tenant compte uniquement des tuiles Omicron situées dans une fenêtre de ˘1 s centrée sur l'instant de la fusion du candidat fournit par PyCBC. Cela permettra d'éliminer les potentiels bruits transitoires chevauchant les injections de longue durée éloignés du moment fusion. Nous envisageons également de calculer la distance euclidienne (i.e. dans le plan temps-fréquence) au lieu de la distance temporelle entre les tuiles et le chirp PyCBC. Le taux de fausse alarme FAR (ou inverse FAR, IFAR) d'un candidat donne une idée quantitative de la fréquence à laquelle le bruit génère un candidat. Il est défini comme le taux de bruit de fond dont la statistique de classement est égale ou supérieure à celle observée pour le candidat en question [START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF][START_REF] Morrá | False alarms induced by gaussian noise in gravitational wave detectors[END_REF]. Elle donne donc une interprétation fréquentiste à la statistique de classement.

. Nouvelles détections OG/GRB conjointes?

La seconde étape pour augmenter le nombre de détections communes entre GRB et OG de travailler sur trouver plus de coincidences entre détecteurs gamma comme Fermi/GBM et les détecteurs d'OG. Je me suis ici concentrée sur le seul instrument Fermi/GBM. Nous avons crée un algorithme automatique pour analyser une grande quantité de données à la fois dans les canaux OG et GBM sans avoir besoin d'une détection confirmée dans l'un des deux canaux.

Depuis O1, plusieurs approches indépendantes ont été testées pour la recherche d'associations OG/GRB, telles que PyGRB [START_REF] Abbott | Search for gravitational waves associated with gamma-ray bursts during the first advanced LIGO observing run and implications for the origin of GRB 150906b[END_REF] et X-pipeline [START_REF] Sutton | X-pipeline: An analysis package for autonomous gravitational-wave burst searches[END_REF][START_REF] Abbott | Search for gravitational waves associated with gamma-ray bursts during the first advanced LIGO observing run and implications for the origin of GRB 150906b[END_REF], qui supposent la détection d'un GRB et effectuent une recherche approfondie d'un signal OG proche (ou plus généralement de transitoires OG dans le cas de X-pipeline). Parmi les analyses à faible latence, RAVEN [START_REF] Abbott | Search for gravitational waves associated with gamma-ray bursts during the first advanced LIGO observing run and implications for the origin of GRB 150906b[END_REF][START_REF] Piotrzkowski | Searching for Sub-threshold Gravitational Wave Candidates with RAVEN[END_REF] suppose une détection OG et une détection électromagnétique et vérifie leur compatibilité temporelle et spatiale. Cependant, beaucoup de ces recherches ont des limitations statistiques ou informatiques qui empêchent leur application à un grand nombre d'événements candidats de faibles significances. Par exemple, X-pipeline et PyGRB nécessitent des heures ou des jours (sur un cluster de CPU) pour analyser les données OG autour de l'heure d'un seul GRB et partent de l'hypothèse que le GRB est une détection robuste en premier lieu.

Motivés par la possibilité que les GRBs courts proviennent de CBCs et par l'observation conjointe de GW170817 [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF] et GRB 170817A [START_REF] Goldstein | An ordinary short gamma-ray burst with extraordinary implications: Fermi-GBM detection of GRB 170817a[END_REF][START_REF] Savchenko | Integral detection of the first prompt gamma-ray signal coincident with the gravitational-wave event gw170817[END_REF] provenant d'une source BNS commune, nous développons une méthode pour rechercher les coïncidences entre les événements transitoires dans les données Fermi/GBM et les candidats CBC de LIGO/Virgo, afin d'augmenter le nombre de détections conjointes OG/GRB. Cette recherche est une recherche approfondie dans le sens où elle ne prend pas en compte uniquement les événements sûrs. Au contraire, dans notre approche, nous utilisons la liste complète des candidats Fermi/GBM et des candidats OG d'un cycle d'observation spécifique. L'objectif est de trouver les paires de candidats Fermi/GBM et OG qui pourraient avoir une origine commune, de les ordonner grâce à une statistique de classement et de leur attribuer un FAR. Notre statistique Bayésienne prend en compte la force du candidat dans leur canaux GBM et OG respectif et indépendemment l'un de l'autre et la proximité temporelle et spatiale des deux candidats. Afin de valider notre statistique de classement, nous l'avons d'abord appliqué sur les données de O2 pour vérifier que l'on retrouve bien GW170817 -GRB 170817A. Pour estimer la significance de nos associations candidates nous devons les comparer au bruit de fond de notre analyse. Pour estimer le bruit de fond, nous avec générer de fausses associations décalant temporellement les candidats GRB et cherchant des coincidences entre les candidats OG and les candidats GRB avec un décalage temporel. Le résultat final est présenté dans la Figure 2. Si nous avons une détection conjointe, nous verrons le nombre de coïncidences cumulées (sans décalage temporel) s'écarter de plus en plus du bruit de fond (région orange). Nous avons ici une association qui dévie de plus de 4σ. Il s'agit de GW170817 -GRB 170817A qui est détecté avec un IFAR " 1348 yr.

Nous avons ensuite appliqué notre méthode sur les données de la campagne O3. Nous avons utilisé les candidats OG générés par trois analyses CBC: PyCBC, GstLAL [START_REF] Sachdev | The gstlal search analysis methods for compact binary mergers in advanced ligo's second and advanced virgo's first observing runs[END_REF] et MBTA [START_REF] Adams | Low-latency analysis pipeline for compact binary coalescences in the advanced gravitational wave detector era[END_REF] . Les résultats sont présentés sur la Figure 3. Dans les trois cas, l'association avec l'IFAR le plus élevé est composé de GW190915_235702 un signal BBH de O3 et du bruit dans le canal GBM. Cette association obtient un FAR de " 1 tous les 2 ans avec GstLAL. Il semble très peu probable que cette paire ait une origine astrophysique commune du fait de son FAR élevé. Les associations suivantes ont des statistiques de classement proches de 0. Elles ne sont donc pas suffisamment significatives pour être étudiées. Ces résultats nuls sont cohérents avec d'autres recherches conjointes OG/GRB sur les données O3 qui ont été effectuées [START_REF]Search for gravitational waves associated with gamma-ray bursts detected by fermi and swift during the ligo-virgo run o3a[END_REF][START_REF] Abbott | Search for gravitational waves associated with gamma-ray bursts detected by fermi and swift during the LIGO-virgo run o3b[END_REF]. Avec l'amélioration de la sensibilité de nos détecteurs et de la prochaine génération de détecteurs OG, comme le télescope Einstein, le taux de vraies détections augmentera de manière significative, et donc le risque d'avoir de fausses coïncidences, par exemple un signal BBH proche dans le temps d'un GRB. Une façon d'éviter que les BBH bruyants ne limitent l'importance de potentielles vraies associations est de séparer les associations par M chirp . Une autre façon d'éviter la contamination par les signaux BBH bruyants est d'avoir une meilleure localisation dans le ciel des candidats. Une bonne localisation dans le ciel éliminera les coïncidences accidentelles démontrant que les deux candidats ne sont pas spatialement liés, réduisant ainsi le taux d'associations contenant des sigaux astrophysiques qui ne proviennent pas de la même source.

. Un regard vers l'avenir: Einstein Telescope

Dans le chapitre 6, j'ai étudié le potentiel scientifique de la prochaine génération d'instrument en utilisant plus particulièrement le télescope Einstein (ET) [START_REF] Sathyaprakash | Scientific objectives of einstein telescope[END_REF], avec lequel nous espérons détecter " 7 ˆ10 4 signaux BNS par an [START_REF] Singh | Exploring compact binary populations with the Einstein Telescope[END_REF]. ET sera situé à quelques centaines de mètres sous terre afin de réduire le bruit sismique et de gagner ainsi en sensibilité. Il cible également une gamme de fréquences plus large ([1 Hz, 10 kHz]) par rapport aux détecteurs 2G. L'un des principaux modèles étudiés jusqu'à présent est un détecteur de forme triangulaire composé de trois interféromètres avec un angle d'ouverture de 60 degrés. Le grand nombre de détections attendu aura un impact important sur la manière d'analyser ces données et ces questions sont actuellement étudiées par la collaboration ET.

Dans ce chapitre, je me suis intéressée à la durée des signaux BNS dans le détecteur, qui augmentera considérablement avec ET par rapport aux détecteurs 2G. Nous voulons donc étudier l'impact d'une durée de signal plus longue sur les détections BNS avec ET. Puisque la gamme de fréquence sera plus large qu'avec nos détecteurs actuels, la partie spiralante des signaux passeront plus de temps (des heures à des jours, en fonction de la masse de la binaire) dans la bande passante du détecteur. Par exemple, un signal similaire à celui de GW170817 aurait duré environ une journée dans la bande passante du détecteur ET (avec f start " 2 Hz). Jusqu'à présent, les signaux OG n'ont été observés dans LIGO/Virgo que pendant quelques secondes (pour BBH), ou quelques minutes (pour BNS). Nous avons donc considéré la réponse des détecteurs 2G (représentée par leurs diagrammes d'antenne) constante dans le temps. Avec ET, la rotation de la Terre ne sera pas négligeable pendant la durée du signal dans le détecteur, et l'approximation des diagrammes d'antenne constants dans le temps pourrait ne plus être valable. 0.4. Un regard vers l'avenir: Einstein Telescope A priori, les signaux BNS seront les plus affectés en raison de leur faible masse. Pour étudier l'effet de la rotation de la Terre sur les signaux BNS avec ET, nous devons quantifier la perte de SNR due à l'approximation. Nous pouvons d'abord simuler des signaux BNS provenant de différents endroits du ciel avec et sans l'approximation des diagrammes d'antenne constants dans le temps, puis calculer la ressemblance (le match, m) entre les deux formes d'onde. Plus le match est proche de 0 plus les signaux sont différents. Plus il est proche de 1 plus les signaux se ressemblent. La réponse du détecteur dépend de la localisation dans le ciel de la source, il est donc naturel de penser que le match va aussi dépendre de la position dans le ciel. Nous générons donc une carte du mismatch (= 1 ´m) dans le plan ascension droite -déclination (i.e. le système de coordonnées équatoriales). Cette carte est représentée sur la partie gauche de la Figure 4. Ici, nous avons fixé l'inclinaison de la source à 0 ˝. La ressemblance entre les signaux avec et sans l'approximation est grande presque partout sauf pour quatre positions dans le ciel qui correspondent aux régions où la réponse du détecteur ET est faible. Nous générons ensuite une population de BNS en prenant en compte l'effet cosmologique du redshift (les étoiles ne sont pas uniformément réparties dans l'Univers) et pour chaque signal BNS, nous calculons le SNR observé avec ET utilisant un modèle avec les paramètres intrinsèques corrects et qui modélise la rotation de la Terre, ρ opt et un modèle qui la néglige mais avec les paramètres intrinsèques corrects, ρ approx " ρ opt ˆm. En utilisant un seuil sur ces SNR (on choisit ici un seuil à SNR=8), on peut estimer la fraction de signal que nous perdons en faisant l'approximation.

Les résultats obtenus sont présentés dans la partie droite de la Figure 4. Sur 45000 sources injectées, 14437 ont un SNR supérieur à 8 sans l'approximation contre 14397 avec l'approximation. Les sources non détectées avec l'approximation mais qui auraient été détectées sans l'approximation sont faibles et ont leur ρ approx proche de 8. Cela conduit à une valeur de ρ approx proche mais inférieure à 8. La figure 4 indique tout d'abord que l'effet de la rotation de la Terre est négligeable puisque nous ne manquons que quelques signaux en utilisant l'approximation des diagrammes d'antenne constants dans le temps. Si l'on considère une source située dans une région où le match est faible et qui a un ρ opt très élevé, alors, même avec un faible match, la source sera probablement détectée avec l'approximation. De même, si son ρ opt est très petit, quelle que soit la valeur du match, le signal BNS ne sera pas détecté.

Même si l'effet de la rotation de la Terre semble négligeable du point de vue du SNR récupéré, il existe toujours des sources pour lesquelles le match entre les formes d'onde avec et sans l'approximation est faible d'après la partie gauche de la Figure 4. Cela peut être problématique pour le test de cohérence des analyses CBC. En effet, nous avons vu précédemment que les analyses CBC tels que Py-CBC effectuent un test du χ 2 . Elles repondèrent notamment le SNR des candidats en fonction de leur valeur χ 2 . La valeur de χ 2 d'un candidat est liée à sa valeur SNR [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF][START_REF] Gareth | Establishing significance of gravitational-wave signals from a single observatory in the pycbc offline search[END_REF]. Plus précisément, elle dépend du match entre le signal et le modèle de forme d'onde. Plus le match est élevé, plus le χ 2 est faible. Lorsque le match entre le modèle de forme d'onde (pour laquelle l'effet de rotation de la Terre n'est pas pris en compte) et le signal est faible, elle peut conduire à une large valeur de χ 2 . Cet effet est étudié dans [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF]. Un faible match peut conduire à une mauvaise valeur de χ 2 , ce qui se traduit par un SNR pondéré à la baisse. Pour en revenir à notre simulation, même si le SNR optimal de la source est élevé (ρ opt " 10 2 ), ce qui conduit à ρ approx ě 8, si le match est faible, le test χ 2 peut écarter le candidat en réduisant son SNR. Par conséquent, nos analyses CBC actuelles peuvent être utilisées pour l'ET et, pour l'instant, l'effet de la rotation de la Terre semble être négligeable; toutefois, des études complémentaires devront déterminer si nos tests de cohérence peuvent encore être utilisés tels quels ou si des modifications sont nécessaires pour s'assurer que nous ne rejetons pas accidentellement des signaux. Dans [START_REF] Singh | Exploring compact binary populations with the einstein telescope[END_REF], une solution proposée pour éviter de tenir compte de la rotation de la Terre consiste à analyser le signal toutes les cinq minutes, de sorte que la modification des diagrammes d'antenne due à la rotation de la Terre est négligeable pour une telle durée.

. Conclusion

GW170817 -GRB 17081A a ouvert la voie à l'astronomie multi-messagers avec les OG. Cette détection conjointe a définitivement établi un lien entre les GRB courts et les fusions NS. Cependant, des questions fondamentales demeurent, entre autres : les propriétés de GW170817 sont-elles communes à toutes les fusions NS ou représentent-elles un cas exceptionnel ? Quelle est la fraction de GRB courts associés à des fusions NS ? Des GRBs longs peuvent-ils également être associés à des fusions BNS ? Pour répondre à ces questions, il faut donc davantage de détections conjointes de OG/GRB et, à cette fin, nous avons mis en place une 0.5. Conclusion analyse approfondie pour rechercher symétriquement des associations OG/GRB dans les données LIGO/Virgo et Fermi/GBM. Notre méthode est basée sur une statistique Bayésienne et prend en compte de manière égale l'importance des candidats OG et GBM ainsi que leur proximité temporelle et spatiale. Pour garantir sa validité, nous l'avons d'abord évaluée sur des données couvrant O2 et avons trouvé GW170817 -GRB 170817A avec une signification conjointe satisfaisante (IFAR ą 1300 yr). En appliquant la méthode aux données O3, nous n'avons pas trouvé d'associations significatives pouvant provenir d'une source astrophysique commune. Notre méthode est la recherche la plus approfondie que nous ayons pu mettre en oeuvre jusqu'à présent. Nous avons utilisé l'état de l'art des données Fermi/GBM et OG. Notre méthode s'inspire de la sélection bayésienne de modèles, qui est bien comprise et largement utilisée. Nous n'avons pas trouvé d'associations intéressantes. L'association la plus forte contient une détection BBH confiante dans le canal OG et un candidat GBM qui correspond probablement à du bruit. Bien que nous ne nous attendons pas à une telle contrepartie aux fusions BBH, nous ne voulons pas passer à côté d'une physique intéressante, et nous sommes donc restés totalement agnostiques sur le type de CBC que nous recherchons. Avec la prochaine génération de détecteurs OG et l'augmentation du taux de détection, les coïncidences accidentelles entre les BBH et les GRB seront beaucoup plus fréquentes. Une façon d'éviter que les BBH bruyants ne limitent l'importance de l'association réelle est de les séparer par M chirp . Une autre façon d'empêcher la contamination du fond par des signaux BBH forts consiste à améliorer la localisation du ciel. En effet, cela permettra d'éliminer les coïncidences accidentelles démontrant que les deux candidats ne sont pas spatialement liés. Afin d'explorer les possibilités d'amélioration de la sensibilité de la recherche OG, j'ai participé à l'analyse des données OG au sein du groupe PyCBC. Je me suis attaquée à un projet visant à discriminer les bruits transitoires des signaux astrophysiques. Nous avons obtenu des résultats mitigés : la méthode est puissante pour les systèmes de masse élevée et inefficace pour les signaux de faible masse. Nous avons des idées d'amélioration, telles que le calcul de la métrique uniquement pour les tuiles dans une fenêtre prédéterminée autour du temps de coalescence du candidat PyCBC. Une fois ces modifications apportées et leur efficacité testée, la métrique pourrait devenir un indicateur puissant de l'origine astrophysique ou instrumentale/environnementale du candidat.

De plus, je me suis intéressée à la prochaine génération de détecteurs OG pour les fusions de NS. Le télescope Einstein prévoit plus de 10 4 de détections BNS par an, ce qui portera l'astronomie multi-messagers à un nouveau niveau. Jusqu'à présent, nous avons considéré que la réponse du détecteur à un signal était constante dans le temps en raison de la courte durée passée par un OG dans la bande passante du détecteur. Ainsi, nous avons toujours négligé l'effet de la rotation de la Terre, en considérant le diagramme d'antenne du détecteur constant dans le temps. Avec ET, la rotation de la Terre doit peut-être être pris en considération. Nous avons généré une population BNS, en incluant l'effet cosmologique du redshift. Nous avons calculé la ressemblance entre les formes d'onde et le SNR optimal avec et sans l'approximation. Nous avons constaté que le nombre de sig-

INTRODUCTION

Since their first detection in 2015, gravitational waves (GWs) have become a major vector of information for astrophysics. They open the way to new observation tools and, thus, understanding of our Universe. All massive objects are a potential source of GWs, and the Universe is full of them. Among all the possible sources of GWs, the merging binary systems of black holes or neutron stars (BBH, NSBH, BNS) are the most luminous sources for our current ground-based GW detectors (Second generation (2G) detectors). Other potential sources include supernovae, black hole (BH) oscillations, or spinning neutron stars (NSs). These sources can be directly studied through the GWs they emit. Indeed, many properties of the sources are encoded in the detected gravitational waveform: some intrinsic parameters, such as the mass, spins...; and extrinsic ones, like the distance or sky location... One specific source draws attention: when two NSs orbit each other in a binary system, slowly inspiraling and finally merging, GWs are emitted that can be directly detected by LIGO and Virgo, the 2G GW detectors. However, this is not the only signal that can be detected from such events. NS mergers are multi-messenger sources that can produce short gamma-ray bursts (sGRBs) (thus, their prompt emission, afterglow, and kilonova counterparts can also be observed by instruments), and possibly neutrinos and cosmic rays, in addition to GWs. Observations of GRBs coming from an NS merger bring complementary information about the merger ejecta, how the GRB has been launched (e.g. orientation of the jet), and enable finding the sky location of the source precisely. The first and only complete multi-messenger observation of a BNS merger occurred during the 2 nd GW observing run on August 17 th 2017 with the joint detection of a GW and a sGRB: GW170817 -GRB 170817A, that demonstrated the long-hypothesized association between sGRBs and NS mergers. This joint detection gave rise to the era of multi-messenger astronomy with GWs: multi-messenger astronomy consists in combining observations of different signals ("messengers") of the common astrophysical source.

This thesis is structured as follows: In Chapter 1, I first describe from an observational point of view this unique joint GW/GRB detection GW170817 -GRB 170817A that enabled the connection between sGRBs and the merger of NSs. I also give an overview of the implications of this joint detection in astrophysics and cosmology.

But the connection between GRBs and NS mergers has only been made possible thanks to the detection of GW170817 and the inference of the properties of the source that has been characterized as a BNS. Thus, in the second part of Chapter 1, I describe GW astronomy from a theoretical to an observational point of view: I start presenting GW theory and then describe our current ground-based detectors and future missions planned to increase the number of detections and the variety of detected sources. In the last part of the introduction, I proceed similarly to the 23 GW part and describe GRBs from a phenomenological and observational point of view.

With these concepts being introduced, I will be able, in Chapter 2 and Chapter 3, to describe the various undertaken projects in the framework of the PyCBC group of LIGO/Virgo collaboration. These works aimed at improving the sensitivity of the search to hope for more GW detections. Improving this sensitivity directly impacts multi-messenger astronomy since it enables expecting more NS merger detections, allowing us to search for a GRB counterpart more confidently. In Chapter 4, I describe my main project, which consists in developing and performing searches for NS mergers using the data from Advanced LIGO, Advanced Virgo detectors, and Fermi/GBM instrument.

Finally, the major part of my Ph.D. occurred before the beginning of the 4 th GW Observing Run (O4). Therefore, in Chapter 5, I discuss the preparation of O4 in the framework of the PyCBC group. Eventually, in Chapter 6, I look to the future of GW astronomy with a project we carried out with an intern, Lucas Gold-Dalg, about Einstein Telescope (ET).

CHAPTER 1

GRAVITATIONAL WAVES AND GAMMA-RAY BURSTS IN THE ERA OF MULTI-MESSENGER ASTRONOMY

This chapter introduces the study of the merger of binary compact objects in the multi-messenger era. In particular, here, we are interested in GWs coming from compact binary coalescence (CBC) systems and their gamma-ray counterpart. We start with a specific example, the first and only joint detection of a GRB associated with a GW coming from a BNS merger, GW170817 -GRB 170817A, and then generalize the study of GW and GRB physics.

1.1 . August 17 th , 2017 1.1.1 . An emblematic history On February 11, 2016, the LIGO Scientific Collaboration [START_REF] Aasi | Advanced ligo. Classical and Quantum Gravity[END_REF] and Virgo Collaboration [START_REF] Acernese | Advanced virgo: a second-generation interferometric gravitational wave detector[END_REF] announced the first confirmed detection of GWs from colliding BHs. The LIGO's twin observatories observed the GW signal on September 14, 2015. During Advanced LIGO's 1 st observing run (O1), no detections or significant candidates had component masses lower than 5 M d .

For the 2 nd observing run (O2), Advanced LIGO started the observations on November 30 th 2016 and was joined by Virgo on August 1, 2017. At that time, two BBH detections had already been announced from the O2 run. Toward the end of the O2 run, on August 17 th , 2017 at 12:41:04 UTC, the first GW signal coming from a BNS merger was observed. At the end of O2, ten GWs from BBH and one from BNS have finally been detected.

With the 3 rd GW Observing Run (O3) (April 1 2019 -April 30 th 2020), the GW catalog counts 90 detections with two signals from NSBH, one from BNS and the rest from BBH mergers.

. GW170817 Status of the detectors

The network of GW detectors composed of LIGO Hanford (H1), LIGO Livingston (L1), and Virgo (V1) detected a "100 s (calculated with a starting frequency of 24 Hz) GW inspiral signal with a slower waveform evolution than all BBH systems observed at that time, implying a much lower chirp mass. The inferred properties of the signal were also compatible with a BNS merger. The signal was first detected in low-latency by H1, and not in L1 due to an instrumental transient event (called a glitch, see Chapter 2, Sec. 2.1.3) overlapping the GW signal. After the subtraction of the glitch during the offline analysis, as visible in Fig. 1.1, the presence of a Chapter 1. Gravitational waves and Gamma-ray Bursts in the Era of multi-messenger Astronomy coincident signal in the LIGO detectors was confirmed. At that time, it was the loudest GW signal ever detected with a network signal-to-noise ratio (SNR) of ρ net " a ρ 2

H1

`ρ2

L1

`ρ2 V1 " 32.4 with ρ H1 " 18.8, ρ L1 " 26.4 and ρ V1 " 2.0, the SNR in H1, L1 and V1 respectively (for the definition of SNR, see Chapter 2, Sec. 2.1.2). The significance of this signal, presented by its rate of false alarms, was estimated at less than one per 8.0 ˆ10 4 years.

As shown in Fig. 1.1, the signal is not visible in Virgo data, and we can notice transient noise above 150Hz (described as scattered light glitches) in its spectrogram (i.e. plot of the time-frequency evolution of the signal). Despite the absence of a loud GW detection, Virgo was used for the sky localization and estimation of the source properties of the GW signal.

Source inferred properties

The properties of GW sources are inferred by matching the data with waveforms predicted by the theory of general relativity (GR) [START_REF] Dal Canton | Designing a template bank to observe compact binary coalescences in advanced ligo's second observing run[END_REF] (details in Sec. 1.9). The available information about the source parameters of GW170817 can be expressed as a posterior probability density function (PDF) using Bayesian methods. The properties of the source for GW170817 are summarized in Table 1.1. Two spin priors have been tested to infer the properties of GW170817: in this table, we show the results of the union of the low (|χ| ď 0.05) and high (|χ| ď 0.89) spin prior. These properties seem to point to a BNS merger for the following reasons:

First, by constraining the chirp mass in the detector frame, one can estimate the masses in the source frame since they are related by:

m det " mp1 `zq (1.1)
Where z is the redshift of the source. In GW170817's case, the inferred masses very likely correspond to a BNS with masses within [1.36, 2.26] M d for the primary component and [0.86,1.36] M d for the second object and a source frame chirp mass of 1.188 `0.004 ´0.002 M d . Second, the tidal deformability Λ, a parameter specific to NS mergers (BHs have 0 Λ), has been estimated at < 1400 (dimensionless).

Furthermore, the aligned spin components are consistent with zero, which is expected for NS mergers (at that time, the fastest-spinning known NS has a dimensionless spin ď0.4 and the maximum spin of NS in a galactic binary was about 0.05 [START_REF] Nitz | Accuracy of gravitational waveform models for observing neutron-star-black-hole binaries in advanced LIGO[END_REF]).

Finally, the energy emitted E rad by gravitational radiation for GW170817 has been constrained. The estimated bound in Table 1.1 is in agreement with E rad obtained from numerical simulations of BNS systems consistent with GW170817 [START_REF] Bernuzzi | Quasiuniversal properties of neutron star mergers[END_REF][START_REF] Cullen | Matter effects on LIGO/virgo searches for gravitational waves from merging neutron stars[END_REF].

GW170817 was localized within a sky region of 28 deg 2 in area (90% probability) and 380 Mpc 3 in volume, near the southern end of the constellation Hydra. The sky localization of GW170817 is shown in Fig. 1.2. Virgo was essential in reducing the localization to a single region of the sky as visible in Fig. 1.2. The GW skymap was estimated using the H1-L1 delay between the arrival time of the 1.1: Bounds on the interred properties of the source for GW170817 (90% posterior probability intervals), extracted from [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF].

GW170817 signal and the H1/L1/V1 signal amplitudes. Moreover, GW170817 was the closest ever observed GW source with a luminosity distance to the source of D L " 40 `8 ´14 Mpc. Follow-up observations detailed in the following sections led to the identification of NGC4993 as the host galaxy for GW170817.

1.1.3 . The γ-ray counterpart: GRB 170817A Theoretical studies [START_REF] Metzger | What is the Most Promising Electromagnetic Counterpart of a Neutron Star Binary Merger[END_REF][START_REF] Piran | The electromagnetic signals of compact binary mergers[END_REF] predict BNS mergers to be multi-messenger events giving signatures across the electromagnetic spectrum including gamma-ray emission, as detailed in Sec. 1.3.1. About 1.7s after GW170817 merger time, the Fermi Gamma-ray Burst Monitor (Fermi/GBM) [START_REF] Charles | The Fermi Gamma-ray Burst Monitor[END_REF] and the Anti-Coincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory (SPI-ACS INTEGRAL) [START_REF] Rau | The 1st integral spi-acs gamma-ray burst catalogue[END_REF], two instruments used to observe the most energetic form of light in the universe, the GRBs, independently detected a sGRB called GRB 170817A [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF]. Fig. 1.3 shows the coincident signals in the GW and the GRB channels (both Fermi/GBM and SPI-ACS). The light curves show excesses of photon counts representing GRB 170817A about 1.7 s after GW170817 end time.

Fermi/GBM

This GRB was autonomously detected onboard the Fermi/GBM [START_REF] P F Michelson | Fermi gamma-ray space telescope: high-energy results from the first year[END_REF][START_REF] Goldstein | An ordinary short gamma-ray burst with extraordinary implications: Fermi-gbm detection of grb 170817a[END_REF] detector and the signal exceeded a significance of 5σ in three of its NaI scintillators. The GBM detectors observed two apparently distinct components: a first peak that lasts about 0.5 s, shorter and spectrally harder than the second observed peak softer, a weaker emission that lasts a few seconds, so-called the "soft tail". The temporal and spatial agreement between the Fermi/GBM and LIGO-Virgo data led to a significance of 5.3σ [START_REF] Abbott | Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817a[END_REF].

INTEGRAL SPI-ACS

The search for short transients in INTEGRAL SPI-ACS [START_REF] Savchenko | Integral detection of the first prompt gamma-ray signal coincident with the gravitational-wave event gw170817[END_REF] identified a single peak at T ACS 0 " T GW 0 `1.88 s with an SNR of 4.6. The significance of the association between the GBM observation of GRB 170817A and the event observed by SPI-ACS is 4.2σ. SPI-ACS would not have alone reported this event as a GRB. However, it would have been reported with joint analysis searching around The time delay is computed as the start of the gamma-ray emission relative to the T GW 0 . GW170817, with an independent joint significance of 3.2σ [START_REF] Abbott | Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817a[END_REF]. A comparison of the properties of the GRB 170817A signal in Fermi/GBM and in INTEGRAL is described in Table 1.2.

This GRB detection resulted in a joint paper between LIGO/Virgo, Fermi/GBM, and INTEGRAL collaborations [START_REF] Abbott | Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817a[END_REF].

Finally, the GBM and INTEGRAL localization of GRB 170817A (including systematic error) is shown in Fig. 1.4 with the 50% and 90% credible regions covering "350 deg 2 and "1100 deg 2 , respectively. The overlap between the GW and the GRB localization is clearly seen here.

. Other counterparts

This unambiguous association confirms that BNS mergers are progenitors of (at least some) sGRBs and marked the beginning of the search for BNS's electromagnetic counterparts across the entire spectrum. They are represented in Fig. 1.5, and in the following paragraphs, we detail the search for such counterparts in GW170817-GRB 170817A's framework.

AT 2017gfo

The merger of two NSs has been predicted to produce an optical + near-infrared (NIR) transient (lasting a few days) known as a "kilonova". The ejecta from these mergers composed of neutrons are subject to rapid neutron capture nucleosynthesis, called r-process, creating heavy elements. The radioactive decay of these species produced and ejected during the merger process [50] powers a transient called a kilonova.

About 11 hours after the merger, the detection of an optical counterpart to GW710817, initially called "AT 2017gfo" (and later KN170817), was first reported [START_REF] Valenti | The discovery of the electromagnetic counterpart of GW170817: Kilonova AT 2017gfo/DLT17ck[END_REF][START_REF] Daniel | GW170817 -the first observed neutron star merger and its kilonova: Implications for the astrophysical site of the r-process[END_REF] by The One-Meter, Two-Hemisphere team as a new bright transient in the iband [START_REF]LIGO/Virgo G298048: Pan-STARRS izy photometry monitoring of SSS17a/DLT17ck[END_REF] and later identified as a multiple-component ("blue-red") kilonova since it evolved rapidly from blue colors with a spectral peak at optical wavelengths on a timescale of a day to redder (NIR) colors. The detection image is visible During weeks, the transient was followed by telescopes observing UV, optical, and near-infrared with photometry and spectroscopy, as the X-ray and radio counterparts of GRB 170817A (see next paragraph). This detection confirmed that BNS mergers produce kilonovae with emission properties in agreement with theoretical predictions [START_REF] Arcavi | Optical emission from a kilonova following a gravitational-wave-detected neutron-star merger[END_REF].

GRB 170817A afterglow

GRB emission is expected to be a two-phase event: the initial emission phase, the prompt emission, and the second, the afterglow, occurring when the jet collides with the surrounding interstellar medium that can be detected in a large range of frequencies, including X-rays. These phases are described later in Sec. 1.3.2. Two types of afterglow have been associated with GRB 170817A: an X-ray and a radio counterpart. We discuss both counterparts in the following paragraphs.

The GRB emission can also be characterized as a three-phase event, considering the kilonova counterpart (detailed above) between the prompt and afterglow emission. X-ray counterpart In addition to the UV/Optical/IR counterpart searches, missions carried out X-ray observations to find GRB170817A afterglow. While the UV-optical-IR observations mapped the emission from the ejecta, X-ray observations are important to provide information on the geometry of the outflow, its energy output, and the orientation of the system. The source SSS17a was initially not visible at radio and X-ray wavelengths. Due to an unfavorable sky position, no X-ray emission was detected at T 0 `0.19 days allowing the Monitor of All-Sky X-ray Image (MAXI) [START_REF] Mihara | Maxi : Monitor of all-sky x-ray image[END_REF] that was observing the location of GW170817, only to constrain the X-ray flux upper-limits to 8.6 ˆ10 ´9 erg cm ´2 in the 2 -10 keV band [START_REF] Sugita | MAXI upper limits of the electromagnetic counterpart of GW170817[END_REF]. Other missions such as Super-AGILE [START_REF]SuperAGILE: The hard X-ray imager for the AGILE space mission[END_REF][START_REF] Tavani | The AGILE mission[END_REF], NUclear Spectroscopic Telescope ARray (NuSTAR) [START_REF]The Nuclear Spectroscopic Telescope Array (NuS-TAR) High-energy X-Ray Mission[END_REF] and Swift [START_REF]The Swift Gamma-Ray Burst Mission[END_REF] brought constraints on this flux without any detection of the afterglow. Finally, on 26 August 2017, 9 days after the GW and GRB emission, the Chandra X-ray Observatory (CX0) [START_REF] Weisskopf | Chandra X-ray Observatory (CXO): overview[END_REF] detected X-ray emission with a 50ks exposure at the position of SSS17a [START_REF] Troja | The x-ray counterpart to the gravitational-wave event GW170817[END_REF]. This observation is illustrated in the bottom panel in Fig. 1.5. X-ray afterglow observations also revealed the behavior of a GRB jet viewed off-axis with respect to the observers' line of sight (i.e. the observer not located on the jet axis) [START_REF] Van Eerten | OFF-AXIS GAMMA-RAY BURST AFTERGLOW MODELING BASED ON a TWO-DIMENSIONAL AXISYMMETRIC HYDRODYNAMICS SIMULATION[END_REF].

Radio counterpart

GRB afterglow can also be observed in the radio frequency. Studying the radio counterpart provides information about the trace of the fast-moving ejecta from an NS coalescence which gives knowledge about the energetics of the explosion, the geometry of the ejecta, and the environment of the merger. The first radio counterpart consistent with the location of SSS17a/AT 2017gfo was detected with the Very Large Array (VLA) [START_REF] Thompson | The Very Large Array[END_REF] on 2017 September 2 and 3 at two different frequencies (3 GHz and 6 GHz) via two independent observations [START_REF] Alexander | The electromagnetic counterpart of the binary neutron star merger LIGO/virgo GW170817. VI. radio constraints on a relativistic jet and predictions for late-time emission from the kilonova ejecta[END_REF] represented in the bottom right panel in Fig. 1.5.

Several years after this unique joint detection, many observatories still measure a late-time radio and the X-ray afterglow associated with GRB 170718A [START_REF] Balasubramanian | Continued radio observations of GW170817 3.5 yr post-merger[END_REF][START_REF] Wang | GRB 190829a-a showcase of binary late evolution[END_REF].

Neutrino counterpart

NS coalescence is likely to be a source of neutrinos emitted in the relativistic outflow produced by the merger [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF][START_REF] Eichler | Nucleosynthesis, Neutrino Bursts and Gamma-Rays from Coalescing Neutron Stars[END_REF]. The detection of GW170817 led to the search for coincident, high-energy (GeV-EeV) neutrinos [START_REF] Albert | Search for high-energy neutrinos from binary neutron star merger GW170817 with ANTARES, IceCube, and the pierre auger observatory[END_REF] by IceCube [START_REF] Aartsen | The IceCube neutrino observatory: instrumentation and online systems[END_REF], ANTARES [START_REF] Ageron | ANTARES: The first undersea neutrino telescope[END_REF] and the Pierre Auger Observatory [START_REF] Pierre | The pierre auger cosmic ray observatory[END_REF]. No significant candidate has been found with any of these searches, but according to [START_REF] Albert | Search for high-energy neutrinos from binary neutron star merger GW170817 with ANTARES, IceCube, and the pierre auger observatory[END_REF], it is expected with GRBs observed at a large off-axis angle, which is the case of GRB 170817A, as discussed in the next section. This null result still was used by [START_REF] Albert | Search for high-energy neutrinos from binary neutron star merger GW170817 with ANTARES, IceCube, and the pierre auger observatory[END_REF] to constrain the neutrino fluence using the computation from [START_REF] Adrián-Martínez | High-energy neutrino follow-up search of gravitational wave event GW150914 with ANTARES and IceCube[END_REF]. The fluence represents the integral of the energy flux over the duration of the burst. This quantity is not specific to neutrinos, and we discuss the GRB fluence in Sec. 1.3.2.

. Implication for fundamental science

Implication of GRB physics: properties of the merger

As mentioned above, EM counterparts are important to understand what happens during the merger: the geometry of the jet, the velocity and mass ejecta, and the interaction between them. The X-ray and radio counterparts help constrain the jet viewing angle and structure. The jet launched from the GRB compact source called the central engine, interacts with the dense merger ejecta. Depending on its parameters (kinetic energy, opening angle) and those of the ejecta (velocity and mass), the jet may or may not remain collimated as a relativistic jet until emerging [START_REF] Duque | Compact object coalescences and gamma-ray bursts in the gravitational-wave era[END_REF]. Several scenarios can be considered [START_REF] Abbott | Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817a[END_REF]. Among them: (i) The ultra-relativistic uniform top-hat model in which the jet has a constant emissivity and Lorentz factor, Γ, within the jet aperture. In this scenario, we view the jet from beyond the half-jet opening angle. (ii) A structured jet which is more complicated than a simple top-hat model and provides a broader range of angles from which the observer could still detect emission. (iii) A cocoon emission scenario in which the observed emission for GRB 170817A originates from a different mechanism than for most sGRBs: if the jet is energetic enough and deposits a small amount of energy in the cocoon, it may keep its collimation throughout its propagation, and appear as a relativistic jet [START_REF] Duque | Compact object coalescences and gamma-ray bursts in the gravitational-wave era[END_REF]. These three potential scenarios, which have been considered in the first place to explain the observed properties of GRB 170817A, are represented in Fig. 1.6. However, the structured jet model was favored because of several observations:

• The initial gamma-ray emission is weak compared to standard observed sGRBs suggesting a significant angle between the jet and the observer.

• If this observer is on the jet axis, the afterglow appears as a luminous fading transient visible across the electromagnetic spectrum from the first few minutes after the burst [START_REF] Troja | The x-ray counterpart to the gravitational-wave event GW170817[END_REF], which is not consistent with GRB 170817A's observations. It also indicates an opening angle between the jet and the observer. Hence, the afterglow only becomes apparent once the jet has spread and decelerated enough that the beaming cone of the emission includes the observer [START_REF] Troja | The x-ray counterpart to the gravitational-wave event GW170817[END_REF][START_REF] Piran | The electromagnetic signals of compact binary mergers[END_REF][START_REF] Rhoads | How to tell a jet from a balloon: A proposed test for beaming in gamma-ray bursts[END_REF]]. An off-axis observer sees that the onset of the afterglow is delayed by several days or weeks [START_REF] Van Eerten | OFF-AXIS GAMMA-RAY BURST AFTERGLOW MODELING BASED ON a TWO-DIMENSIONAL AXISYMMETRIC HYDRODYNAMICS SIMULATION[END_REF].

Thanks to the very late times afterglow observation that showed an X-ray peak luminosity at "160 days post-merger, a structured jet profile (and not a tophat or a cocoon emission), where the outflow energetics and Lorentz factor vary with the angle from the jet axis, was preferred to explain both the GRB and afterglow properties. The structured jet has an estimated width of 4 ˝ [START_REF] Troja | A year in the life of GW170817: the rise and fall of a structured jet from a binary neutron star merger[END_REF], and the GRB viewing angle of this off-axis jet was estimated at θ GRB view " 22 ˝(up to " 30 depending on the models) [START_REF] Troja | A year in the life of GW170817: the rise and fall of a structured jet from a binary neutron star merger[END_REF].

The optical counterpart gives information about the ejecta material. When two NSs merge, a small part of NS material (" 10 ´3 -10 ´2 M d ) is ejected into interstellar space with a velocity expected between [0.1 -0.3]c. Two types of ejecta are expected to contribute [START_REF] Abbott | Estimating the contribution of dynamical ejecta in the kilonova associated with GW170817[END_REF]: dynamical ejecta produced at the time of the merger and post-merger winds produced by the remnant system (e.g. from an accretion disk around a BH or massive NS) [START_REF] Daniel | GW170817 -the first observed neutron star merger and its kilonova: Implications for the astrophysical site of the r-process[END_REF]. The observed properties of KN170817 suggest the dominant ejection method came from accretion disk outflows, from a total disk mass "0.1 M d . The observed kilonova fits with a multicomponent model (here three components: blue, red, purple, represented in the lights curves in Fig. 1.7) with different mass and velocity ejecta for each component: M ej " p0.02, 0.047, 0.011q M d and v ej " p0.27, 0.15, 0.14qc [START_REF] Villar | The combined ultraviolet, optical, and near-infrared light curves of the kilonova associated with the binary neutron star merger gw170817: Unified data set, analytic models, and physical implications[END_REF]. The kilonova observation also allowed an independent estimation of the viewing angle consistent with the radio and X-ray afterglow analysis.

Implication in astrophysics and cosmology

This exceptional discovery demonstrates the long-hypothesized association between sGRBs and NS mergers. This confident joint detection also gave a great opportunity for astrophysics and cosmology tests.

Neutron star equation of state Constraints

Multi-messenger observations of NS mergers can help constrain the NS equation of state (EoS) that describes the relation pressure-density of the NS and is measured by establishing the relation between the mass and the radius of the star (an explicit formula is given in Sec. 1.2.2). One can compare the measurement of the binary mass from the GW signal with the four possible models of the merger remnant powering the sGRB: (i) a stable NS, (ii) a long-lived (Á1s) supermassive NS, (iii) a short lived (À1s) hypermassive NS, (iv) a prompt (À10ms) BH. Combinations of binary mass and remnant type lead to different predictions for the EM signature. These expectations are presented in Fig. 1.8.

In addition, the information given by the tidal deformability imprinted in the GW waveform and by the EM counterpart about the ejecta helps to test different EoS. Indeed the tidal deformability is related to the EoS by Eq. 1.2:

Λ " p2{3q EoS dependent hkkkkkkikkkkkkj k 2 ˆGm c 2 R ˙´5 (1.2)
where k 2 is the l = 2 relativistic Love number [START_REF] Damour | The Motion of Compact Bodies and Gravitational Radiation[END_REF] and m the mass of the NS. In GW170817 -GRB170817A's case [START_REF] Abbott | Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817a[END_REF], for each EoS that has been tested, the maximum stable baryonic mass M Static B and gravitational mass M Static G of a non-rotating (static) NS are computed. The BH remnant scenario is only possible if its baryonic mass is larger than M B Static . This study [START_REF] Abbott | Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817a[END_REF] showed that only EoSs with M Static B < 3.2 M d (low-spin prior) or with M Static B < 3.7 M d (wider spin prior) are compatible with the BH remnant scenario. Finally, given the limits of the tidal deformability and the inferred masses of GW170817, constraints on the radii of both GW170817 NSs have been placed: 12 ă R ă 13 km [START_REF] Abbott | Measurements of neutron star radii and equation of state[END_REF] ruling out some EoS (e.g. APR [START_REF] Schneider | Akmalpandharipande-ravenhall equation of state for simulations of supernovae, neutron stars, and binary mergers[END_REF]).

Constraining the BNS rate

By itself, the GW can provide information about the astrophysical merger rate of BNS systems. At that time, GW170817 was the only identified BNS-mass signal in O2 detected with a false-alarm rate (FAR) below 1{100yr. A BNS merger rate in the local universe has been inferred [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF] (assuming a flat mass distribution of the components of BNS systems between 1 and 2 M d ) leading to R BNS " 1540 `3200 ´1200 Gpc ´3yr ´1. With the results of the next observing runs, better constraints on the merger rates have been placed. The current estimations (using GWTC-3 cumulative population) are presented in Table 1.3. Here are presented the union of the merger rates predicted with four different models. These results are taken from [START_REF]The population of merging compact binaries inferred using gravitational waves through gwtc-3[END_REF].

Test of the celerity of gravitational waves The propagation speeds of EM and GWs are supposed to be identical, and the intrinsic emission times similar, so we do not expect an arrival delay (or a little) between photons and GWs over cosmological distances [START_REF] Abbott | Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817a[END_REF]. GW170817 -GRB 170817A joint detection and its measured time delay of (+1.74 ˘0.05) s was a great occasion to constrain the GW celerity [START_REF] Abbott | Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817a[END_REF]. We assume that the difference in travel time ∆t between photons and GWs is small and that the travel distance D is known. So the fractional speed difference during the travel can be written as follows:

∆ν{ν EM « ν EM ∆t{D where ∆ν " ν GW ´νEM (1.3)
This led to the resulting constrain on the fractional speed difference:

´3 ˆ10 ´15 ď ∆ν ν EM ď `7 ˆ10 ´16 (1.4)
Evaluating the Hubble constant The kilonova KN170817 observation in coincidence with GW170817 made it possible to locate the source in the galaxy NGC 4993. In addition, using the luminosity distance directly measured with the GW signal, the Hubble constant H 0 can be inferred leading to H 0 " 70 `12 ´8 km s ´1 Mpc ´1. The posterior distribution inducing this result is shown in Fig. 1.9. This figure also shows that this value is consistent with SHOES and Planck collaboration estimation. However, estimating H 0 with GW170817 did not help understand the Hubble tension between the local (SHOES) and cosmological (Planck) measurement of H 0 . According to [START_REF] Hotokezaka | A hubble constant measurement from superluminal motion of the jet in gw170817[END_REF], 15 more localized GW170817-like events (comparable SNR, favorable orientation), with radio images and light curve data are needed to expect to solve the Hubble tension. In comparison, 50-100 GW events without such data would be necessary.

Here we gave an overview of the implications of this joint detection for fundamental physics. However, other tests have been done with GW170817 -GRB 170817A that are not detailed here, among others: the Lorentz Invariance Violation limits or the test of the Equivalence Principle [START_REF] Abbott | Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817a[END_REF].

1.1.6 . How lucky were we to detect GW170817? Some of the extrinsic parameters of the GW170817 show that we were lucky to detect this event during O2. First, the proximity of GW170817 (D 170817 «40 Mpc) is unusual and makes it the closest detected event even today. In O3, the LIGO-Virgo potential BNS-like GW signals that were detected were located at a much greater distance [START_REF]GRANDMA observations of advanced LIGO's and advanced Virgo's third observational campaign[END_REF]. If we consider the current estimate of the local BNS rate to be R BNS = 10 -1700 Gpc ´3yr ´1, we can evaluate the expected rate of BNS mergers up to GW170817 distance:

R " R BNS ˆ4π 3 ˆD3 170817 (1.5)
This gives us an average rate of 1 event per R ´1 " 2 -373 yr. This first result seems to indicate that GW170817-like observations would be rarer than we thought. Moreover, the sky localization of GW170817 has much smaller uncertainties ("30 deg 2 ) compared to O3 skymap size, which was much larger (on average around a few 100 deg 2 ) [START_REF] Duverne | Multi-Messenger astronomy, localisation of transient sources of gravitational waves and optical follow-up of gravitational wave candidates[END_REF]. GW170817 was not only a close event, but its orientation (low inclination angle) allowed the detection of the gamma emission and suggested a non-zero viewing angle, a condition required to detect the GRB afterglows. Finally, a complete multi-messenger observation, like GW170817, has an estimated rate larger than one every 239 `713 ´146 years (rate computed in [START_REF] Mochkovitch | Prospects for kilonova signals in the gravitational-wave era[END_REF]), which is why we can consider it an extremely lucky event.

. Gravitational waves

In 1915, Einstein stated his theory of general relativity (GR). GR links the geometry of space-time with its dynamics. One of the key predictions of this theory is the existence of gravitational radiation, together with BHs and the expansion of the Universe. GWs were predicted one year later, in 1916, by Einstein.

At Chapel Hill conference [START_REF] Peter | Summary of the chapel hill conference[END_REF], in 1957, the first demonstration of the measurability of GWs by experiment was made. The first proof of the existence of GWs was finally provided 20 years after Einstein's death, in 1974, with the discovery of the binary pulsar PSR B1913+16 [START_REF] Hulse | Discovery of a pulsar in a binary system[END_REF] and the observation of its orbital decay.

GWs can be defined as deformations of the curvature of space-time propagating at the speed of light. GWs are detectable when produced by large accelerated masses in very strong gravitational fields. The first direct evidence of GWs had to wait until 2015, one hundred years after Einstein's prediction: the detection of GW150914 [START_REF] Abbott | First results from the search for binary black hole coalescence with advanced LIGO[END_REF] by the two Laser Interferometer Gravitational-Wave Observatory Chapter 1. Gravitational waves and Gamma-ray Bursts in the Era of multi-messenger Astronomy 40

(LIGO) instruments [START_REF] Aasi | Advanced ligo. Classical and Quantum Gravity[END_REF]. This section introduces mathematical concepts necessary to formulate GW theory properly. We also describe the various sources that can emit GW, focusing on BNS.

. General relativity and gravitational waves

The derivation of the following formulas can be found in numerous textbooks, e.g. [START_REF] Langlois | Relativité générale, Des fondements géométriques aux applications astrophysiques[END_REF].

Einstein's equations

In 1905 Einstein introduced a radical revision of the mechanics' basis, in particular the notion of time, based on the following two postulates of special relativity:

• Principle of relativity: the equations describing the laws of physics have the same form in all inertial reference frames.

• Invariant light speed : in a vacuum, light propagates at a constant speed c, irrespective of the state of motion of the source.

In 1915, Einstein added to these postulates another theory, the general relativity (GR) and especially the equivalence principle that testifies that "all bodies are affected by gravity, and, in fact, all bodies fall with the exact same acceleration in an external gravitational field". Nowadays, we can divide this principle into the three following equivalence principles:

• Weak equivalence principle: Given the same initial position and velocity, all test bodies fall along the same trajectories.

• Einstein equivalence principle: In a local inertial frame, all non-gravitational laws of physics are given by their special-relativistic form.

• Strong equivalence principle: It is always possible to remove the effects of an exterior gravitational field by choosing a local inertial frame in which all the laws of physics, including those of gravity, take the same form as in the absence of this exterior gravitational field.

GR introduces the notion of curvature of space-time, so we need to describe it in a non-Euclidean way with a four dimensions vector space with the signature (-,+,+,+). We define the coordinate system:

x µ " tx 0 , x 1 , x 2 , x 3 u " tct, x, y, zu

And using Einstein's summation convention, vectors are defined as:

u " u µ e µ and v " v µ e µ (1.7)

where e µ are basis vector elements. With this convention, the scalar product between u and v is written as:

gpu, vq " g µν u µ v ν (1.8)
where g µν is the metric tensor.

The metric becomes a dynamic object in GR, contrary to the Minkowskian geometry of special relativity. Einstein's equations are used to determine the metric and its evolution. These equations link a geometric tensor that depends on the curvature of space-time and a tensor associated with the distribution of matter in energy and impulse. These equations indicate that the presence of matter causes a deformation of space-time. Einstein's equations generalize, from a relativistic point of view, Poisson's equation ∆U " 4πGρ m which links the Newtonian gravitational potential and the mass density of the source:

G αβ " R αβ ´1 2 Rg αβ " 8πG c 4 T αβ (1.9)
where R αβ is the Ricci tensor, R the Ricci scalar, T αβ the stress-energy tensor, and the 8πG factor allows us to find the Poisson equation in the Newtonian limit.

Linearized Einstein's equations

Einstein's equations are a complex system of coupled non-linear differential equations. Linearizing them enables to study the set of solutions close to a particular exact solution by introducing linear perturbations around it. Here we consider a space-time weakly deformed compared to a flat empty space. Thus, the metric g µν can be written as:

g µν " η µν `hµν , |h µν | ! 1 (1.10)
where η µν is the flat empty space Minkowski metric defined as:

η µν " ¨´1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ‹ ‹ ' (1.11)
and h µν is the small perturbation. One can express the Ricci tensor's components thanks to a Christoffel symbol's computations and replace them in Eq. 1.9. So now if we substitute Eq. 1.10 from Eq. 1.9 we get to:

G αβ " ´1 2 pl hαβ ´Bα B µ hµ β ´Bβ B µ hµ α `ηαβ B µ B ν hµν q (1.12) with hµν " h µν ´1 2 hη µν , h " η ρσ h ρσ (1.13)
Keeping in mind that GR states that physics is independent of the coordinates system, we can choose Lorenz Gauge that imposes the condition:

B µ hµν " 0 (1.14)
so Eq. 1.12 can be simplified and explicitly written as:

p▽ 2 ´1 c 2 B Bt 2 q hµν " ´16πG c 4 pT µν ´1 2 g µν T k k q (1.15)
or as:

G αβ " ´1 2 B σ B σ hab (1.16)
Chapter 1. Gravitational waves and Gamma-ray Bursts in the Era of multi-messenger Astronomy 42

Propagation of gravitational waves

In the absence of matter, Einstein's linearized equations in vacuum are written:

B σ B σ hµν " 0 (1.17)
Which is the D'Alembert equation, meaning that a solution of this equation, known as GWs, propagates at the speed of light. Using an appropriate gauge called the traceless-transverse gauge, h T T µν , defined by:

h T T " 0, B µ h T T µν " 0, h T T 0i " 0 (1.18)
And by placing ourselves in the Fourier space, we can write the solution as a superposition of plane waves:

h T T µν " H µν e ikσx σ (1.19)
By applying the gauge conditions, we reduce the ten degrees of freedom implied by Einstein's equations to two GW polarizations h `and h ˆ. For a plane wave propagating along the z-axis, Eq. 1.19 can be written as:

h T T µν " ¨0 0 0 0 0 h `hˆ0 0 h ˆ´h `0 0 0 0 0 ‹ ‹ ' e ´ipωt´kzq (1.20)

Detection of gravitational waves

In 1957, during the Chapel Hill conference [START_REF] Peter | Summary of the chapel hill conference[END_REF], Bondi, Feynman, Weiss, and others came up with the idea that we might be able to detect the effect of GWs on matter. The energy carried away by GW induces a change in the relative distance of a set of test masses. We can consider two particles A and B separated by a distance of L that can be measured the following way: A light beam propagates from A to B and comes back to A after reflection. Then L is expressed as:

L " 1 2 cpτ rec A ´τ tra A q (1.21)
where pτ rec A ´τ tra A q is the proper time that elapses between transmission and reception of the light beam. And when A and B are two free and immobile particles, with the traceless-transverse gauge we get:

L " a g ij ∆x i ∆x j (1.22)
where ∆x i " x i B ´xi A " L 0 n i and L 0 " a δ ij ∆x i ∆x j . Equation 1.22 is now equivalent to: and in the weak field approximation, if we introduce L ´L0 " δL, we finally express the evolution of the relative distance between A and B as:

L " L 0 b p1 `hTT ij qn i n j (1.23)
δL L 0 " 1 2 h T T ij n i n j (1.24)
where h " h T T ij n i n j is the GW strain amplitude. This demonstrates that the relative distance between the two test masses (here, A and B) is proportional to the GW amplitude h. Moreover, the two GW polarizations manifest themselves by distinct deformations, as shown in Fig. 1.10.

To detect GWs from compact binaries (see Sec. 1.2.2), we need to have an instrument sensitive to the order of h " 10 ´21 and during the 60's, Gertsenshtein and Pustovoit together [START_REF] Gertsenshte Ǐn | On the Detection of Low-Frequency Gravitational Waves[END_REF] with Weber suggested that measuring the differential effect of the metric could be done with a Michelson interferometer with which we could compare the length of the two arms. More details are given in Sec. 1.2.3.

Gravitational wave Emission

In the presence of matter, Eq. 1.17, which was previously correct for a GW propagating in vacuum, becomes:

B σ B σ hµν " ´16πGT µν (1.25)
This equation is similar to the electromagnetism equation in the presence of a source, so it can be resolved in the same way (depending on the symmetry of the source). EM radiation can be decomposed into a series of multipoles (l " 1, 2, ...), with the strongest being the electric dipole radiation (l " 1). Similarly, for GWs, mass conservation forbids emission by monopole radiation. In addition, momentum conservation excludes dipole radiation. Therefore, GW radiation requires at least a time-varying quadrupole moment, l " 2 (or a higher nature) to be emitted [START_REF] Schutz | Gravitational radiation[END_REF]. So when the GW is emitted by a distribution of matter, one can write, for an observer at a distance r from the source:

hij pt, ⃗ xq " 2G rc 4 : I ij pt ´r c q (1.26)
where I ij is the quadrupole moment of the source, with I ij " ş d 3 yρy i y j . From this equation, we can derive the power emitted by the GW, or the gravitational luminosity, known as the Einstein quadrupole formula:

L G " G 5c 5 ; Q ij ; Q ij (1.27)
where ⟨.⟩ is the time average operator over several periods of time and Q ij " I ij ´1 3 δ ij δ kl I kl is the reduced quadrupole moment. The power L G quantifies the total amount of energy, per time unit, emitted by the source as GWs.

What criteria should a source check?

The product of the mass M of the moving part of the system and the square of the size R of the system can give an estimation of the quadrupole moment of a system. Thus, the 3 rd -order time derivative of the quadrupole moment can be approximated by:

; Q " ε M R 2 T 3 " εM R 2 ´ω 2π ¯3 (1.28)
ε is a dimensionless factor describing the source asymmetry and T the source characteristic time scales related to ω by T " 2π ω . The metric perturbation at a distance r can be approximated as:

h " ε GM L 2 ω 2 c 4 r (1.29)
The luminosity of GWs from a given source is approximately:

L G " ε 2 c 5 G ˆRs R ˙2 ´v c ¯6 (1.30)
and c 5 {G " 10 42 Watt gives us the approximate order of magnitude for the GW luminosity. In Eq. 1.30, v is the mean velocity of the source's internal motion which is non-spherical, (v " R T ) and R s " 2GM c 2 the Schwarzschild radius. One can deduce that the maximum GW luminosity is reached when R " R s and v " c, meaning that the source needs to be compact and relativistic. Finally, the parameter ε should be as large as possible so, to be detectable, the source should be asymmetric.

Gravitational waves

. Sources

In this section, we describe the different GW sources. When searching for GWs, the possible sources can be divided into four categories: CBCs, unmodeled bursts, continuous waves, and stochastic. We start with CBCs, the only source detected with ground-based GW detectors during the three first GW Observing Runs. We continue by giving an overview of GW sources that have not yet been discovered with LIGO and Virgo interferometers but are possible strong GW emitters.

Compact Binary Coalescence

Before describing the coalescence of compact binary systems, it is necessary to define black holes and neutron stars.

Black hole (BH)

A BH [START_REF] Bambi | Astrophysical black holes: A review[END_REF] is a region of space-time in which gravity is so strong that nothing can escape or communicate with the exterior region. John Michell in 1783 and, independently, Pierre-Simon Laplace in 1796 discussed the possibility of the existence of such extremely compact objects. The simplest BH solution was discovered immediately after Albert Einstein proposed the theory of GR, in 1916, by Karl Schwarzschild [START_REF] Schwarzschild | On the gravitational field of a mass point according to Einstein's theory[END_REF] (now called the Schwarzschild solution). It describes the spacetime of a spherically symmetric and electrically uncharged BH. Since then, many observations (primarily by quasar observations [START_REF] Valiante | On the formation of the first quasars[END_REF] for supermassive BH and by GWs for stellar-mass BHs) have pointed out the existence of stellar-mass BHs and the supermassive BHs [START_REF] Volonteri | Formation of supermassive black holes[END_REF] (located at the center of many galaxies). A BH is considered a simple object because it can be described by three parameters only: its mass M, spin angular momentum, and electric charge. However, for astrophysical BHs, the electric charge can be completely negligible.

The search for BH candidates in the Universe started in the 1970s. Today we have observational pieces of evidence for the existence of at least two classes of objects: stellar-mass BHs with M between [3 -" 10 2 ] M d and supermassive BHs M between [10 5 -10 10 ] M d . A potential third class of objects, intermediatemass black holes [START_REF] Greene | Intermediate-mass black holes[END_REF], with a mass filling the gap between the stellar mass and the supermassive ones is also investigated. Still, we do not yet have confident mass measurements of such BH. Another class of BH, not with an astrophysical origin this time but a cosmological one, is constituted of primordial black holes (PBHs) [START_REF] Escrivà | Primordial black holes[END_REF] which is a theoretical type of BH formed in the early Universe from the collapse of over-dense regions of space. Nowadays, during the GW observing runs, physicists carried sub-solar mass searches (see Chapter 2, Sec. 2.2.2) in the hope of finding proof of the existence of PBHs, among other objects.

Neutron star (NS)

NSs are one of the densest objects in the Universe. The neutron discovery by Chadwick in 1932 prompted Landau to predict the existence of NSs [START_REF] Dmitrii G Yakovlev | Lev landau and the concept of neutron stars[END_REF]. Nowadays, the term "neutron star" refers to a star with a mass M on the order of 1.5 M d , a radius R of " 12 km, and a central density n c as high as 5 to 10 times the nuclear equilibrium density n 0 " 0.16f m ´3 of neutrons and protons found in laboratory nuclei [START_REF] Lattimer | The physics of neutron stars[END_REF]. Although neutrons dominate the nucleus of NSs, some protons, electrons, and muons also exist. The equations of hydrostatic equilibrium determine the mass-radius (M-R) relation. For a spherical object in GR, these are the so-called Tolman-Oppenheimer-Volkov (TOV) equations [START_REF] Sumiyoshi | Equation of state in neutron stars and supernovae[END_REF]: dP dr " ´Gpmprq `4πr 3 P {c 2 qpρ `P {c 2 q rpr ´2Gmprq{c 2 q (1.31)

dmprq dr " 4πρr 2 (1.32)
An NS has five major regions, the inner and outer cores, the crust, the envelope, and the atmosphere. [START_REF] Lattimer | The physics of neutron stars[END_REF]. The interior structure of an NS conjectured in [START_REF] Maggiore | Science case for the einstein telescope[END_REF] The NSs and the BHs observed by our GW detectors have an astrophysical origin. They are formed by the collapse of massive stars between 8 -50 M d . The stars in the lower end (M Á 8 -10 M d ) of this mass range will result in an NS, and those in the upper end of this mass range will become a BH. These two objects can be differentiated mainly by their masses and spin, although tidal deformability can also be considered. A BH is supposed to have a mass ě 5 M d contrary to a NS that has between [" 1 -3] M d . Moreover, we often consider in searches that the spin of a BH can go up to " 0.9 -1, contrary to an NS that has a lower spin (up to " 0.1).

GW from the merger of compact binaries

The merger of binary systems composed of compact objects (BH or NS) is one of the most promising sources for the ground-based GW detectors, LIGO and Virgo, as they have a quadrupole nature. These systems lose energy through the emission of gravitational radiation. During this process, they emit a characteristic "chirping" GW signal of predominantly increasing amplitude and frequency. During the coalescence of a compact binary system, we can distinguish three phases represented in Fig. 1.11. During the inspiral phase, the two objects are orbiting around the center of mass. They merge during the merger phase, and finally, the resulting object of the merger, the remnant (most likely a BH), dissipates energy during the ringdown phase. The GW signal during the inspiral phase can be computed with post-Newtonian approximation. For the merger, modeling the waveform is more complicated, and numerical relativity becomes a necessary tool. Finally, the physics of the ringdown is well described by the BH perturbation, however the ringdown phase depends on the properties of the merger which is why it is also complicated to model.

If we consider a binary system with two objects of masses m 1 and m 2 (with M " m 1 `m2 in a circular motion with an angular speed Ω one can write:

Ω " pGM q 1{2 d 3{2 (1.33)
And the energy of the system is: where µ " m 1 m 2 M is the reduced mass, M " m 1 `m2 is the total mass, and d is the separating distance between the two objects. The quadrupole moment of the system is simplified as follows:

E " ´GM µ 2d (1.34)
I ij " ż d 3 xρx i x j " m 1 px 1 q i px 1 q j `m2 px 2 q i px 2 q j (1.35)
One can compute the component I xx , I yy and I zz and substitute them in Eq. 1.30. This gives us the following:

L G " 32 5
G 4 µ 2 M 3 d 5 c 5 (1.36)
This GW emission results in a loss of the total energy of the binary system:

9 E " ´LG (1.37)
This implies that the two objects become closer and closer to each other and the period P " 2π{Ω decreases. From Eq. 1.33 and Eq. 1.34 one can deduce the link between the variations of the energy of the system, the distance d, and the period P:

9 E E " ´9 d d " ´2 3
9 P P (1.38)
So the distance as a function of the time, after a time integration, can be expressed as:

d 4 " 256 5 G 3 µM 2 pt c ´tq (1.39)
Chapter 1. Gravitational waves and Gamma-ray Bursts in the Era of multi-messenger Astronomy 48

Where t c is the theoretical coalescence time expressed by:

t c " 5c 5 256G 3 a 4 0 M 2 µ (1.40)
with a 0 the initial distance between the two compact objects. Knowing that the GW emissions occur at twice the orbital frequency, the time evolution of the frequency is:

f GW " 2 ω 2π " 2 T (1.41)
With a derivation, we get to:

9 f f " ´9 T T (1.42) and 9 f " 96 5 π 8{3 G 5{3 µM 2{3 f 11{3 (1.43)
And by integration, we finally deduce the time evolution of the GW frequency and strain amplitude (also known as the waveform):

f GW 9pt c ´tq ´3{8 (1.44) h9 1 d 9pt c ´tq ´1{4 (1.45)
The coalescence of the binary system emits a GW signal with a frequency and amplitude that increase in time in a typical shape called a chirp. The characteristic amplitude of the signal is given by the chirp mass:

M " pm 1 m 2 q 3{5 M 1{5 (1.46)
The theoretical time evolution of the GW amplitude strain is represented in the bottom panel of

Other sources

The expected signal for the three types of sources described in the following paragraphs are presented in Appendix A, Fig.

A.2.

Burst sources There are several plausible sources of short-duration GW transients (GW bursts, GWBs) [START_REF] Kalmus | Search for gravitational wave bursts from soft gamma repeaters[END_REF] that have not yet been observed, such as NS excitations, non-linear metric effects, pulsar glitches or also cosmological sources like cosmic string cusps and kinks [START_REF] Damour | Gravitational wave bursts from cosmic strings[END_REF]. Core-collapse supernovae (CCSN) remain one of the most exciting possibilities, as mentioned in the 80s by Kip Thorne [START_REF] Thorne | Multipole expansions of gravitational radiation[END_REF]. At the end of all fusion reactions, if the mass reaches the Chandrasekhar limit, gravity becomes the dominant force, and stars with a mass Á 8 -10 M d start collapsing, producing a CCSN. A compact remnant, a BH, or a heavy NS is then formed, and a GW emission is difficult to predict and occurs during or after the explosion, with a duration of a few milliseconds up to seconds. LIGO and Virgo's detectors have not observed GWs coming from such events yet, but it would be an important discovery for multi-messenger astronomy since supernovae are multi-messenger events that could be observed through GWs, photons but also neutrinos, as suggested by the supernova SN1987A, [START_REF] Burrows | Neutrinos from SN 1987A[END_REF]. As will be seen in Sec. 1.3.2, long-duration gamma-ray burst (lGRB) events are commonly associated with a sub-class of CCSN (with a mass"30 M d ).

Continuous waves

Continuous GWs [START_REF] Tenorio | Search methods for continuous gravitational-wave signals from unknown sources in the advanceddetector era[END_REF] (CWs) are long-lasting forms of gravitational radiation produced by systems that have a fairly constant and well-defined frequency, such as binary systems of stars or BHs orbiting each other (long before the merger) or a single star swiftly rotating about its axis with irregularity on it. One of the expected sources for LIGO and Virgo detectors is rapidly rotating NS known as pulsars [START_REF] Manchester | 50 years of pulsars[END_REF], but more exotic sources could include decaying ultralight boson clouds around spinning BHs.

Stochastic background

The stochastic background of GWs [START_REF] Christensen | Stochastic gravitational wave backgrounds[END_REF] (SGWB) is a sum of weak GW signals from independent sources. We have never detected these GWs so far, but observations of GWs by LIGO and Virgo suggest that there is also a stochastic background composed of BBH and BNS mergers over the history of the universe [START_REF] Christensen | Stochastic gravitational wave backgrounds[END_REF]. However, contrary to GWs coming from binary inspiral from a specific location in the sky, a stochastic background will be coming from all directions, so it is assumed to be isotropic. Moreover, a stochastic background would appear as noise in a single GW detector, as shown in Fig. A.2. In addition to this astrophysical background, [START_REF] Regimbau | The astrophysical gravitational wave stochastic background[END_REF], cosmological sources can also contribute to the SGWB [START_REF] Caprini | Cosmological backgrounds of gravitational waves[END_REF], and some models include sources like PBHs or cosmic strings.

Focus on a multi-messenger source: neutron star

In this section, BNS and NSBH are referred to as NS mergers. These types of mergers are canonical multi-messenger events in the sense that they can be observed through photons and GWs, and they are potential sources of neutrinos and cosmic rays. When an NS or a BH is produced at the end of the life of massive stars, if two NSs or an NS and a BH have been formed already bound together, they can become a compact binary. Suppose the two NSs of a BNS system are initially separated with a distance larger than the size of the progenitor. In that case, the time of the inspiral phase of the GW emission coming from the merger of the BNS will be a thousand times the age of the Universe [START_REF] Burns | Neutron star mergers and how to study them[END_REF]. On the contrary, if the two companions have a common envelope stage and initial separation of ď5 R d (either the two massive stars are not distinct or the primary forms a com-pact object before being enveloped by the secondary during its supergiant phase), they will merge within the current age of the Universe, inspiraling only through GW radiation [START_REF] Burns | Neutron star mergers and how to study them[END_REF]. Finally, a few systems can be formed dynamically, where the two compact objects have been formed separately, and then because of gravity, they become close enough to each other. In this case, the system starts losing energy by GW radiation, resulting in a GW emission, which is weak long before the merger due to a slow orbital evolution and then increases close to the merger since the orbital evolution accelerates. During the early inspiral stage, BNS and NSBH systems will likely be undetectable in photons. Some theories also predict precursor emission in gamma-rays, X-rays, and radio with luminosities " 10 42 -10 47 erg{s [START_REF] Burns | Neutron star mergers and how to study them[END_REF]. Close to the merger, the orbital radius is similar to the size of the NS, and the GW luminosity increases with a peak at "10 56 erg{s around the merger time. The emitted GW frequency enters the band of the ground-based interferometers minutes before the merger stage. Thus, within the last "100 s before the merger, detecting the precursor EM emission becomes possible if the binary is close enough to us. In the surrounding "seconds, the NSs can be so disrupted that they release matter that can power ultra-relativistic jets (discussed in Sec. 1.3.1) and mildly relativistic quasi-isotropic outflows resulting in EM and likely neutrino counterparts [START_REF] Burns | Neutron star mergers and how to study them[END_REF].

Finally, specifically talking about NSBH mergers, they can be classified into two categories depending on the NS disruption. The NS disruption occurs when tidal acceleration due to the inspiral exceeds the self-gravity of the NS. This tidal disruption depends on the properties of the NS and mass ratio. When no disruption occurs, the NSBH is described as a Heavy NSBH merger, and otherwise, we refer to them as Light NSBH mergers as they have lower mass and should produce bright EM radiation.

. Detection of gravitational waves Ground-Based GW Detectors

As mentioned in Sec. 1.2.1, Gertsenshtein and Pustovoit, followed by Weiss in the 60s, were the first to suggest the use of an interferometer for GW detection. Scientists spent the following years creating the design, understanding the noise, and controlling the interferometer cavities until 1999, the year that marked the end of the construction of LIGO's original GW detectors (initially LIGO and iLIGO), and 2004, the end of the construction of Advanced Virgo. A summary timeline is shown in Fig. 1.12.

In addition to LIGO-Hanford, LIGO-Livingston, and Virgo, we can mention GEO-600 [START_REF] Dooley | Status of GEO 600[END_REF], a small version of the main ones, first used to develop advanced technologies, and KAGRA [START_REF]Overview of kagra : Kagra science[END_REF] which is still under development but joined the end of O3 in 2020. All these detectors are based on the same working principle. They are optical setups where a laser beam is split and set to follow different optical paths before recombining and interfering. In other words, an interference pattern is created and can be measured and analyzed. The detectors quoted above are "L"-shaped interferometers (with two arms), and their goal is to measure the tiny arms-length variations induced by a passing GW. Each arm has a Fabry-Perot The GW can only be detected if the measurement made by the photodiode is more powerful than the typical fluctuations in the instrument's static state in the absence of a GW. This static state is commonly interpreted as Gaussian noise and is quantitatively represented by the noise power spectrum density (PSD), an estimate of which is given by:

S n pf q " lim T Ñ8 2 T ˇˇˇˇż T {2 ´T {2 nptqe 2πif t dt ˇˇˇˇ2 (1.47)
in strain 2 /Hz. Here n(t) is the photodiode's static signal i.e. the noise. The PSD represents the contribution of each frequency in the detector bandwidth to the total noise. We can also define the amplitude spectral density (ASD) by a S n pf q. The ASD is used to construct the sensitivity curve of the different detectors. Examples of these curves are shown in Fig. 1.14. Here the sensitivity of H1, L1, and V1 detectors during the 2 nd part of the 3 rd GW observing run (O3b) are represented. The strain, on the y-axis, is a proxy for the sensitivity. The higher the strain value for a specific frequency, the worst the detector sensitivity to this frequency. During O3b Virgo was less sensitive to the high frequencies than both LIGO detectors and L1 was more sensitive to lower frequencies (" [10 -70] Hz) than H1 and V1. This was mainly due to the absence of Signal Recycling (see Fig. In the following paragraphs, we detail the different types of noise polluting the GW detection in the current interferometers.

Response of the detector

In Sec. 1.2.2, we deduced the time evolution of the GW strain amplitude (see Eq. 1.45). An explicit form of the waveform can be approximated, neglecting the spins and the higher-order modes of GWs (for details on GW harmonic modes, see Appendix C), for t < t c , by:

h `ptq " ´1 `cos 2 pıq 2 ˆGM c 2 D ˙ˆt c ´t 5GM{c 3 ˙´1{4 ˆcosr2ϕ c `2ϕpt´t c ; M, µqs (1.48)
and

h ˆptq " ´cos 2 pıq ˆGM c 2 D ˙ˆt c ´t 5GM{c 3 ˙´1{4 ˆsinr2ϕ c `2ϕpt ´tc ; M, µqs (1.49)
Which is the GW strain amplitude for the two polarizations. Here, D is the distance from the source, ı is the inclination angle of the orbiting plane, and ϕpt ´tc ; M, µq is the orbital phase of the binary. µ, M and M have already been defined in Sec. 1.2.2. Here t c and ϕ c are the coalescence time and phase. Moreover, the dependence of h `and h ˆto the inclination ı implies that the signal is stronger in the detector when the source is face-on (ı " 0 ˝) or face-off (ı " 180 ˝) than edge-on (ı " 90 ˝) for which only the + polarization of the signal remains. The waveform in a particular detector depends on the detector antenna response (F ànd F ˆ) to the two polarizations of the gravitational waveform [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF]:

hptq " δLptq L " F `pα, δ, ψ, tqh `ptq `Fˆp α, δ, ψ, tqh ˆptq (1.50)
Chapter 1. Gravitational waves and Gamma-ray Bursts in the Era of multi-messenger Astronomy 54

α and δ are the right ascension and the declination of the source (which determines the source sky location). ψ is the polarization angle measured between the projection of the y-axis and the source angular momentum on the tangent place. Moreover, when looking for an inspiral signal in our current ground-based detectors, we know that it will only be observable in the detector for seconds to minutes. Indeed, the duration of the signal in the detector is linked to the minimum frequency at which the detector starts observing, f low , by the following formula (computed at first order):

T chirp " 5 256η GM c 3 ˆGM c 3 πf low ˙´8{3 (1.51)
and the existing GW detectors start at f low "20 Hz. Here, η is the mass ratio.

One can then consider the antenna patterns F `and F ˆof our current detectors constant in time during T chirp and defined as:

" F `" 1 2 cos2ψ p1 `cos 2 αq cos2δ ´sin2ψ cosα sinδ F ˆ" 1 2 sin2ψ p1 `cos 2 αq cos2δ `cos2ψ cosα sinδ (1.52)
These antenna pattern response functions are defined in the sky plane represented in Appendix A, Fig.

A.3.
A map of the antenna pattern Advanced Virgo's response is shown in Fig. 1.15. This figure represents the sensitivity of Virgo to CBC depending on the sky location of the source. To produce this figure, we have set ψ to 0. From this plot, we can see that the detector is sensitive to almost all sky except four "blind" spots, the bisectors of the interferometer. It also implies that finding the sky location of a GW source is complicated, which is why having a whole network of GW detectors is important.

Detector noise

The GW signal coming from a CBC is expected to be very weak, so increasing the sensitivity of ground-based detectors is necessary to detect many GW signals. Thus, the instrument noise has to be understood in addition to the stationary detector noise. The main contributions to the noise budget for LIGO Hanford in O3 are illustrated in Appendix A, Fig. A.4. The noise implied by the design of the detector is briefly and qualitatively described in the following paragraphs.

Quantum noise [107]

The propagation of photons, following a Poisson distribution, affects the GW detector. This effect is mainly visible in 2 ways:

• The Radiation pressure noise (RPN) comes from the uncertainty in the position of the mirror due to the fluctuations. Indeed, the photons' impact on the mirror produces a displacement of the mirror [START_REF] Lartaux-Vollard | Beating the standard quantum limit for the gravitational wave detector Advanced Virgo[END_REF]. Therefore, such displacement of the mirrors could be detected as a phase shift in the interference fringe at the photodiode. • The Quantum shot noise limits the sensitivity at high frequencies. Shot noise (SN) comes from the uncertainties in measuring the number of photons on the photodiode. The SN contribution decreases with the increase in the laser power, however, the RPN contribution increases.

The minimum quadratic sum of this noise is represented by the standard quantum limit which comes from Heisenberg's uncertainty principle.

Seismic noise [START_REF] Somlai | Seismic noise measures for underground gravitational wave detectors[END_REF] This noise affects detector sensitivity in the range of 0.1-10 Hz. It is caused by the ground motion. Understanding seismic noise is important to identify the persistent and variable ground vibration producing a characteristic spectrum in the detector. Among the sources of this noise, we can mention phenomena such as wind, ocean waves, earthquakes... Seismic noise triggers GW detectors via vibrations transmitted through the suspension and other isolation systems.

Thermal noise [START_REF] Gregory M Harry | Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings[END_REF] The thermal noise comes from the dissipation near the mirror surface and near the laser beam spot. Thus, the thermal noise is present in the pendulum and the mirrors themselves. The thermal noise limits the detector sensitivity between 40 Hz and 2000 Hz, which is its most sensitive frequency band. In addition, the suspension wires produce resonances around 450 Hz, and their multiple vibration modes are called the violin modes [START_REF] Lartaux-Vollard | Beating the standard quantum limit for the gravitational wave detector Advanced Virgo[END_REF].

Newtonian noise [START_REF] Beker | Newtonian noise and ambient ground motion for gravitational wave detectors[END_REF] The Newtonian noise (NN) manifests itself when density fluctuations around the test mass induce a local change in the gravitational field. NN reduces the detector's sensitivity at low frequencies, in particular below 10 Hz, together with the seismic noise.

The future of the search for gravitational waves

Next runs

The network of GW detectors is currently composed of the four interferometers described in Sec. 1.2.3: LIGO Hanford, LIGO Livingston, Advanced Virgo, and KAGRA. The two LIGO detectors are located 3000 kilometers apart in the USA. The X-arm and Y-arm are oriented as (N36°W, W36°S ) for H1 and (W18°S, S18°E) for L1 (N=North, S=South, E=East, W=West). Virgo has been constructed in Italy, and its arms are oriented as (N19°E, W19°N). The fourth GW Observing Run (O4) started in May 2023 and will last 18 months (+ 2 months of engineering run). The two LIGO detectors will be joined by Virgo later in the run. The detectors' sensitivity can be described by its BNS range which is the maximum distance at which the interferometer would detect a sky and inclination averaged fiducial 1.4 -1.4 M d BNS with an SNR of 8. The comparison of the BNS range of the past runs and the expected ones for O4 and O5 are presented in Fig. 1. [START_REF] Wang | GRB 190829a-a showcase of binary late evolution[END_REF]. We can see here that KAGRA will likely be significantly less sensitive than LIGO detectors, which have increased their sensitivity in O4 and O5 compared to the past runs.

3G detectors (Einstein Telescope (ET) and Cosmic Explorer (CE))

ET [START_REF] Sathyaprakash | Scientific objectives of einstein telescope[END_REF] is a proposed underground infrastructure for which construction is expected to begin in 2026. The underground structure and the new technology implementation will increase the detector sensitivity, reducing seismic noise. The size of the interferometer will also be increased according to the current size of Virgo (from the 3 km arm length of the Virgo detector to 10 km). The entire population of stellar and intermediate-mass BHs will be accessible over the entire history of the Universe, enabling us to understand their origin, evolution, and demography. On the NS side, ET will be able to observe the onset of tidal effects with a high SNR, providing information about the interior structure of NSs. The excellent sensitivity extending to kilohertz frequencies will also give us details of the merger and post-merger phase. ET will work together with Cosmic Explorer (CE) [START_REF] Hall | Cosmic explorer: A next-generation ground-based gravitational-wave observatory[END_REF] aiming to begin operation in the 2030s, and that has a design concept featuring two facilities, one 40 km on a side and one 20 km on a side, each housing a single L-shaped detector.

Laser Interferometer Space Antenna (LISA) LISA [START_REF] Pau | Laser interferometer space antenna[END_REF] is a project planned by ESA and NASA. It is a space-based GW observatory expected to launch in 2036. LISA is constituted of three spacecraft, each of one containing two test masses. Each spacecraft is linked to the two others via Laser interferometry. The main objective of LISA is to detect GWs from supermassive BHs, galactic binary stars, and violent events in the Universe in a frequency range from 10 ´4 to 10 ´1 Hz, which is currently inaccessible to our ground-based experiments.

. Gamma-Ray Bursts

In the previous section, we introduced concepts of GR, GW theory, and detection. As seen in Sec. 1.1, we observed in the past a GRB accompanying a GW emission. In the following section, a description of GRBs is given. We first discuss the discovery of GRBs and the models explaining their emission: long GRBs are associated with a sub-class of core collapse of massive stars (the supernovae), and short GRBs are believed to originate in the CBC system containing at least one NS (BNS or NSBH). In the second part, we present the observational pieces of evidence, based on the GRB characteristics, in favor of these models. We end this section on a more experimental level by presenting several existing detectors aimed at observing GRBs.

. History and model A bit of history

The discovery of GRBs was accidentally made in the late 1960s. The U.S. Air Force managed the launch of "Vela" satellites [START_REF] Klebesadel | Observations of gamma-ray bursts of cosmic origin[END_REF] carrying X-ray, gamma-ray, and neutron detectors. The mission of these satellites was to monitor the "Partial Test Ban Treaty" that forbade nuclear explosions in space. The first observation of a GRB by the Vela satellites occurred in 1967, but the actual determination happened two years later thanks to an improved version of Vela with higher resolution. The latter was launched to determine the localization of these gamma-rays and exclude a terrestrial or solar origin. These new objects with a cosmic origin were later named GRBs [START_REF]The Direction and Spectral Variability of a Cosmic Gamma-Ray Burst[END_REF]. GRBs are bursts of highly energetic gamma rays and have a duration ranging from a few milliseconds up to minutes. GRB emissions are usually detected below a few MeV; however, we have now observed GRBs with an energy up to TeV.

The Compton Gamma-ray Observatory (CGRO) [START_REF] Murdin | Compton gamma ray observatory (cgro)[END_REF], launched in 1991, revolutionized GRB observations. Aboard Compton, we can count four instruments which are the Burst And Transient Source Experiment (BATSE), an all-sky monitor (20 -1000 keV), the Oriented Scintillation Spectrometer Experiment (OSSE) (0.05 -10.0 MeV), the Imaging Compton Telescope (COMPTEL) (0.8 -30.0 MeV) capable of imaging 1 steradian, and the Energetic Gamma Ray Experiment Telescope (EGRET) (30 -3 ˆ10 4 MeV).

The BATSE instrument brought a breakthrough since it highlighted the isotropy of GRB directions, regardless of the source intensity, as shown in Fig. A.5 from Appendix A which was the first clue for the cosmological origin of GRBs.

Another mission provided important observations in the GRB science. The Italian-Dutch satellite BeppoSAX [START_REF] Boella | the wide band mission for x-ray astronomy[END_REF], in 1997, was the first instrument to detect counterparts to GRBs in other wavelengths: an X-ray afterglow (details in Sec. 1.3.2) from GRB 970228 [START_REF] Costa | Discovery of an x-ray afterglow associated with the gammaray burst of 28 february 1997[END_REF]. It also detected a GRB afterglow which led to the first redshift measurement, another clue for the cosmological origin of at least some GRBs.

Emission process of Gamma-Ray Bursts

GRB emission occurs following the accretion of a massive disk onto a newly-born compact object. Two GRB jets, reaching ultra-relativistic velocities with a typical bulk Lorentz factor Γ " 100, are ejected in two opposite directions. In the following sections, we will use the terms short and long GRBs (sGRBS/lGRBs) to differentiate between the GRBs with a duration lower than "2 s (sGRBs) and higher than this threshold (lGRBs). This classification will be explained in Sec. 1.3.2. In the following paragraphs, we first present the model describing the jet ejection, then focus on the long and short GRBs progenitor models.

The fireball model (jet emission)

This is the model [START_REF] Piran | Gamma-ray bursts and the fireball model[END_REF] that is favored to describe how the energy from the central engine is transformed into radiation. It has been proposed by Meszaros and Rees 1993 [120] and Piran et al. 1993 [121]. The fireball model describes the GRB jet emission regardless the type (short or long) of GRBs and thus independently of the progenitor itself. Within the fireball model, a GRB is described as an ultrarelativistic outflow. Internal shocks [START_REF] Rees | Unsteady Outflow Models for Cosmological Gamma-Ray Bursts[END_REF] in this outflow are believed to produce the prompt γ radiation, and an external shock [123] forms the broad-band afterglow as shown in Fig. 1.17.

Suppose we consider a central engine containing a mass M 0 (a BH in most cases). In the region surrounding the BH, a fraction of energy is converted into GWs and neutrinos, and another fraction is transformed into a fireball of photons, leptons, and baryons. In the fireball model, the fireball expands under adiabatic pressure. The initial energy is extracted from BH via the accretion disk to produce the fireball that develops into a jet with an initial Γ " 1.

The particles in the jet carry kinetic energy E " ΓM 0 c 2 coming from the initial thermal energy, and the more the jet is accelerated, the more the Γ value increases until Γ " E{pM 0 c 2 q. Because the energy release of the source is irregular, the expanding shells inside the jet move with different bulk Lorentz factors and collide with each other, producing internal shocks that convert the kinetic energy into high-energy photons (the prompt emission).

The expanding fireball becomes optically thin to gamma rays during the shock breakout. This can happen before (breaking out of the stellar envelope) and during the prompt phrase. The external shock occurs when the jet has expanded far into the interstellar medium and begins to interact with the surrounding gas/dust. These external shocks radiate synchrotron radiation in the range of X-ray, UV, optical, infrared, and radio energies (the afterglow emission, see Sec. 1.3.2) [START_REF] Hussein | Search for gamma-ray bursts with SVOM/MXT space telescope : Development and characterization of the onboard scientific software[END_REF].

Long GRB core collapse

The link between supernovae and lGRBs was established in 1998 and confirmed in 2003 with GRB 030329 [START_REF] Dado | The supernova associated with GRB 030329[END_REF]. The first association of a lGRB with a supernova (SN) [START_REF] Bloom | The Observed Offset Distribution of Gamma-Ray Bursts from Their Host Galaxies: A Robust Clue to the Nature of the Progenitors[END_REF] brought out the collaspar model. Goodman [START_REF] Goodman | Are gamma-ray bursts optically thick?[END_REF] and Paczynski [START_REF] Paczynski | Gamma-ray bursters at cosmological distances[END_REF] were the first to describe the collapsar model, explaining that the rapid rotation of a star going SN can power an ultra-relativistic jet like a GRB. According to this model, lGRBs could be produced in the collapse of massive stars. The progenitor star collapses into a BH, and an accretion disk is formed within the stellar envelope. The mechanism that converts the energy into the jet is still not completely understood. The energy deposited in the surrounding matter will produce jets, and if they are powerful enough, they will penetrate the stellar envelope and produce a lGRB. Short GRB core engine The idea of NS mergers producing sGRBs appeared at the end of the 1990s [START_REF] Paczynski | Gamma-ray bursters at cosmological distances[END_REF][START_REF] Eichler | Nucleosynthesis, Neutrino Bursts and Gamma-Rays from Coalescing Neutron Stars[END_REF] and has been confirmed by the joint detection GW170817 -GRB 170817A [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF]. In this model, the disrupted but still bound material accretes onto the remnant object (most likely a BH), and in at least some cases, this produces a highly collimated ultra-relativistic jet that results in a sGRB [START_REF] Burns | Neutron star mergers and how to study them[END_REF]. A huge amount of energy from the accretion disk is deposited near the surface of the resulting compact object, which launches an ultra-relativistic fireball away from the central engine. This outflow is collimated into a jet by the material and by the magnetic fields emanating from the system. Figure 1.18 gives a complete survey of the expected GW and EM signatures from minutes before until years after the NS merger. Among all the expected signatures, the easiest way to detect NS mergers is through the observation of their prompt sGRB emission, due in part to the large number of sGRB observations compared to the other counterparts. As described in [START_REF] Burns | Neutron star mergers and how to study them[END_REF], a thousand sGRBs have been detected so far, which is currently three orders of magnitude more than GW detections from NS mergers, two more than claimed kilonovae, and one more than sGRBs afterglow. They also typically lead the observation campaign and help narrow the GW localization for the other counterparts.

. Characteristics of GRBs and pieces of evidence for two different progenitors

We can distinguish two phases in the GRB emission: the initial emission phase (the prompt emission) is detailed in the following subsection; the second, the afterglow, is discussed in the next one.

Prompt emission

The prompt emission is caused by converting a fraction of the jet's kinetic energy into radiation. The prompt emission is detected as a bright, impulsive emission of soft gamma-rays ("10 keV -10 MeV) with a total duration between 10 ´1 s and "10 3 s, and isotropic equivalent luminosities typically in the range of L iso " 10 50 -10 53 erg{s. During the prompt emission, GRBs can be characterized by their temporal and spectral properties. These properties allow us to separate them into two categories based on their duration and spectral hardness.

GRB duration

The gamma-ray light curve is an essential tool for studying the duration of GRBs. This duration is represented by the T 90 statistic, defined as the time interval in which the integrated photon counts increase from 5% to 95% of the total counts above the background. Several light curves are represented in Fig. 1.19 to illustrate the notion of T 90 . This sample includes long and short GRBs with either single or multi peaks.

Furthermore, a study with a sample of GRBs detected by BATSE shows a bimodal distribution as demonstrated in Fig. 1.22, allowing us to define a separation in the duration of GRBs by a traditional dividing line: sGRBs (T 90 ă 2 s with an average T 90 " 0.5 s) and lGRBs (T 90 ą 2 " 3 s with an average T 90 " 30 s). However, this separation is not always accurate since we can see an overlap between the short and long GRBs distribution in Fig. 1.22. Moreover, the T 90 value is instrument-dependent according to the instrument sensitivity (the less sensitive at a given energy, the lower T 90 ) [START_REF] Bromberg | Short versus long and collapsars versus non-collapsars: A quantitative classification of gamma-ray bursts[END_REF][START_REF] Qin | A comprehensive analysis of fermi gamma-ray burst data. iii. energydependent t90 distributions of gbm grbs and instrumental selection effect on duration classification[END_REF].

Figure 1.19 also shows that the light curves of GRBs are irregular and complex. Some GRBs (like GRB910216B in Fig. 1.19) are composed of a single peak, and some show multiple peaks, such as GRB 920221 in Fig. 1.19. The number of peaks in the light curves can be explained by the multiple shock waves created by the central engine, that with the surrounding media, or developed within the jet due to the inhomogeneous outflow. We can also notice that the range of GRB duration is very large, going from tens of milliseconds to hundreds of seconds.

A last property that is an essential tool in the temporal study of GRBs is the spectral lag. Cheng et al. (1995) [START_REF] Chen | Distribution of spectral lags in gamma-ray bursts[END_REF] identified a delay in the arrival times of lowenergy photons with respect to high-energy photons. This property can also be considered an important criterion for classifying long and short GRBs. Indeed, a study [START_REF] Yi | On the spectral lags of the short gamma-ray bursts[END_REF] of 1008 lGRB spectral lags and 308 sGRB lags observed by BATSE and [START_REF] Bernardini | Comparing the spectral lag of short and long gammaray bursts and its relation with the luminosity[END_REF] [START_REF] Bernardini | Comparing the spectral lag of short and long gammaray bursts and its relation with the luminosity[END_REF] (among others) shows contrasts in the distribution of spectral lag for short and long GRBs: sGRBs have a spectral lag consistent with zero while most of lGRBs have a positive spectral lag. However we do not have a complete understanding of the correlations between the spectral lag and the type of GRBs yet, but many studies show that it might be related to a curvature effect (i.e. the light curve in a softer band tends to have a longer tail, and a larger spectral lag compared to the one in the harder band [START_REF] Yi | On the spectral lags of the short gamma-ray bursts[END_REF]) [START_REF] Salmonson | On the kinematic origin of the luminosity-pulse lag relationship in gamma-ray bursts[END_REF][START_REF] Ioka | Peak luminosity-spectral lag relation caused by the viewing angle of the collimated gamma-ray bursts[END_REF][START_REF] Lu | Spectral lags caused by the curvature effect of fireballs[END_REF][START_REF] Shen | Spectral lags and the energy dependence of pulse width in gamma-ray bursts: contributions from the relativistic curvature effect[END_REF] and also that the spectral lag is strongly connected to the duration of the pulse for lGRBs [START_REF] Ryde | Interpretations of gamma-ray burst spectroscopy[END_REF][START_REF] Yi | On the spectral lags of the short gamma-ray bursts[END_REF]. [START_REF] Asaf Pe'er | Physics of gamma-ray bursts prompt emission[END_REF]). This sample of light curves shows short and long GRB events.

GRB spectral hardness

By definition, the gamma-ray spectrum represents the energy distribution of the photons. Spectral hardness is calculated using detected counts, which is the direct measurement of the detector. Spectra are obtained by combining the detector counts with the instrument response to get the number of photons per energy bin per time.

The spectrum hardness ratio r h , which is the ratio of the counts in two arbitrary separated energy bands, is defined as r h " C E2 {C E1 , where C E2 (resp. C E1 ) is the number of counts with energy in E2 (resp. E1) band, with E2 > E1 [START_REF] Hussein | Search for gamma-ray bursts with SVOM/MXT space telescope : Development and characterization of the onboard scientific software[END_REF]. A correlation between GRBs' duration and hardness ratio has been empirically observed: sGRBs have, on average, a harder spectrum, i.e. higher r h than lGRBs. (due to a harder low-energy spectral component rather than a different peak energy). The hardness ratio is performed in counts, and as such it is detector-dependent. For an instrument with more than two energy bands, one can define more than one hardness ratio. Also, two instruments can have a slightly different distribution, but the same trend of short-hard/long-soft is seen regardless of the instrument.

Spectral properties enable to put constraints on GRB emission models. The majority of the observed GRBs (67% of Fermi/GBM GRBs) [START_REF] Oganesyan | Detection of low-energy breaks in gamma-ray burst prompt emission spectra[END_REF] can be fitted with a mathematical function called the Band function [START_REF]BATSE Observations of Gamma-Ray Burst Spectra. I. Spectral Diversity[END_REF]. The photon number spectra in this model are given by the following "broken power law" [START_REF] Hussein | Search for gamma-ray bursts with SVOM/MXT space telescope : Development and characterization of the onboard scientific software[END_REF]:

N ph pEq " A $ & % p E 100KeV q α e ´E E 0 if E ă pα ´βqE 0 " pα´βqE 0 100KeV ı α´β e pβ´αq p E 100KeV q β if E ě pα ´βqE 0 .
(1.53)

Where:

• α is the low photon spectrum index with typical values between 0 and -2, • β is the high photon spectrum index with typical values between -2 and -4,

• E 0 is the break energy between the two spectral regimes and,

• A is an overall normalization.

The low and high spectral indices fit the data above and below the E peak parameter, where E peak indicates the maximum of the spectral energy distribution. The indices and E peak help describe the amount of energy or power produced by the GRB at a given energy. GBM spectral fits are compared and chosen as best using a ratio = C-stat/degrees of freedom. "C-stat" [START_REF] Cash | Parameter estimation in astronomy through application of the likelihood ratio[END_REF] is a statistic based on the log-likelihood Cash statistic, and the degrees of freedom are that of the spectral function.

As an example, the photon spectrum in cm 2 {s{MeV of GRB170817A is provided in Fig. 1.20 (top panel in each figure). The left panel shows the first pulse of the GRB, and the right one represents the photon spectrum of the soft tail, as discussed in Sec. 1.1.3.

The spectral properties of the two categories, short and long GRBs, detected by BATSE, Integral, and Fermi, are generally similar [START_REF] Hines | Physics of gamma-ray bursts prompt emission[END_REF], with minor differences. Searches done with Fermi data [START_REF] Nava | Spectral properties of long and short gamma-ray bursts: comparison between batse and fermi bursts[END_REF] confirm that short bursts have on average a harder α compared to long bursts with p⟨α GBM,short ⟩q " ´0.46 that was consistent with have BATSE found: p⟨α GBM,short ⟩q " ´0.58˘0.10 and p⟨α GBM,long ⟩q " ´1.050

.14 [START_REF] Ghirlanda | Short versus long gamma-ray bursts: spectra, energetics, and luminosities[END_REF]. This study [START_REF] Nava | Spectral properties of long and short gamma-ray bursts: comparison between batse and fermi bursts[END_REF] has also shown that sGRBs detected by Fermi are found in a different region in the E obs peak-Fluence (integral of the energy flux over the duration of the burst) plane than long events, the former having larger peak energy and lower fluences compared to the latter ones as presented in Fig. 1.21.

Thus, GRBs are commonly classified into two categories based on their duration and spectral hardness. lGRBs have a softer prompt emission spectrum than sGRBs. The bimodality of the distribution in the duration-spectral hardness Horizontal blue dashed line: lower limit for the GBM instrument. Horizontal red dashed line at "50 keV: lower limit for the BATSE instrument. Horizontal red dashed line at "1 MeV: upper limit for BATSE (for the GBM, there is no upper limit in this plane). The vertical dashed line (left panel): an example of fluence selection. Dashed curve (right panel): photon flux selection criterion adopted by BATSE. Extracted from [START_REF] Nava | Spectral properties of long and short gamma-ray bursts: comparison between batse and fermi bursts[END_REF] . plane is represented in the main plot of Fig. 1.22. These different properties of lGRBs and sGRBs point towards the possibility of having at least two different progenitors of GRBs, and so the different progenitor models seen in Sec. 1.3.1.

GRB afterglow

The second phase in the GRB emission is called the afterglow and is produced due to the interaction between the relativistic GRB jet and the ambient medium. Here, we give more details about the GRB afterglow. BeppoSAX [START_REF] Boella | the wide band mission for x-ray astronomy[END_REF] detected the first X-ray afterglow, a counterpart from GRB 970228 [START_REF] Costa | Discovery of an x-ray afterglow associated with the gammaray burst of 28 february 1997[END_REF]. This bright X-ray emission was discovered with a power law decaying in intensity with time. In the years that followed this first detection, optical and radio afterglow detections were observed. The accurate positions given by the afterglow enabled the identification of the host galaxies of many bursts and redshift measurements. The detection of afterglows constitutes an important step in GRB science. One can define the GRB afterglow as the result of the interaction between the relativistic jet and the ambient medium, extending from the radio band to TeV energies. The afterglow happens with a delay of tens of seconds after the prompt. It can be detected on a large range of frequencies, from γ-rays to the radio band with a flux decaying smoothly as a power law in time for weeks or months, and the typical frequency of the radiation being time-dependant and moving from the X-ray to the radio band. Their afterglow provides another distinction between the two classes: many studies [START_REF]The Afterglows of Swift-era Gamma-Ray Bursts. II. Type I GRB versus Type II GRB Optical Afterglows[END_REF][START_REF]The prompt-afterglow connection in gamma-ray bursts: a comprehensive statistical analysis of Swift X-ray light curves[END_REF][START_REF] Avanzo | Short gamma-ray bursts: A review[END_REF][START_REF]Multi-color observations of short GRB afterglows: 20 events observed between 2007 and 2010[END_REF] on samples of GRBs showed that the sGRB afterglows are on average significantly fainter than those of lGRBs.

Host galaxies

In addition to the difference in duration and spectral hardness, the age of host galaxies seems to be a distinction between short and long GRBs. sGRBs are found in galaxies on average older than the host galaxies of lGRBs [START_REF] Hussein | Search for gamma-ray bursts with SVOM/MXT space telescope : Development and characterization of the onboard scientific software[END_REF][START_REF] Nugent | Short GRB host galaxies. II. a legacy sample of redshifts, stellar population properties, and implications for their neutron star merger origins[END_REF]. Thanks to the GRB afterglow, one can study the host galaxies of GRBs and, in particular, compare the two classes to GRBs: In general, lGRBs are found in galaxies that are faint, blue, and very star-forming [START_REF] Le Floc'h | Are the hosts of gamma-ray bursts sub-luminous and blue galaxies? 400[END_REF][START_REF] Savaglio | Unveiling the fundamental properties of Gamma-Ray Burst host galaxies[END_REF]. On the contrary, we did not observe any connection between the host galaxy types and the star formation activities of sGRBs [START_REF] Berger | Short-Duration Gamma-Ray Bursts[END_REF][START_REF] Duque | Compact object coalescences and gamma-ray bursts in the gravitational-wave era[END_REF]. Finally, lGRBs are usually produced close to their host galaxy centers, in UV-bright regions, while sGRBs can occur far from their host galaxies [START_REF]Demographics of the Galaxies Hosting Short-duration Gamma-Ray Bursts[END_REF][START_REF] Duque | Compact object coalescences and gamma-ray bursts in the gravitational-wave era[END_REF][START_REF] Duque | Compact object coalescences and gamma-ray bursts in the gravitational-wave era[END_REF]. These observations constitute evidence of at least two different types of GRB progenitors.

. GRB Detectors

In this subsection, I give an overview of the existing instruments used to observe GRBs and discuss their detection principle. I mainly focus on the Fermi Gammaray Space Telescope since my main project is related to Fermi data.

Nowadays, various missions detect GRBs uniformly distributed in the sky almost daily. The instruments can measure the photons' energies and estimate their incoming direction. The photons are collected to build the GRB light curves and spectra (see Fig. 1.3 and Fig. 1.20). Different detectors have been constructed to cover different energy ranges and localizing requirements. Among them (in chronological order):

Chapter 1. Gravitational waves and Gamma-ray Bursts in the Era of multi-messenger Astronomy 66

The Neil Gehrels Swift Observatory

The Swift mission [START_REF]The Swift Gamma-Ray Burst Mission[END_REF], launched in 2004, is dedicated to the detection of GRBs prompt and afterglow emission. Aboard Swift, we can find three instruments: (1)

The Burst Alert Telescope (BAT) [START_REF] Scott | The burst alert telescope (BAT) on the SWIFT midex mission[END_REF] is used to detect the prompt emission of GRBs, with an energy range of 15 -150 keV.

(2) The X-ray Telescope (XRT) [START_REF] David | The Swift X-Ray Telescope[END_REF] is dedicated to afterglow detection, with an energy range of 0.3 -10 keV.

(3) Finally, the Ultra-Violet/Optical Telescope (UVOT) [START_REF] Peter | The swift ultra-violet/optical telescope[END_REF] sensitive to wavelengths between 170 and 600 nm is used to detect the ultra-violet and the optical afterglow.

Fermi Gamma-ray Space Telescope

The Fermi Gamma-ray Space Telescope [START_REF] P F Michelson | Fermi gamma-ray space telescope: high-energy results from the first year[END_REF] is a space observatory launched on June 11, 2008. It aims to detect the most energetic phenomena taking place in the universe through observations of γ-ray radiation. Fermi is composed of two onboard instruments. (1) The Large Area Telescope (LAT) [START_REF] Ackermann | The fermi large area telescope on orbit: Event classification, instrument response functions, and calibration[END_REF] employs a pairconversion technique and is sensitive to very-high-energy gamma rays (20 MeV -300 GeV) from objects such as active galactic nuclei (AGN), with an effective detection area of "0.9 m 2 for GeV energies and field of view that covers 20% of the sky. The principle is similar to particle physics detectors. The incoming photon interacts with heavy nuclei in one of the photon conversion layers producing an electron-positron pair. The particles are tracked as they move through the photon conversion layers before reaching the calorimeter at the bottom of the instrument. Thanks to a tracking system and the calorimeter, the pair's trajectory and energy are measured, and finally, the initial photon's energy and incoming direction can be reconstructed.

(2) The Gamma-ray Burst Monitor (GBM) [START_REF] Charles | The Fermi Gamma-ray Burst Monitor[END_REF] instrument is used to observe GRBs coming from the entire sky not occulted by the Earth within the energy range of 8 keV -40 MeV. The photon flux from the emission of a GRB jet depends on the distance of the source, the luminosity at the source, and the orientation of Fermi/GBM (if it faces the jet, for instance). Depending on the value of these three parameters, Fermi/GBM can or cannot detect the GRB. The GBM flight hardware comprises 14 NaI(T1) detectors, which are used to measure the low energy spectrum from 8 keV to 1 MeV, and 2 BGO detectors with an energy range of "200 keV to "40 MeV. A "trigger" occurs when there is an increase in the count rates of two or more NaI detectors above an adjustable threshold. The GBM flight software contains algorithms to compute the locations of trigger events based on the relative rates in the NaI detectors and to evaluate the probability that a trigger arises from a GRB. This paragraph briefly introduces the tool developed to analyze Fermi/GBM data. We will provide a detailed description of the analysis in Chapter 4.

Figure 1.23 shows the display of GRB 130502A (top) and GRB 170111B (bottom) produced by the GBM Targeted Search, a more sensitive search pipeline for GBM short GRBs than performed onboard (complete description in Sec. 4.1). The x-axis represents the GBM trigger Mission Elapsed Time (MET) 1 , and the y-axis shows the different best-fit duration timescales. The content of each rectangle is the log-likelihood ratio (LLR) calculated by the search. With this search pipeline, a sGRB with a similar waterfall shape can easily be discriminated from the background (more details in Chapter 4). For Fermi/GBM, the background can be divided into photon and charged particle components. The former is produced by the actual overall photon flux coming from the ensemble of sources in the celestial sphere around Fermi, such as the Sun, the Earth, the cosmic gamma-ray background, and gamma-ray pulsars. The latter includes cosmic rays and any charged particle interacting with the satellite materials or with the photomultiplier [START_REF] Pillas | Deep multimessenger search for compact binary mergers in ligo, virgo and fermi/gbm data from[END_REF].

Very High Energy (VHE) Gamma-ray detectors

Contrary to Swift and Fermi, the High Energy Stereoscopic System (H.E.S.S.) [START_REF] Hofmann | The high energy stereoscopic system (hess) project[END_REF] is a ground detector composed of Imaging Atmospheric Cherenkov Telescopes aimed to investigate GRBs in the energy range from tens of GeV to tens of TeV. With a similar working principle, one can mention the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) [START_REF] Alessio | Searching for grbs at vhe with magic: the status before cta[END_REF] telescopes sensitive to GRBs with energies in the range 25 GeV -30 TeV. Until now, several VHE GRBs have been observed by H.E.S.S.: GRB 190829A [START_REF] Wang | GRB 190829a-a showcase of binary late evolution[END_REF] observed between " 0.18 -3.3 TeV, and GRB 190114C [START_REF] Sahu | Origin of sub-tev afterglow emission from gamma-ray bursts grb 190114c and grb 180720b[END_REF] observed between " 0.1 -0.5 TeV which MAGIC has also detected. In addition, detections of delayed sub-TeV photons from GRBs by MAGIC and 0 MET corresponds to 2001-01-01 00:00 UTC. HESS show an encouraging future of GRB afterglow studies with the Cherenkov Telescope Array (CTA) [START_REF] Inoue | Gamma-ray burst science in the era of the cherenkov telescope array[END_REF], the next-generation gamma-ray observatory.

Future missions

SVOM [START_REF] Atteia | The SVOM mission[END_REF] is a Franco-Chinese mini-class satellite with four instruments onboard. SVOM is dedicated mainly to the study of GRB physics and is supposed to be launched in early 2024. In addition to the spaced-based instruments, SVOM comprises a complementary set of ground-based detectors and a network for communication between ground and space. The different components of the space-based instrument are shown in Fig. 1.24: (1) the Gamma-ray monitor (GRM) [START_REF] Dong | Svom gamma ray monitor[END_REF] (15 -5000 keV).

(2) ECLAIRs [START_REF] Schanne | The ECLAIRs telescope onboard the SVOM mission for gamma-ray burst studies[END_REF] (4 -150 keV). (3) the Microchannel X-ray Telescope (MXT) [START_REF]The microchannel x-ray telescope on board the svom satellite[END_REF] (0.2 -10.0 keV). (4) the Visible Telescope (VT) [START_REF] Fan | The Visible Telescope onboard the Chinese-French SVOM satellite[END_REF] (GRBs up to redshift z " 6.5 and limiting magnitude of +22.5 Mv).

Most of the current missions discussed above are presented in Fig. 1.24, showing their different components.

. Open questions about GRBs Classification now questioned?

As discussed in Sec. 1.3.2, GRBs are commonly separated into two categories based on their duration and spectral hardness properties. These two classes of GRBs -short and hard GRBs and long and soft GRBs -have different types of progenitors. However, a recent study [START_REF] Rastinejad | A kilonova following a long-duration gamma-ray burst at 350 mpc[END_REF] reported the discovery of a likely kilonova associated with the nearby (350 Mpc), minute-duration GRB 211211A.

As shown in Fig. 1.18, the kilonova is expected to be a remnant of a BNS merger. This suggests that lGRB might be emitted from merger events. The associated kilonova has similar properties (luminosity, duration, and color) to that which accompanied GW170817. Figure 1.25 provides the properties of GRB 211211A. The burst's duration and spectral hardness lie close to the mean of the lGRB population. An accompanying afterglow " 1 minute after the burst has been observed by the Swift X-ray Telescope (XRT) and Ultra-Violet Optical Telescope (UVOT). In addition to the kilonova, other clues link GRB 211211A to a neutron star merger.

• the observed exponential decline in X-rays at a few hundred seconds after the trigger (see Fig. 1.18), which is consistent with sGRBs.

• The spectral lag during the initial GRB 211211A burst of 4˘9 ms between the 25 -50 and 100 -150 keV BAT bands is more consistent with short than long GRBs.

• The host galaxy stellar population (regarding its mass and star formation rate) is more consistent with the hosts of short than long GRBs.

A similar case [START_REF] Levan | Jwst detection of heavy neutron capture elements in a compact object merger[END_REF] was found with GRB 230307A, a long-duration exceptionally bright GRB, detected by James Webb Space Telescope (JWST) [START_REF] Gardner | The james webb space telescope[END_REF] and Fermi/GBM, which seems to contain a kilonova similar to AT2017gfo.

In upcoming observing runs, looking for coincidences between GWs and lGRB might be worthwhile and can increase the number of multi-messenger signals that can be recovered.

On the contrary, GRB 200826A is a sGRB with a likely supernova counterpart [START_REF] Rossi | The peculiar short-duration grb 200826a and its supernova*[END_REF]. This GRB is commonly qualified as a peculiar event since its duration (" 0.5 s) is consistent with sGRBs, but it has a soft spectral hardness as lGRBs. Furthermore, a possible associated supernova was found compatible with the lGRB hypothesis. This suggests that the duration alone is not sufficient to classify the GRBs and that GRBs produced by a sub-class of CCSNe can reach durations of 0.5 s.

Very high energetic (ąGeV-TeV) GRB emission

The detection of VHE γ-rays is not expected from bursts beyond a redshift of z ě 0.1 due to their suppression by pair production effect when the γ-rays interact with the low-energy photons forming the Extragalactic Background Light (EBL). Thus, high-redshift sources would not be detectable. However, several challenging cases have been observed in recent years:

• A study [START_REF] Neronov | Very-high-energy gamma-ray emission from high-redshift blazars[END_REF] done with Fermi-LAT data reported a possible detection of VHE γ-ray flux at energies above 100 GeV from blazars with redshift z ą 0.5.

• In 2020, MAGIC detected GRB 201216C, a long GRB at VHE with a redshift estimated to be z " 1.1 [START_REF] Fukami | Very-high-energy gamma-ray emission from GRB 201216C detected by MAGIC[END_REF], which is the most distant object ever detected by the ground-based gamma-ray telescopes. .

• Several missions (LHASSO [START_REF] Ma | Chapter 1 lhaaso instruments and detector technology *[END_REF] and CARPET [START_REF]1+1946/GRB 221009A: detection of a 250-TeV photon-like air shower by Carpet-2[END_REF] among others) recently observed photons with energies of 18 and 251 TeV from GRB 221009A [START_REF]Grb 221009a: Discovery of an exceptionally rare nearby and energetic gamma-ray burst[END_REF] with a redshift estimated to be z"0.151.

VHE emission is usually described and predicted by inverse Compton scattering and synchrotron self-Compton scattering of lower energy photons by electrons [START_REF] Alvarez-Muñiz | Grb 941017: A case study of neutrino production in gamma-ray bursts[END_REF][START_REF] Wang | Prompt high-energy gamma-ray emission from the synchrotron self-compton process in the reverse shocks of gammaray bursts[END_REF] at different regions of the jet. However, it is now needed to understand and model the EBL attenuation of a flux of photons with VHE, and other emission scenarios are currently investigated for GRB 221009A, including dark matter theories [START_REF] González | Grb 221009a: A light dark matter burst or an extremely bright inverse compton component?[END_REF].

. The purpose of GW-GRB joint searches

In this introductory chapter, we saw that the joint detection of GW170817 and GRB 170817A marked a milestone for multi-messenger astronomy. It confirmed that at least a fraction of sGRBs originates in NS mergers. This joint detection also had implications in GRB physics (jet formation, ejecta of the merger ...), in astrophysics more generally (constraining the speed of gravity, testing different neutron star EOS, estimating the BNS merger rate...), and in cosmology (measuring the Hubble constant H 0 ). However, many open questions remain. Among others: Are the properties of GW170817 common to all NS mergers or do they represent an exceptional case? As explained in Sec. 1.3.4, we also faced an interesting case in the past years, challenging the sGRB-lGRB classification, where a kilonova might have been associated with a lGRB [START_REF] Rastinejad | A kilonova following a long-duration gamma-ray burst at 350 mpc[END_REF]. This raises the question of the fraction of short and long GRBs associated with NS mergers.

The purpose of GW-GRB joint searches

On the GRB physics side, future detections and their associated parameter inference of the BNS remnant object (in most cases, a BH) would help understand the leading mechanisms to power a GRB. It would also bring information about jet formation, which is currently poorly understood. Joint detections would also improve source localization, improving the follow-up in longer wavelengths.

On the cosmology side, the expansion rate of the local Universe, H 0 , is linked to the luminosity distance d L by H 0 d L " cz when the redshift z ! 1. Multi-messenger observations could help to solve the tension mentioned in Sec. 1.1.5 between early probe (CMB) and late universe probes (SN Ia) found at high redshifts. Different ways to measure H 0 with GWs exist, but finding an EM counterpart should improve the estimation. Indeed finding a kilonova or an afterglow would allow for more precise localization of the source, allowing to detect the source redshift and, thus, estimate the Hubble constant.

About the NS EOS, we saw that combining information from the GW and the EM emissions can help constrain the NS EoS. As shown in Fig. 1.8 in Sec. 1.1, the predictions for EM signature vary depending on the binary mass and remnant type. A way to test these predictions and define the mass transitions between remnant types would be to detect EM emissions from NS mergers. A study from [START_REF] Margalit | The multi-messenger matrix: The future of neutron star merger constraints on the nuclear equation of state[END_REF] estimates that we need "10 detected NS mergers to constrain the maximum mass of a non-spinning NS to within a few percent precision, assuming a mass ratio of 1.

More joint detections would also help constrain the celerity of GWs more precisely [START_REF] Abbott | Multi-messenger observations of a binary neutron star merger[END_REF].

Finally, since a GW/GRB association would be a strong proof of a CBC involving NS, it would also help constrain the BNS merger rate and the fraction of BNS that power jets/GRBs.

That is why, through this thesis, we focused on looking for coincidences in LIGO/Virgo and Fermi/GBM data in the hope of finding more GW/GRB joint detections. For this purpose, work on GW data analysis has been done to help improve the search sensitivity in the framework of the PyCBC pipeline. In the second step, a workflow was built to analyze a large amount of data in both the GW and the GBM channels without requiring a confident detection in one of the two channels.

CHAPTER 2

GRAVITATIONAL WAVE DATA ANALY-SIS

We saw in the previous chapter that GW170817 -GRB 170817A was an exceptional event, and in order to answer the fundamental questions listed above, more joint detections are needed. To maximize the chances of having such events again, an appropriate sensitivity should be reached by both the GW and GRB searches. Thus, this chapter introduces the CBC searches focusing mainly on the PyCBC search pipeline. The second part of this chapter and the next chapter present the work undertaken within the PyCBC group of LIGO/Virgo and the work done to explore the improvement of the PyCBC search sensitivity. Several independent pipelines carry out the CBC data analysis. In this chapter, we will focus on the PyCBC search pipeline, which is a CBC-modeled search [START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF]. Other CBC-modeled pipelines also exist. Among them:

1. GstLAL [START_REF] Cannon | Gstlal: A software framework for gravitational wave discovery[END_REF] operates in "low-latency" and in "offline" as PyCBC. Pipelines for unmodeled GW data analysis have also been created, such as coherent WaveBurst (cWB) [START_REF] Drago | Coherent waveburst, a pipeline for unmodeled gravitational-wave data analysis[END_REF]. Contrary to PyCBC, GstLAL, and MBTA, cWB is a coherent search (in contrast to coincident methods) in the sense that it combines from the beginning data streams from all the available detectors. cWB is an unmodeled search since it identifies GW transients using as few assumptions on the signal morphology as possible. The search generates time-frequency (TF) maps of the data in which each TF pixel with an energy above a given threshold is kept for further analysis.

. CBC searches

Here, we make the assumption that noise is Gaussian and stationary, we know this is not the case but we treat this issue as a second-order problem.

. Modeled searches

A modeled search for GW signals uses GW waveform models called a template bank of waveforms to recover GW signals. In the case of the CBC systems, the inspiral part of the waveform can be computed with post-Newtonian approximations as we saw in 1.2.2 and 1.2.3, so the CBC search consists in searching for a signal of known form in the data also containing noise. This is done by matched filtering, also called optimal filter (see Sec. 2.1.2). Within this technique, we work with templates of waveforms to compare and find matches between the data and the gravitational waveforms predicted by GR. A GW signal coming from CBC systems can be described by several parameters used to construct the template of the waveform. These parameters are summarized in Table 2.1. The CBC parameters space (described by the parameter vector θ) can be divided into two categories: extrinsic parameters (describing location, distance, merger time, and system orientation that are observer-dependent) and intrinsic parameters (physical parameters that are intrinsic to the binary). The tidal deformability (specific to systems involving NS) and the eccentricity also belong to the parameter space. However, these parameters are usually neglected because they can be computationally expensive compared to what we gain in efficiency by including them [START_REF] Singer | Rapid bayesian position reconstruction for gravitational-wave transients[END_REF]: many searches have shown that the loss in SNR by choosing not to include them can be neglected. In the case of eccentricity, isolated astrophysical binaries become circularized by the time their signal becomes measurable by ground-based detectors [START_REF] Cokelaer | Searching for gravitational-wave signals emitted by eccentric compact binaries using a non-eccentric template bank: implications for ground-based detectors[END_REF]. In conclusion, the most important parameters to search over remain the signal amplitude, the coalescence time and phase, the masses, and sometimes the spins [START_REF] Babak | A template bank to search for gravitational waves from inspiralling compact binaries: I. physical models[END_REF].

The GW strain in a particular detector depends on the detector response to the two polarizations of the gravitational waveform and is given by Eq. 1.50. However, since the antenna response functions of our current GW ground-based detectors (LIGO, Virgo, KAGRA) are very nearly constant in time over the duration of the short inspiral signal (see Eq. 1.52), the strain in a particular detector can be written as follow:

hptq " ´ˆGM c 2 D eff ˙ˆt 0 ´t 5GM{c 3 ˙´1{4 ˆcosr2ϕ 0 `2ϕpt ´t0 ; M, µqs (2.1)
with ϕ 0 the termination phase defined by: It is important to mention here that Eq. 2.1 is only valid for the inspiral with zero spins, neglecting the higher-order modes of GWs. Thus, this equation is inaccurate for a signal like GW150914 [START_REF]Observation of gravitational waves from a binary black hole merger[END_REF].

2ϕ 0 " 2ϕ c ´arctan ˆFF `2cospiq

. Finding a signal hidden in the data: Matched-filtering

Matched filtering principle

Several GW analysis pipelines use matched-filtering techniques, a method that finds GW signals in the detectors' data by correlating them with the expected waveforms. The comparison between the data and these waveforms is made by computing the times series of the signal to noise ratio (SNR or ρ), representing the cross-correlation between the whitened data and the whitened and normalized template. Each maximum (above a predetermined threshold, pipeline-dependent) is stored as a trigger and corresponds to a potential GW signal in the data. The FINDCHIRP algorithm [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF] is the implementation of matched filtering used by Py-CBC. The FINDCHIRP algorithm computes the matched-filter response for each template in the template bank, it then rejects instrumental artifacts that produce large responses of the matched filter (computing the χ 2 discriminant which is used to discriminate between signal candidates and noise artifacts, details provided in later in this section), and it finally selects candidates based on the matched filter and χ 2 outputs.

Looking at the detectors' outputs, two hypotheses have to be considered: the null hypothesis, either the GW detector strain is composed of Gaussian station-ary noise only (sptq " nptq with a power spectral density S n pf q (defined as ⟨ñpf qñ ˚pf 1 q⟩ " 1 2 S n p|f |qδpf ´f 1 q), or the GW hypothesis, there is a signal inside the detector noise (sptq " hptq `nptq). The Bayes theorem can answer which of the two hypotheses is favored by the data with an odds ratio: Explicitly writing the probability P ps|nq and P ps|h`nq and computing the log-likelihood maximized over the amplitude of the signal lead to the formula of the matched-filter, based on the following inner product: ⟨s, h⟩ " 4

ż 8 0 spf q h˚p f q S n pf q df (2.4)
which enables to define the output of the correlation of the data with a filter template h template ptq:

xpt 0 q " 4ℜ ż 8 0 spf qr ht emplate pf q t 0 "0 s S n pf q e 2πif t 0 df (2.5)
where h is the template waveform in the frequency domain. FINDCHIRP uses Fast Fourier Transform (FFT) correlation, so it is necessary to explicit the Fourier transform of the template waveform. A frequency-domain waveform version can be obtained assuming the stationary phase approximation [START_REF] Droz | Gravitational waves from inspiraling compact binaries: Validity of the stationaryphase approximation to the fourier transform[END_REF] (more details in Chapter 6). By definition,

hpf q " ż 8 ´8 dte 2iπf t hptq (2.6)
And together with Eq. 2.1 and the stationary phase approximation, this leads to (for f > 0, and for f < 0, hpf q " h˚p ´f q):

hpf q " ˆ1 Mpc D eff ˙A1 Mpc pM, µqf ´7{6 e ´iψpf ;M,µq (2.7)
where ψpf ; M, µq is the GW phase that depends on t 0 and ϕ 0 and A 1 Mpc is a normalised amplitude written as:

A 1 Mpc pM, µq " ´ˆ5 24π
˙1{2 ˆGM d {c 2 1 Mpc ˙ˆπGM d c 3 ˙´1{6 ˆM M d ˙5{6 (2.8)
D eff is chosen to be 1 Mpc in the FINDCHIRP algorithm, and A 1 Mpc pM, µq is a constant in frequency with dimensions of (time) ´1{6 and that only depends on the mass parameters of the source.

As mentioned above, these equations are only valid for a (2,2) inspiral waveform with no spins. A generic BBH template must be written hpf q " Apf ; ⃗ θqe iψpf ; ⃗ θq were A, ψ are functions that are not fully known analytically. Equation 2.5, together with Eq. 2.7 and Eq. 2.8, shows that the filtering depends on the intrinsic parameters of the binary, which are explored by constructing the template bank. In 2.7, some parameters describing the waveforms remain unknown: the amplitude (but for matched-filter templates, the amplitude can be normalized), the coalescence phase, and the masses. Regarding the phase ϕ 0 , it can be found by maximizing xpt 0 q over ϕ 0 .

Finally, the SNR is constructed by introducing a normalization constant for each template:

σ 2 m " 4 ż 8 0 | h1 Mpc,m pf q| 2 S n pf q df (2.9)
We also define the quantity z: zpt 0 q " x re pt 0 q `ix im pt 0 q " 4 ż 8 0 spf qr ht emplate pf qs t 0 "0,ϕ 0 "0 S n pf q e 2iπf t 0 df (2.10)

And finally, the matched filter output SNR time series is expressed as:

ρ 2 m ptq " |z m ptq| 2 σ 2 m (2.11)
for a given template h m , with m the waveform label in the template bank. As a summary, FINDCHIRP algorithm aims to construct ρ m ptq and to identify the values of the parameters t 0 , ϕ 0 , and m that maximize it.

A last quantity to introduce here is the optimal SNR that corresponds to the expected SNR if the waveform in the bank completely matches the waveform of the GW signal:

ρ opt " d 4 ż 8 0 | hpf q| 2 S n pf q df (2.12)
Estimating the PSD

The matched-filter techniques imply weighting the data by the inverse of the PSD, as seen in Eq. 2.9. The PSD can directly be estimated from the data thanks to Welch's method [START_REF] Welch | The use of fast fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms[END_REF] that computes the average power spectrum (S n pf q) of the data, also called mean average power spectrum. Sometimes the mean used by Welch's method can be biased by glitches contaminating the data thus, the median average power spectrum is preferred instead of the mean [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF].

χ 2 Consistency Test
To discriminate between possible astrophysical signal candidates and noise artifacts (with an instrumental or environmental origin) the FINDCHIRP algorithm calculates a consistency χ 2 test. This test determines if the power in the data in the time-frequency plane is well-distributed along the expected power of the matching template waveform. The method is described in [START_REF] Teukolsky | Numerical recipes[END_REF]. To construct the χ 2 test, the template is split into p frequency bins of equal power, and a matched filter ρ i is computed for each bin.

By projecting the data signal against two orthogonal phases of the template h(t), one can rewrite the SNR as:

ρ 2 ptq "
ps|h cos q 2 `ps|h sin q 2 ph cos |h cos q 2 (2.13)

And if we call ρ cos and ρ sin the two orthogonal phases of the matched filter, the χ 2 statistic can be written as:

χ 2 " p p ÿ i"1 « ˆρ2 cos p ´ρ2 cos,i ˙2 `ˆρ 2 sin p ´ρ2 sin,i ˙2ff (2.14)
The larger the value of χ 2 , the more it indicates that the noise transient hypothesis (compared to the signal hypothesis) is likely. An alternative version, for glitches with excess power in higher frequency than the best matching template would contain, is the High-Frequency Sine-Gaussian χ 2 Discriminator [START_REF] Alexander | Distinguishing short duration noise transients in LIGO data to improve the PyCBC search for gravitational waves from high mass binary black hole mergers[END_REF]. To discriminate this kind of glitches, we measure this excess power by placing sine-Gaussian tiles at the time of the trigger at frequencies where astrophysical signals are not expected. This sine-Gaussian χ 2 r,sg is then defined as the sum of the SNRs squared of each individual sine-Gaussian tile and finally used to reweight the triggers' SNR. This discriminator is then combined with the re-weighted SNR to generate a new single-detector test statistic. It results in a new re-weighted SNR [START_REF] Alexander | Distinguishing short duration noise transients in LIGO data to improve the PyCBC search for gravitational waves from high mass binary black hole mergers[END_REF].

Trigger selection

As mentioned in Sec. 2.1.2, the first step to generate candidate events or triggers and assign significance to them consists in imposing an SNR threshold. Then, the triggers exceeding the predetermined threshold (5.5 in PyCBC) must pass the χ 2 test. Moreover, we expect a true signal to produce a peak in the matchedfilter output around the correct termination time t 0 . However, loud signals may produce several peaks above the SNR threshold, which also stands for glitches. Thus, an algorithm clusters together triggers that lie in a time window chosen by the pipeline [START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF]. And finally, since the trigger is generated with a value of ρ and χ 2 , only the trigger with the largest value of ρ is kept in the window.

Finally, the significance of the candidate events is computed to compare them with the background. We will see in the following section (Sec. 2.1.3) how the PyCBC search pipeline evaluates it.

. PyCBC search pipeline

The PyCBC search pipeline search has been used since the first Advanced LIGO observing run and has proven itself by identifying 8 GW events among the 11 events that belong to GWTC-1 (O1 and O2 results) [START_REF] Abbott | GWTC-1: A gravitational-wave transient catalog of compact binary mergers observed by LIGO and virgo during the first and second observing runs[END_REF]. During the first half of O3, 39 new events were reported in the GWTC-2.1 catalog, and PyCBC detected 27 of them. The PyCBC search during the second half of O3 (GWTC-3 catalog) will be presented in this chapter.

PyCBC search is based on the matched-filtering method described in Sec. 2.1.2 using a bank of GW template waveforms (see 2.1.1). In the next section, we discuss some of the PyCBC configuration features to identify CBC signals. The main steps of matched-filtering in PyCBC described below are summarized in Fig. 2.1, starting from the detectors' output and ending with the release of the candidate events in PyCBC.

PyCBC template bank specifiticies

Template banks are discrete objects, so we cannot have an exact match between the waveforms of the template banks and the GW signals. With PyCBC, the maximum match between the signal a and any waveform of the bank h, called the fitting factor (FF), should be greater than 97% and is defined by the following formula:

FF :" max i mpa, hpθ i qq (2.15)
where θ i is the set of points in the parameter space covered by the template bank, and m is called the match between two CBC waveforms a and b and written as:

0 ď mpa, bq :" max tc,ϕc 4ℜ " ş 8 0 ãpf q b˚p f q Snpf q df ı }a} }b} ď 1 (2.16)
The match describes the overlap between a signal and a template or two templates, independently of their relative amplitudes, phases, and time translations. The PyCBC search generates a template bank covering the four-dimensional space of mass and aligned spin of the two components. The template bank is independent of the detector and remains the same throughout the search. Before template bank generation, a PSD averaged over time and detectors is measured. The template bank generated in PyCBC is composed of non-spinning and alignedspin waveforms. The eccentricity, the tidal/matter effects, and the higher-order modes are also neglected. The method chosen by PyCBC for creating such a template bank is described in [START_REF] Capano | Implementing a search for gravitational waves from binary black holes with nonprecessing spin[END_REF]. For O3, the waveforms in the PyCBC template bank have been simulated with two different approximants: For BNS and low-mass NSBH, TaylorF2 [START_REF] Messina | Quasi-5.5pn TaylorF2 approximant for compact binaries: Pointmass phasing and impact on the tidal polarizability inference[END_REF] a frequency domain post-Newtonian approximant (based on the Stationary Phase Approximation) for point masses with aligned spin in quasicircular orbits is used. For high mass NSBH and BBH waveforms, PyCBC uses SEOBNRv4 [START_REF] Bohé | Improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors[END_REF] model that uses Effective One Body approximation for spinning point masses in quasi-circular, non-precessing orbits. PyCBC template bank in O3 is represented in Fig. 2.2 in the m 1 ´m2 (top) and in the s 1z ´s2z parameter space. For low-mass templates (m i ă 2 M d ) the spin s iz is restricted to [-0.05,0.05] and for templates with m i ą 2 M d it can go up to ˘0.998. The total mass of the binary is limited to 500 M d and the mass ratio to 98. The PyCBC offline bank comprises " 10 5 templates and the maximal loss allowed by PyCBC in matched filter SNR of 3%. Moreover, the waveforms from the template bank are subject to a cut based on their duration: the bank does not include templates shorter than 0.15 s. This threshold has historically been placed because approximants used in previous runs (2015-2016) did not work with such duration. Since the cwB [START_REF] Drago | Coherent waveburst, a pipeline for unmodeled gravitational-wave data analysis[END_REF] search was already very good at detecting short transients, this was not a priority for PyCBC. Nowadays, this cut is still applied to prevent the search from being contaminated by short-duration glitches that match the time-frequency shape of the GW signal, making them challenging to distinguish [START_REF] Dal Canton | Designing a template bank to observe compact binary coalescences in advanced ligo's second observing run[END_REF]. However, this cut might be removed in O4 PyCBC offline analysis since the ranking statistic used in O4 may be sufficient for modeling the background variation as a function of the template.

Finally, the exact placement of the templates [START_REF] Roy | Effectual template banks for upcoming compact binary searches in advanced-LIGO and virgo data[END_REF] depends on the detector's noise PSD S n pf q. A single noise PSD averaged over time and detector is used to place the templates. The noise PSD is measured every 2048 seconds over the observation period, independently in each detector, using the median method mentioned in 2.1.2 and the harmonic mean is the method chosen by PyCBC to average the PSD over detectors (the two LIGO detectors [START_REF] Dal Canton | Designing a template bank to observe compact binary coalescences in advanced ligo's second observing run[END_REF]). This method is described in [START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF].

Non-Gaussian noise in detector data

Section 1.2.3 gives a qualitative overview of the noise source that pollutes the data in our current ground-based GW detectors. These noise sources are not always Gaussian and stationary and in this section we discuss the existence of non-Gaussian noise transients (called glitches) that often do not resemble the templates since they do not follow the CBC chirp track in the time-frequency plane. However, they can produce high SNR triggers that complicate GW signal detection. Figure 2.3 shows the time-frequency shape of a sample of glitches depending on their origin.

For well-modeled GW transient sources (like CBC), knowing the expected signal waveform significantly helps reject such glitches. One process to remove these non-Gaussian noise transients before the matched-filtering is called gating. The search needs to identify the time of glitches that gating will suppress. This can be done with a separate search for excess power in the input strain data [START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF]. Then, the data are set to zero thanks to a window function (A Tukey window in PyCBC) centered on the time of the glitch. An example is shown in Fig. 2.4. The gating is robust for short-duration glitches. Indeed, without gating, these loud noise transients would have affected the SNR time series and blind the search: a loud glitch on the top of a GW signal would have resulted in a bad χ 2 value, making signal detection impossible, reducing the sensitivity of the search. For longer-duration glitches (not as loud as the short ones, but still able to produce triggers), the gating becomes impossible since the duration of the data to be suppressed becomes too significant. In that case, the glitch will be removed thanks to the χ 2 test. Surviving as a GW candidate with PyCBC: Consistency, Coincidence, and Significance

As mentioned above, PyCBC uses matched-filtering and χ2 test to generate triggers. The search pipeline also uses the reduced χ 2 given by χ 2 r " χ 2 {p2p ´2q with p the number of frequency bins. For signals, χ 2 r should be around one, and to down-weight noise triggers, a reweighted SNR is computed [START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF][START_REF] Gareth | Extending the PyCBC search for gravitational waves from compact binary mergers to a global network[END_REF]:

ρ " " ρ{rp1 `pχ 2 r q 3 q{2s 1{6 if χ 2 r ą 1, ρ, if χ 2 r ď 1.
(2.17)

The pipeline removes all triggers with a reweighted SNR below a predetermined threshold.

Triggers surviving the consistency tests1 are then submitted to the coincidence test. PyCBC requires an exact match: the triggers are compared to those from other detectors, and coincident triggers should be seen with consistent parameters (arrival time and template parameters). The succeeding triggers are considered coincident events and are ranked according to the ranking statistic presented in [START_REF] Gareth | Extending the PyCBC search for gravitational waves from compact binary mergers to a global network[END_REF] (Equation 13).

The final step of the pipeline is to assign a statistical significance to the candidate by measuring their false alarm rate as a function of the ranking statistic. The false alarm rate quantifies how often we expect noise to produce a candidate with the same ranking statistic (or higher) as the candidate in question. This false-alarm rate value is measured using time shifts. This procedure is represented in Fig. 2.5: we time-shift the single detector triggers from one detector with respect to triggers from the second detector, and the coincidence test is re-computed to create a background sample that does not contain coincident GW signals. We repeat this procedure for many time slides to increase the statistical sample of background. PyCBC computes the background for "all possible time slides" in a chunk (as described in Sec. 2.2, PyCBC decomposed the observing run into segments called chunks covering " one week of data).

This false-alarm rate (FAR) is summarized by Eq. 2.18 where n b is the number of triggers in the background with a higher ranking statistic ρc than the candidate and T coinc is the artificial observing time computed with the time slides.

F " 1 `nb T coinc (2.18)

Injections and search sensitivity

To give a clear description of the work done in the PyCBC group (Chapter 3) it is necessary to provide some details about how PyCBC tests its performance in terms of sensitivity. It is beneficial when you want to improve your sensitivity to prepare the GW data analysis for future GW Observing Runs. The sensitivity of a given search is expressed in terms of the volume of space containing events to which the search would be sensitive, multiplied by observing time, V T, under the assumption of mergers uniformly distributed in space and time: VT=[sensitive distance] 3 ˆ[analysis time]. VT is a 4-volume metric that is used to decide whether a search is better than another. It is computed with Monte-Carlo integration methods [START_REF] Tiwari | Estimation of the sensitive volume for gravitational-wave source populations using weighted monte carlo integration[END_REF]. The VT calculation is useful for search diagnostic and optimization.

To explore the sensitivity of the search, we inject simulated signals into the data and try to recover them. These simulated signals are commonly called "injections". They are injected into the data to test the ability of the search to recover them. When analyzing the data (see next section), we check if these injections have been found by the search, and if they have been missed, we investigate the reasons to ensure the validity of the search. These investigations are described in the next section.

The sensitivity of the search is directly related to the number of found and missed injections. One can compare the VT of the current search configuration with the previous ones and produce figures similar to Fig. 2.6 that shows an increase in VT by a factor of 1.23 ˘0.10 with PyCBC for the three-detector analysis over the HL (Hanford-Livingston) analysis for both source types, constant over all IFAR values considered. The VT is also used to estimate the rate density R of CBC. During O3 the parameter space covered by the injections that have been used for the rate study is listed below:

• BBH: 2 M d ă m 1,2 ă 100 M d , |χ 1,2 | ă 0.998, z ď 1.9 • BNS: 1 M d ă m 1,2 ă 2.5 M d , |χ 1,2 | ă 0.4, z ď 0.15 • BNS: 1 M d ă m 1,2 ă 2.5 M d , |χ 1,2 | ă 0.4, z ď 0.15 • NSBH: 2.5 M d ă m 1 ă 60 M d , |χ 1 | ă 0.998; 1 M d ă m 2 ă 2.5 M d , |χ 2 | ă 0.4, z ď 0.25
If we call Λ the number of expected observed events in a time T, we can measure the rate density as R " Λ ⟨V T ⟩ (expected number of observed signals / the ability of the search to recover them). The computation is detailed in [START_REF]Upper limits on the rates of binary neutron star and neutron-star-black-hole mergers from advanced ligo's first observing run[END_REF] using PyCBC and GstLAL results from O1. They found a rate which is less than 12.600 Gpc ´3yr

´1

for BNS and less than 3.600 Gpc ´3yr ´1 for NSBH systems. Adding O2 and O3 results, these rates have been specified and are presented in Table 1.3 (Chapter 1, Sec. 1.1.5).

. PyCBC Offline analysis

When GW detectors are acquiring data, PyCBC contributes to the GW data analysis thanks to 2 different searches:

• The low-latency adaptation of the PyCBC algorithm, PyCBC Live [START_REF] Nitz | Rapid detection of gravitational waves from compact binary mergers with PyCBC Live[END_REF]. The same techniques as PyCBC are used in low latency, and the background is generated with time slides of the past five hours of data.

• An offline search which aims to more accurately assign the significance to the candidate events [START_REF] Gareth | Establishing significance of gravitational-wave signals from a single observatory in the pycbc offline search[END_REF], detect new sources not covered by the low-latency search (e.g. sub-solar mass search see 2.2.2), discover new events that could have been missed in low-latency (limited by the speed at which it must send alerts), and more generally prepare a catalog of events (e.g. GWTC-3 [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]) with a confident list of events which be used for further studies (parameter estimation, population study, tests of GR ...).

The beginning of my thesis coincided with the end of 3 rd GW Observing Run, giving me the opportunity to be involved in the PyCBC offline search. O3 data have been divided into data segments of " one week called chunks. Thus, my first work consisted in running the PyCBC analysis over one of these chunks (number 39). In the following sections, I will discuss the results of chunk 39, which perfectly describes the typical analysis done with PyCBC.

. Chunk 39

Chunk 39 is a segment of data from O3b, the second part of O3. It lasted for 7.664 days from 2020-03-09 03:01:21 to 2020-03-16 18:58:04 UTC. It is also helpful to introduce the time convention, in LIGO/Virgo collaboration, called the GPS time. All GW data are recorded with timestamps in the GPS time system (recording the number of seconds since the start of the GPS epoch at midnight on January 6 th 1980). Such GPS times are stored with nanosecond precision. Thus, another way to define the start and end time of chunk 39 is: GPS Interval [1267758099,1268420302). In PyCBC offline analysis, we divide the task into two parts: We first check the closed box results and then the open box results. The closed box is looking at injections (on real data) and checking that the analysis is reliable, and if the closed box looks sane then we allow ourselves to look at the data and "open the box". Both steps are described below.

Closed box analysis

The goal here is to 1) identify any instrumental issues that are degrading the sensitivity of the search. This noise should be visible in only one detector, so the displays of the single detector triggers (triggers observed in only one detector) should help answer question 1). By looking at these single detector triggers, the questions we should keep in mind are:

1. Do these single detector triggers look like GW signals? i.e. Does the track in the spectrograms/q-scan plots (Time-Frequency plots) look like a chirp?

2. Do we see glitches with the same morphology (i.e. size, shape in the q-scan) happening repeatedly?

3. If so, are they in the same detector? In multiple detectors?

4. Are there repeated glitches that occur in a short time interval? (i.e. same day, within a few hours)

2) PyCBC also injects simulated signals in the data to check the performance of the search, so we also want to know if we are missing any injections that should be seen. About question 2), to understand why some injections are missed, we need to look at the SNR of the injection in all available detectors. Indeed, one recurring reason an injection can be missed is that it is too quiet to dig out from the noise. But it happens that injections are missed for other reasons and looking at the parameters of the injections (mainly the mass ratio and the spins) for example, can tell us if the injection is missed because it is outside of the search parameter space. Indeed PyCBC template bank does not cover well extreme mass ratio (q > 98), anti-aligned spins, or also precession (when the x or/and y component of at least one of the two binary compact objects is non-zero), and the parameter space covered by the injections is a bit different from that of the template bank. The waveforms from the template bank are subject to a cut based on their duration as mentioned above. Thus, at high mass, for example, the boundaries of the template bank have an odd shape explaining why some injections do not fall into the template bank parameter space.

The ultimate goal of these investigations is to know if anything could be done to remove the worst triggers from the search and if we see several injections missed for similar reasons, how we could tune the search to see them.

Single detector triggers

As seen through this chapter, instrumental and environmental noise affects the data quality. The single detector triggers are triggers seen in only one detector. The two LIGO detectors are oriented such that they should detect the same GWs. That is why we expect to see coincident signals in the search. Thus, PyCBC does not search for single-detector events in O3 (for search for single detector events, see [START_REF] Nitz | A search for gravitational waves from binary mergers with a single observatory[END_REF][START_REF] Callister | Observing gravitational waves with a single detector[END_REF][START_REF] Sachdev | The gstlal search analysis methods for compact binary mergers in advanced ligo's second and advanced virgo's first observing runs[END_REF]) and consider that these single-detector triggers likely to correspond to noise affecting the detector. However, the detectors are not always observing during the runs, and sometimes only one interferometer takes data, which could result in single-detector events. That is also why we check the single detector triggers. Here we describe the types of glitches we encountered in chunk 39 and discuss single-detector triggers with a chirp shape.

In GW detectors, whenever the light is impinging on a surface, part of it can be scattered and may recombine with the main beam, adding some phase noise to it and spoiling the sensitivity of the interferometer. In O3, LIGO data quality was polluted by two separate populations of noise transient due to light scattering: the slow scattering ( long-duration arches in the time-frequency plane) and fast scattering (short-duration arches in the time-frequency plane). " 44% and 45% of all the noise transients with SNR ρ > 10 at LIGO Livingston and LIGO Hanford are caused by light scattering [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]. Chunk 39 has not been spared, and many of the loudest single detector triggers were due to scattered light. Figure 2.7 shows the morphology of the loudest single-detector trigger in L1 with a template duration > 4 seconds. The glitch visible in this plot is most likely due to scattered light. However, although we still observed such glitches at the end of O3b, their rate decreased after the reaction-chain tracking implementation [START_REF] Soni | Reducing scattered light in LIGO's third observing run[END_REF] in January 2020. Indeed, according to [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF], the presence of these slow scattering arches was strongly correlated with the relative motion between the end test mass chain and the reaction-mass chain of the optic suspension system, used to control the motion of the test masses.

In H1 data from chunk 39, we also observe many Blip glitches. These short (" 10 ms) noise transients can be problematic because they resemble the GW signature of massive BBH mergers. These glitches can appear over a large range of frequencies (hundreds of Hz). The Blip name has been given to all glitches with this particular shape, but presently we do not know their sources, and many different physical mechanisms could be responsible for these glitches. However, we know that blips always trigger the same region of parameter space in the PyCBC search [START_REF] Abbott | Effects of data quality vetoes on a search for compact binary coalescences in advanced LIGO's first observing run[END_REF][START_REF] Cabero | Blip glitches in advanced LIGO data[END_REF]. This region corresponds to short waveforms with total masses greater than 75 M d . An example from chunk 39 is given in Fig. 2.8.

In Virgo's case, scattered-light glitches associated with the activity of the sea mainly polluted O3b data. Again, chunk 39 has not been spared, but we can also observe many blip glitches or repeated blips as shown in Fig. 2.9. In chunk 39, most of the loudest V1 single-detector triggers have an extremely high inferred mass ratio. For instance, the first loudest has a primary mass of 193.49 M d and a secondary object with a mass of 2.38 M d leading to q " 81. The single-detector trigger presented in Fig. 2.9 has an estimated mass ratio of 52. Chunk 39 also contains loud single-detector triggers with very high spin components (around 1). The trigger from Fig. 2.9 has estimated spins of s 1z " s 2z « 1. The extreme mass ratio prior is not included in the search, and when we put these triggers in the context of astrophysics, it is very unlikely that they could have an astrophysical origin.

Finally, in all detectors, we found loud single-detector triggers that could have been interpreted as a GW signal due to their chirp-like shape in the time-frequency plane. Examples for Virgo are shown in Fig. 2.10. In the top panel, an excess of power with a chirp morphology is visible around 1268315867.516. The trigger from the spectrogram in the bottom panel could be a high-mass signal. Although they have a chirp-like morphology, they are visible only in one detector, which is insufficient to claim a confident detection for PyCBC. Looking at the results of other searches (GstLAL or MBTA), none of these chirp-like single-detector triggers seem to correspond to a confident detection in GWTC-3.

Missed injections

The top-left panel of Fig. 2.11 shows the distribution of the BBH-like injections that have been found by PyCBC (dots from light to dark yellow) and the BBH-like injections that have been missed by the search (red crosses) in the Chirp mass -Optimal SNR plane. The missed injections with low optimal SNR can be easily explained by the fact that they are too quiet in at least one detector. The missed injections that can worry us are the red crosses found in the same region as the injections with a small FAR (the yellow dots). Several reasons can be explored: As And finally, some of them are affected by glitches before the merger. As for BBH, some loud BNS and NSBH injections have been missed because of glitches before the merger or because they were quiet except for one detector. We also see some injections missed because of precession.

In conclusion, we can say that the PyCBC search seems particularly sensitive to a specific kind of noise: scattered light glitches. This is consistent with the O3 detector characterization analysis of LIGO and Virgo detectors [START_REF]Sensitivity and performance of the advanced ligo detectors in the third observing run[END_REF][START_REF] Acernese | Virgo detector characterization and data quality during the o3 run[END_REF]. Investigations to reduce scattered Light have been done and are presented in [START_REF] Soni | Reducing scattered light in LIGO's third observing run[END_REF]. Understanding why some loud injections have been missed (quiet in one detector,

Open box analysis

The box opening is the final step of the analysis. We look at the foreground candidates (no time shift, see 2.1.3) to check if: (1) we detect the GW signals previously found by the low-latency searches and compare with other searches; [START_REF] Acernese | Advanced virgo: a second-generation interferometric gravitational wave detector[END_REF] we detect new GW signals that have not been detected in low-latency and thus increase the number of detections.

We first check the cumulative number of triggers versus their IFAR in Fig. 2.12. A deviation of the foreground from the expected background (bash line) means we have detected a GW signal. The shades of grey represent the number of σ at which the foreground deviates. Here, one candidate (purple triangle) comes out of the background. The term "Hierarchically Removed Foreground" means that we removed the foreground trigger to calculate the FAR of the next candidate with the time-slides computation properly. The top trigger occurred on 2020-03-11 at 11:58:53 UTC and deviated at more than 4σ from the background.

PyCBC estimated its IFAR to be " 13 708 yr, which is significant enough to claim a confident detection. The SNR of this candidate was about 6.68, 11.87, and 10.23 in V1, H1, and L1, respectively. The spectrograms in Fig. 2.13 show that the GW signal is visible in the three detectors.

Other searches have also found this GW signal with a significance summarized The official name of this GW signal is GW200311_115853, and it has been published in the GWTC-3 catalog [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]. As mentioned in Chapter 1, the parameters of the source can be inferred with Bayesian analysis [START_REF] Christensen | Parameter estimation with gravitational waves[END_REF]. The parameters of GW200311_115853 and the inferred properties of the source are presented in Table 2.3.

Its probability of astrophysical origin, p astro [START_REF] Banagiri | A Unified p astro for Gravitational Waves: Consistently Combining Information from Multiple Search Pipelines[END_REF], which is > 0.99 with each search pipeline, indicates that GW200311_115853 is indeed an astrophysical signal. The p astro calculates the candidate astrophysical vs. terrestrial probability. The search provides five different values: the p astro , p terrestrial , p BBH , p BNS and p NSBH . The inferred masses of GW200311_115853 correspond to a typical BBH signal (masses around 30M d ), as confirmed by its p BBH « 1.

The sky localization of the source has also been inferred with LALinference [START_REF] Veitch | Parameter estimation for compact binaries with groundbased gravitational-wave observations using the LALInference software library[END_REF] and Bayestar [START_REF] Singer | Rapid bayesian position reconstruction for gravitational-wave transients[END_REF]. In Fig. 2.14, we can see the sky localization estimated with Bayestar. Because it is a three-detector detection, the event is exceptionally well-localized with a small uncertainty region. This very precise sky location made it possible to measure H 0 completely independently from EM counterparts with seven other selected GW signals [START_REF] Mukherjee | Cross-correlating dark sirens and galaxies: measurement of h 0 from gwtc-3 of ligo-virgo-kagra[END_REF]. They obtain H 0 " 68.2 `26.0 ´6.2 km{s{Mpc. Combining this measurement with measurement from GW170817 leads to a value of H 0 " 67.0 `6.3 ´3.8 km{s{Mpc.

. PyCBC Subsolar Mass Search

Subsolar Mass Black Holes

Below Chandrasekhar mass (" 1.4 M d ), it is generally assumed there is no astrophysical channel that can lead to the formation of an extremely compact object, more compact than a white dwarf [START_REF] Abbott | Search for subsolar-mass binaries in the first half of advanced LIGO's and advanced virgo's third observing run[END_REF]. The existence of such subsolar-mass (SSM) compact object would imply a new formation mechanism and a primordial origin is one scenario actively investigated. A primordial black hole (PBH) is a hypothetical type of BH formed in the early Universe from the collapse of overdense regions of space. Contrary to stellar-BH, PBHs could be produced with any mass. Thus, an observation of a SSM BH would confirm the existence of another formation scenario, such as the primordial origin of BH (PBH). The detection of such BH would have implications in cosmology: an alternative theory to Dark Matter (DM) composed of Weakly Interacting Massive Particles (WIMPs) [START_REF] Roszkowski | WIMP dark matter candidates and searches-current status and future prospects[END_REF] is the Massive Compact Halo Object (MACHO) [START_REF] Chapline | A new direction for dark matter research: intermediate-mass compact halo objects[END_REF] model suggesting that DM could be composed partially or totally of PBHs [START_REF] Carr | Primordial black holes as dark matter candidates[END_REF][START_REF] Clesse | The clustering of massive Primordial Black Holes as Dark Matter: measuring their mass distribution with Advanced LIGO[END_REF]. Thus, even a null observation of SSM objects during a GW observing run leads to a constraint on the fraction of DM composed by PBHs.

Chunk 8

A search for SSM binaries has been carried out in O3 [START_REF] Abbott | Search for subsolar-mass binaries in the first half of advanced LIGO's and advanced virgo's third observing run[END_REF][START_REF]Search for subsolar-mass black hole binaries in the second part of advanced ligo's and advanced virgo's third observing run[END_REF] using the three matched-filter-based pipelines: GstLAL, MBTA, and PyCBC. The template bank used in the SSM search is designed to recover binaries with primary mass m 1 P [0.2 -10] M d and secondary mass m2

P [0.2 -1.0] M d .
The mass ratio allowed is limited to 0.1 < q < 1.0. For binaries with one component with a mass m i ě 0.5 M d , the limit on its spin is set to 0.9. For m i ă 0.5 M d , it is set to 0.1. The bank is constructed such that the minimum match is 0.97, as for PyCBC general offline search and counts " 10 6 templates. The approximant used to generate the waveform is TaylorF2. In principle, this template bank is not limited to SSM BH, and we could imagine a detection of an SSM NS. However, the template bank does not include any information about tidal deformability (specific to NS mergers), and a study [START_REF] Bandopadhyay | Detectability of subsolar mass neutron stars through a template bank search[END_REF] provides evidence that the tidal effects should be taken into account if we want to avoid a significant loss in SNR. Moreover, as PyCBC does, to test the sensitivity of the SSM search and compute the merger rate of SSM BH (values given in the conclusion), simulated signals have been injected in the data.

The parameter space covered by the injections is described as follows:

•

Single detector triggers and missed injections

About the single-detector triggers, the loudest are mostly glitches (mainly scattered light) and Gaussian noise. No single-detector trigger is particularly interesting neither by its morphology in the time-frequency plane nor its SNR time series. The reasons why some injections have been missed are similar to chunk 39. Here, a lot of them of quiet in all but one detector. We can also see scattered light glitches on the top of the injections. In addition, here almost all missed injections have a high mass ratio (greater than 10) that is outside of the search space. The closed-box analysis indicated a satisfactory performance of the pipeline, allowing us to open the box and look at the foreground.

Foreground results

Figure 2.15 shows the foreground seems consistent with the expected background. We do not see any significant deviation, and the loudest candidate has an IFAR of " 10 ´1 yr, which is not particularly significant.

This trigger is quiet in Virgo, and its SNR is about 6.16 and 6.43 in H1 and L1, respectively. Its time-frequency morphology in all detectors is shown in Fig. 2.16. Together with its SNR time series, we can conclude here that this candidate is consistent with the background, and thus, it is not a plausible GW signal, and the other candidates are not particularly interesting either when looking at their FAR.

. Conclusion

This work gives a global overview of the PyCBC offline search and how to interpret the results from a CBC search. The GW signal GW200311_115853 found in chunk 39 now belongs to the GWTC-3 catalog as a confident BBH event [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]. Thus, GW200311_115853 is one of the 90 GW events detected since O1. During O3a, 44 new events were detected, and O3b brought 35 new GW signals (with a p astro ą 0.5). During O3, we also observed the first robust NSBH detection GW200115 [START_REF]Observation of gravitational waves from two neutron star-black hole coalescences[END_REF]. Moreover, one event has a secondary mass with a high probability of being in the lower mass gap [3 -5] M d . This interval separating the hypothetical maximum NS and minimum BH mass is considered a mass gap since we had never observed any GW signal coming from compact objects with such mass. Finally, no deviation for GR [START_REF]Tests of general relativity with gwtc-3[END_REF], and no exotic source has been found during the run.

The absence of SSM GW signal in chunk 8 and, more generally, during O3a led to a constrain on the fraction of dark matter in primordial black holes f PBH " Ω PBH {Ω DM À 6% that has been estimated in [START_REF] Abbott | Search for subsolar-mass binaries in the first half of advanced LIGO's and advanced virgo's third observing run[END_REF]. Together with the (null) results of O3b, the constraint on DM fraction of PBH has been updated and is shown in Fig. 2.17. For the first time, f PBH " 1 for early binaries [START_REF] Hütsi | Two populations of ligo-virgo black holes[END_REF] is excluded in the whole SSM range covered by the search [START_REF]Search for subsolar-mass black hole binaries in the second part of advanced ligo's and advanced virgo's third observing run[END_REF]. Moreover, with the absence of plausible candidates, the merger rate of SSM BH has been constrained to the range of [220 -24200] Gpc ´3yr ´1.

IMPROVEMENT OF THE SEARCH SEN-SITIVITY TO GRAVITATIONAL WAVES

As seen in Chapter 2, data from GW detectors are contaminated with glitches, complicating the detection of astrophysical signals. Understanding glitches is important to claim the astrophysical nature of a GW candidate. In this chapter, we describe a method proposed by Florent Robinet to improve the sensitivity of the CBC searches against glitches with the Omicron software.

. Omicron algorithm

The Omicron Software [START_REF] Robinet | Omicron: A tool to characterize transient noise in gravitational-wave detectors[END_REF] has been developed to understand and distinguish GW signals from glitches. These glitches often have a particular shape in the time-frequency plane that can be discriminated from an astrophysical signal (see, for example, Fig. 2.3 in Chapter 2). Omicron enables the visualization of transient detector noise and GW events with spectrograms (giving a representation of the time-frequency variation of the signal) from whitened data streams. Omicron computes a Q transform [START_REF] Brown | Calculation of a constant Q spectral transform[END_REF] to scan the data time series and search for excess power in the time-frequency plane. The Q-transform is a variant of the short Fourier transform and converts data series in the frequency domain. With Omicron, the time-frequency plane is tiled, and the size of a tile is frequency-dependent by definition of the Q-transform. Thus, each window duration σ t is linked to the frequency ϕ by σ t " Q{ ? 8πϕ (with Q a quality factor). Examples of tiled time-frequency planes are provided in Fig. 3.1. As expected, the tiles' length is larger for low frequency and smaller when the frequency reaches higher values. This is particularly useful in GW analysis: near the merger, the frequency increases rapidly compared to the beginning of the CBC track where the frequency is lower and varies slowly.

Each tile pτ, ϕ, Qq has a corresponding SNR (ρ) that is attributed according to Eq. 3.1. Here X wt pτ, ϕ, Qq averages the signal amplitude and phase in the time centered on time τ and frequency ϕ. ω is a Gaussian window that also plays a role in the shape of the tile, and x wt ptq is the whitened signal. For pure stationary noise, the expected value of the power spectral density does not depend on the frequency and is equal to 2. Finally, only tiles with a ρ ą 5 are kept. A visual representation of a glitch with Omicron is shown in the spectrogram of Fig. 3.2, also called Omicron scan.

. Motivations and method

. Omicron derived metric

The representation of the power in the detector given by Omicron can be used to identify and reject glitches triggering CBC templates in the PyCBC search. As described in Chapter 2, PyCBC generates triggers by comparing the data to template waveforms and finding the one that best matches the data. This template can be defined by a chirp/CBC track in the time-frequency plane (represented by a white dashed line in spectrograms throughout this chapter).

PyCBC performs a χ 2 test, introduced in Chapter 2, Eq. 2.1.2, to test the consistency of its GW triggers. However, the χ 2 only considers the power distributed along the CBC track. To better reject glitches, we want to consider the power that matches the track and the power distributed outside the CBC track since we expect the excess power triggered by a glitch not to be well-distributed along the track. This method would be a complement to the already-implemented χ 2 test. Since each PyCBC trigger has an associated template waveform that best matches the trigger, one can compare the power distribution given by Omicron (Omicron triggers) to the template given by PyCBC. It would provide a way to ensure the astrophysical origin of the PyCBC triggers and discriminate the glitches.

Throughout this chapter, we use the following convention: what we call "Omicron trigger" corresponds to the result of the clustering in the time dimension of many Omicron tiles in a small region (e.g., the glitch in Fig. 3.2).

We define an Omicron-derived metric (sometimes called "metric") which measures the deviation between the power distribution (Omicron triggers) in the timefrequency plane and the CBC track in PyCBC (what we call PyCBC trigger here).

For each PyCBC trigger:

1. We first find the corresponding Omicron triggers in which at least one tile overlaps it (i.e. the tile contains part of the CBC track).

2. Then, the time-distance d t between the tile center time (τ ) and the CBC track at the same frequency is computed for each tile composing the Omicron triggers.

3. This enables to measure the mean of the d t distribution (weighted by the SNR ρt of each tile):

M " ř Nt t"0 d t ˆρ 2 t ř Nt t"0 ρ2 t (3.3)
where the sums are over all the tiles belonging to the Omicron triggers intersecting the CBC track, and N t is the total number of tiles in the Omicron triggers.

4. Finally, the standard deviation of d t distribution σ is defined as the Omicron metric:

σ " d ř Nt t"0 d 2 t ˆρ 2 t ř Nt t"0 ρ2 t ´M 2 (3.4)
If the trigger is a GW coming from a CBC, we expect the tiles to be welldistributed along the CBC track, and the distribution of d t will peak around 0. This would lead to a small metric value (close to 0). On the contrary, if the PyCBC trigger is a glitch, it is likely that the power will not be well-distributed along the track, and we expect excess power outside of it. In this case, the metric would deviate significantly from 0.

A preliminary test done by Florent Robinet is presented in Fig. 3.3. The GW events and the single-detector (background) triggers seem to be well separated in the log 10 pDuration rssq ´log 10 pMetric rssq plane. This suggests that the method could be implemented in PyCBC to reject glitches. It also indicates that the metric seems to depend on the duration of the signal, and a good way to represent the separation between GW signals and glitches is to place ourselves in the metricduration plane. We investigate this dependence later in Sec. 3.3.1. Additional examples that comfort us in our expectations are provided in Fig. 3.4 and Fig. 3.5. The top panel of Fig. 3.4 shows the spectrogram of the GW signal found in chunk 39 (Chapter 2, Sec. 2.2.1), GW200311_115853. The tiles are distributed following the PyCBC track, and the d t distribution is centered around 0, as visible in the bottom panel of Fig. 3.4. On the contrary, for the glitch in Fig. 3.5, the tiles composing the noise transient are spread out in the timefrequency plane, and the mean of d t distribution « 13. Moreover, the glitch metric is four orders of magnitude higher than GW200311_115853.

We could think of a way to combine the information given by the Omicron mean M (Eq. 3.3) and the metric σ (Eq. 3.4) to discriminate glitches from the GW signals. However, as a first approach, we only use one of them and choose the metric, since the mean alone is not always a good discriminant. Indeed, depending on the nature of the glitch, the distribution of d t might be centered on 0. For instance, we do not expect a large deviation from 0 with a blip glitch due to its similarity with the chirp. We could expect such deviation for scattered light glitches (as visible in the top panel of Fig. 3.5).

Finally, choices in the implementation of the method have been made, which are presented in Fig. 3.6. As a summary:

1. Consider only the Omicron triggers in which at least one tile overlaps the track. 2. When one of the tiles of the corresponding Omicron triggers has a higher frequency than the maximum frequency reached by the PyCBC chirp, we extend the track to the infinite in the time-frequency plane.

3. On the contrary, when its frequency is lower, we discard the tile. Indeed, d t is not defined for such frequency.

4. Sometimes, there are no overlapping tiles. Omicron is an unmodeled search, less sensitive than PyCBC to CBC-like candidates. As a result, Omicron will miss some triggers. In these cases, we cannot compute the metric, and we fix σ " NaN.

. Configurations

Florent Robinet's preliminary study (Fig. 3.3) and the spectrograms produced in Fig. 3.4 and Fig. 3.5 suggest that the Omicron-derived metric can be used in PyCBC search to help discriminate the glitches from astrophysical signals. Depending on the metric value, we should lower or increase the significance of the PyCBC triggers. Several tests have been performed to investigate how the metric can be used:

1. In the first test, we use the metric as a threshold to veto PyCBC triggers: the trigger is rejected if its metric σ > 0.1 s. The threshold on PyCBC triggers is the first approach to see the metric usefulness. A threshold of σ "0.1 s has been chosen by looking at the distribution of the single-detector triggers (mainly composed of noise) over the metric-duration plane in Fig. 3.7. We want to remove as many noise triggers as possible. However, we do not want to accidentally discard a GW signal. A threshold of 0.1 s seems reasonable, according to Fig. 3.7, it discards 30% of the chunk 39 single-detector triggers that likely correspond to background noise triggers. However, this threshold is not optimized, and one could choose a more optimized value by exploring the improvement of the search sensitivity (VT) depending on the threshold value.

2. In the second step, we use a smoother method and reweight the SNR of the PyCBC triggers according to their duration and metric values. This method is justified and described later (Sec. 3.3.2).

In both methods, to deal with the huge number of PyCBC triggers, we only select the triggers with a reweighted SNR (see Eq. 2.17), sometimes called new SNR here, above 7.5.

We then explore the improvement of the PyCBC search sensitivity by reanalyzing one week of O3 data (chunk 39, presented in Chapter 2, Sec. 2.2.1) with the modified SNR and compare it to the baseline analysis by generating a VT plot like Fig. 2.6 in Chapter 2.

. Results

. Trigger selection based on their metric value

The PyCBC triggers have already been generated when analyzing chunk 39. PyCBC also provides the time-frequency evolution of the triggers, and this is what we're using here. The PyCBC triggers are unclustered: to one single glitch/GW/ injection corresponds to several unclustered PyCBC triggers. Here we work with two set of triggers: the H1, L1, V1 injections (simulated signals, described in Chapter 2, Sec. 2.1.3) and the H1, L1, and V1 single-detector triggers (mostly background). For each PyCBC trigger in each set:

• We select the corresponding Omicron triggers in which at least one tile overlaps the CBC track.

• We derive the Omicron metric of the PyCBC triggers. We discard the Py-CBC trigger when its metric is above 0.1; we keep it if it is below. In PyCBC, a simple way to discard a trigger consists in setting its SNR to 0.

• Finally, we run the end of the PyCBC offline analysis for chunk 39 again with the new set of triggers and produce a VT plot to compare the sensitivity before and after the selection. of the injections are below the threshold, some of them have metric values higher than 0.1 s. We explore the reason for such high injection metric values below and present a method to deal with it in the next section.

Exploring the improvement of the sensitivity with the selection

We reanalyze chunk 39 data after discarding the PyCBC triggers with a σ ą 0.1 s and explore the improvement of the sensitivity with this metric-based selection. The method used to compare the sensitivity of the search has been presented in Chapter 2, Sec. 2.1.3. We provide the resulting VT in Fig. 3.9. A ratio V T pmetricq V T pno´metricq above one means that the sensitivity has increased with the trigger selection based on metric value. Here we separate VT ratios by bins of total mass. It enables us to explore the improvement of the PyCBC search sensitivity to different types of CBC sources (NS or BH mergers).

From the VT plot, we can draw a first conclusion: The sensitivity before/after the cut is almost the same, but the ratio is systematically above 1. Thus, the metric threshold does not degrade the sensitivity. We can also notice large error bars due to the lack of injections in the [10 -20] M d . The error bars are also often overestimated. As mentioned in Chapter 2, VT is computed using Monte Carlo integral, and both VT(metric) and VT(no-metric) use the same set of injections to express VT, thus leading to correlations between the uncertainties. However, the correlation between the Monte Carlo errors is ignored, leading to large error bars. For heavy BBH injections, the improvement (around 10%) is better than the lowermass injections. The cumulative plots in Fig. 3.10 show that many BNS/NSBH injection triggers have been rejected, especially when they are loud (high SNR) and NSBH (bottom) injections in L1 versus their SNR with and without the metric application. When the metric is above 0.1 s, the trigger is discarded (by setting its SNR to 0). Here, we used the PyCBC unclustered triggers so one PyCBC injection can correspond to many unclustered triggers.

and have a long duration. An example is given in Fig. 3.11. Indeed, a loud and long signal induces many Omicron tiles associated with the PyCBC injection, thus, a large standard deviation of d t .

The method seems promising, but a way to improve it should be investigated. Setting the triggers' SNR to 0 is a strong requirement, and we usually prefer to lower the significance of the triggers instead of discarding them. Thus, we decide to reweight the SNR of the PyCBC triggers according to their metric values. As shown in Fig. 3.11, the distribution of the number of tiles, and thus the Omicron metric, seems to depend on the duration of the PyCBC trigger, and here we chose a cut that is independent of the duration of the trigger. Thus, we decide to reweight the SNR of the PyCBC triggers according to both their metric and duration value. The reweighting method and its results are presented in the following subsection.

. Reweighting of chunk 39 PyCBC triggers

Method

Instead of cutting on the metric value, we want to think in terms of probability. We want to attribute a weight to each PyCBC trigger depending on its metric and duration value, which quantifies if the trigger is more likely to be signal or noise. Thus, here we introduce the following notations:

• Ppd, m|Sq is the probability that a GW signal gives the duration d and metric m.

• Ppd, m|Bq is the probability that noise gives the duration d and metric m.

To reweight the SNR of the PyCBC triggers, we introduce the weights defined as:

ω " PDF injection PDF background " Ppd, m|Sq Ppd, m|Bq (3.5)
Where PDF injection and PDF background are probability density functions (PDF). The reweighted SNR of each PyCBC trigger is computed following the formula [START_REF] Nitz | Detecting binary compact-object mergers with gravitational waves: Understanding and improving the sensitivity of the PyCBC search[END_REF]:

SNR reweight " a SNR 2 `2 ˆlogpωq (3.6)
Fig. 3.8 suggests that:

• The region where the metric is above one and the duration lower than "5 s is more likely to be noise. Thus, we expect the weight to be close to 0 in this region.

• Above this duration and below this metric value, the GW triggers are more likely to be signals, so we expect high weights in this region.

Results

• The region where the blue crosses (injections) and the red points (single detector triggers) overlap does not give any information on the nature of the trigger. Here, we expect a weight close to 1 in this region.

We introduce here Kernel Density Estimation (KDE) [START_REF] Weglarczyk | Kernel density estimation and its application[END_REF] method from scikitlearn [START_REF]Scikit-learn: Machine learning in Python[END_REF]. A KDE estimates an unknown PDF with a kernel function. We choose a KDE to smooth the distribution of Ppd, m|Sq and Ppd, m|Bq and fix the unequal sparsity of the points in the logpDuration rssq ´logpMetric rssq plane (see Fig. 3.8). The chosen kernel is Gaussian. The KDE estimates the PDF injection and the PDF background , allowing us to attribute weights ω to each PyCBC trigger.

As for neural networks in machine learning, the KDE needs to "learn" where the signal-like region and the noise-like region should be in the logpDuration rssq ĺogpMetric rssq plane. Thus, the KDE is trained on a positive sample (injections) and a negative sample (single-detector triggers/background) before being applied to chunk 39 data and injections. We compute the metric of single-detector triggers and injections from other chunks to train the KDE. As a positive sample, we use the injections of chunk 38. The single detector triggers (more likely to be background triggers) from chunks 33-34-36-37-38 compose the negative sample. As for chunk 39, we only include triggers with a new SNR > 7.5. Finally, the trained KDE is evaluated on chunk 39 to get the weights ω of the single-detector triggers and injections. This reweighting is done for H1, L1, and V1 independently. The results with the data from the three detectors are similar, so only the reweighting of L1 single-detector triggers and injections is shown here.

The training is presented in Fig. 3.12. The distributions of the single-detector triggers and injections from the training sample are visible in the top and middle left panels. These distributions are used to compute the PDF background (top-right) and PDF injection (middle-right). The bottom plot presents the distribution of logpωq in the logpDuration rssq ´logpMetric rssq space. We can distinguish three regions:

• The signal region in red (logpωq > 0).

• The background region in blue (logpωq < 0).

• The white region separating the blue/red regions is the region where we do not have information on the nature of the trigger since, in the training sample, both background and signal contribute equally here.

Figure 3.13 shows that 1969 over 2247 single-detector triggers (background) have a weight that reduces their SNR. Most of the injections have a strongly positive weight that will increase their SNR. However, some injections (14165 over 226778 BBH, BNS, and NSBH injections) are in the noise-like region (blue). Thus, it lowers their SNR. We see in the next section how it will affect the sensitivity. 40] M d , the reweighting appears to degrade the sensitivity more than the cut on the triggers. This is consistent with Fig. 3.13, where a part of the short-duration injections is in the background region (blue). Moreover, the reweighting did not improve the sensitivity for low-mass injections. Further investigations have been made, and we found BNS and NSBH injections with a glitch overlapping the chirp and no tile associated with the injection itself. An example is provided in Fig. 3.15. The PyCBC trigger is related to a chunk 39 NSBH injection in L1. We can see that the search has not gated the glitch overlapping the signal. This leads to a large metric value and, thus, a lower reweighted SNR since the injection stands in the noise-like region (in blue) of Fig. 3.13. Before concluding on the method efficiency, we apply it to the data from another chunk (chunk 2) occurring at the beginning of O3, in which we know the glitch rate is higher. This was before the reaction-chain tracking implementation in LIGO to reduce scattered light noise [START_REF] Soni | Reducing scattered light in LIGO's third observing run[END_REF] (see Chapter 2, Sec. 2.2), so we expect to have much more glitches in this chunk, and our method was initially tested to discriminate these non-Gaussian noise transients from GW signals. Chunk 2 results are presented in the next section.

Comparison of the sensitivity

. Reweighting of chunk 2 PyCBC triggers

We use the same training sample to fit the KDE. Figure 3.16 presents the evaluation of the KDE on L1 chunk 2 data and injections. The results look similar to chunk 39 reweighting in Fig. 3.13. Figure 3.18 shows better results for high mass injections than chunk 39. We Finally, we observe no improvement in the low-mass region. In Sec. 3.4, we discuss the results of all investigations we presented and propose improvements we can implement in the method.

. Discussion and perspectives

The preliminary test in Fig. 3.3 used GW confident events and not injections as we did here. It probably plays a role in the difference between Fig. 3.3 and Fig. 3.8 and the fact that the results are better in the case of GW events (compared to injections).

Our investigations on chunk 39 and chunk 2 triggers show that the reweighting is quite powerful for high-mass signals. This could be useful for CBC searches since the time-frequency shape of short noise transients like blip glitches resemble the GW imprint of CBC with large total mass [START_REF] Cabero | Blip glitches in advanced LIGO data[END_REF]. On the contrary, for low-mass signals, a glitch overlapping the long-duration chirp is easier to detect and gate. We found that the reweighting degrades the sensitivity between [START_REF] Pierre | The pierre auger cosmic ray observatory[END_REF][START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF] M d . We explore the reasons in the next section. Our investigations also suggest that the To solve this, we think of computing the metric considering only the tiles in a ˘1 s window centered on the merger time of the PyCBC trigger. This will remove potential glitches overlapping the long-duration injections far from the merger. We also consider computing the Euclidean distance instead of the time distance between the tiles and the CBC track. Finally, we could investigate using both the Omicron metric and the Omicron mean (i.e. the mean of d t distribution) to reject glitches. Indeed, for some glitches, the mean of d t will deviate from zero.

For others (like Blip), it will be centered on zero, but the metric value (standard deviation of d t ) should be much larger. Finally, we had to define a bandwidth in the KDE generation. Choosing the proper bandwidth is crucial because a small bandwidth leads to undersmoothing, and the PDF plot will look like a combination of individual peaks. However, a huge bandwidth leads to oversmoothing, and the PDF plot will look like an unimodal distribution and hide all non-unimodal distribution properties [START_REF] Odland | tommyod/kdepy: Kernel density estimation in python[END_REF]. Here we have chosen the bandwidth testing different configurations, which is probably responsible for the small and faint white clouds in the middle of the blue and red regions in Fig. 3.12. As an improvement, we could use bandwidth selectors like Sheather and Jones method [START_REF] Botev | Kernel density estimation via diffusion[END_REF] or a KDE with adaptive bandwidths [START_REF] Falxa | Adaptive kernel density estimation proposal in gravitational wave data analysis[END_REF].

. Investigations of the noise-like region at low metric value and template duration «3 s

The bottom panel of Fig 3 .12 shows a noise-like region at low metric value and template duration «3 s. We reproduced the bottom panel Fig 3 .12 and circled the odd region in Fig. 3.19. An excess of background (single-detector triggers) stands in a region where we expect signals/injections. We investigate the relation between these single-detector triggers that lead to unexpected behavior of the reweighting in this region and the destruction of the sensitivity between [START_REF] Pierre | The pierre auger cosmic ray observatory[END_REF][START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF] M d (see Fig. The single-detector triggers in the background training sample standing in this noise-like region belong to chunk 34. The cluster L1 single-detector trigger that produced many PyCBC unclustered triggers around, leading to the circled noise-like region in Fig. 3.19 is presented in Fig. 3.20. This trigger is the singledetector event GW200202_154313 from GWTC-3 [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]. Since PyCBC did not analyze single-detector events in O3 (see Chapter 2, Sec. 2.2), this event caused an excess in the background. The CBC track of GW200202_154313 and the corresponding Omicron tiles are visible in the bottom panel of Fig. 3.20. There is only one tile in the Omicron cluster associated with the CBC track, which completely overlaps the track explaining the small value of GW200202_154313 metric.

To avoid the contamination of the background from such events, PyCBC offline analysis has been run twice on chunk 34: the first with all the triggers and then without the single-detector triggers associated with catalog events [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]. Here, we used the first version without such events suppressed, which explains the contamination of the background and, thus, the noise-like region located in the signal-like region. We remove the data around GW200202_154313 and perform the reweighting again to ensure the suppression of the circled region in Fig. In Chapter 2 and Chapter 3, we discussed the CBC searches, their limitations in sensitivity, and how to improve them to increase the number of detections and be sure of their astrophysical origin. Here we present the GRB search focusing on the Fermi/GBM instrument and the GBM Targeted Search. Then, I emphasize my main Ph.D. project and describe the analysis we developed to search for GW/GRB associations in LIGO/Virgo and Fermi/GBM data.

. GBM Targeted Search

Section 1.3 from Chapter 1 gives an overview of GRB physics and introduces the different instruments used to detect GRBs. Here, we will focus on the data observed with Fermi/GBM, which is onboard the Fermi Gamma-ray Space Telescope. Fermi/GBM is currently the most prolific GRB detector with " 240 GRB per year, and among them " 40 -45 sGRBs [START_REF] Von Kienlin | The fourth fermi-gbm gamma-ray burst catalog: A decade of data[END_REF]. Fermi/GBM can also localize these GRBs with an accuracy of a few degrees [START_REF] Connaughton | Localization of gamma-ray bursts using the fermi gamma-ray burst monitor[END_REF]. The sensitivity of Fermi/GBM to weak sGRBs was initially increased thanks to two offline searches: (1) the GBM Untargeted Search, a ground-based blind search that continuously collects timetagged event (TTE) data, and (2) the GBM Targeted Search [START_REF] Blackburn | High-energy electromagnetic offline follow-up of ligo-virgo gravitational-wave binary coalescence candidate events[END_REF][START_REF] Goldstein | Updates to the fermi gbm targeted sub-threshold search in preparation for the third observing run of ligo/virgo[END_REF]. The Targeted Search produces triggers by coherently searching all NaI detectors for an excess of photon counts compatible with sGRBs over a variety of overlapping time windows, covering durations from 64 ms to 8.192 s. A log-likelihood ratio (LLR) is computed for each time window, allowing for the generation of GBM triggers labeled with a duration, a mission elapsed time (MET), and an LLR. The LLR calculation compares the photon rates observed in the GBM detectors to those predicted when assuming particular spectral shapes for the GRBs. The GBM triggers are also generated with a spectral hardness value. The Targeted Search uses three spectral models: a 'soft' Band function (Band function detailed in 1.3.2), a 'normal' Band function, and a 'hard' exponentially-cutoff power law. The parameters of the models were chosen to describe the spectral diversity of GRBs in the GBM energy band from the lGRBs that are spectrally softer than the spectrally harder sGRBs. Finally, the GBM Targeted Search also produces filtered results thanks to an algorithm that clusters the triggers by only keeping the trigger in regions of the duration-time plane having the highest LLR if LLR ě 5. This threshold is justified in [START_REF] Stachie | Search for advanced ligo single interferometer compact binary coalescence signals in coincidence with gamma-ray events in fermi-gbm[END_REF][START_REF] Goldstein | Updates to the fermi-gbm short grb targeted offline search in preparation for ligo's second observing run[END_REF]. Figure 4.1 shows the waterfall shape of the GBM trigger associated with GRB 170817A. The x-axis represents the MET, and the y-axis shows the different duration windows. The content of each rectangle is the LLR value. The top panel shows the unfiltered result, and we can see that the LLR is computed for each rectangle. The bottom panel presents the results of the clustering algorithm. This algorithm sometimes faces issues leading to several clustered triggers in a short time-duration window, as demonstrated in the bottom panel.

. A deep joint analysis: Context and Method

The work described in this part is extracted from two different papers: a method paper [START_REF] Pillas | Deep multimessenger search for compact binary mergers in ligo, virgo and fermi/gbm data from[END_REF] and a collaboration paper "Deep search for coincident gravitational waves and gamma-ray bursts using Advanced LIGO, Advanced Virgo and Fermi/GBM during the third gravitational-wave Observing Run" which is about to be finalized.

. Motivations

Section 1.4 (Chapter 1) explores the different implications a joint GW-GRB detection can have in astrophysics, GRB physics, and cosmology. To answer these fundamental questions about sources of GWs and GRBs, a significantly larger sample of joint GW/GRB observations is needed. Since the first observing run, several independent approaches have been tried for searching for joint GW/GRB associations, such as PyGRB [START_REF] Abbott | Search for gravitational waves associated with gamma-ray bursts during the first advanced LIGO observing run and implications for the origin of GRB 150906b[END_REF] and X-pipeline [START_REF] Sutton | X-pipeline: An analysis package for autonomous gravitational-wave burst searches[END_REF][START_REF] Abbott | Search for gravitational waves associated with gamma-ray bursts during the first advanced LIGO observing run and implications for the origin of GRB 150906b[END_REF] that assume that there is a GRB detection and perform a deep search for a nearby GW signal (or more generally GW transients in the case of X-pipeline). On the low-latency time scale, RAVEN [START_REF] Abbott | Search for gravitational waves associated with gamma-ray bursts during the first advanced LIGO observing run and implications for the origin of GRB 150906b[END_REF][START_REF] Piotrzkowski | Searching for Sub-threshold Gravitational Wave Candidates with RAVEN[END_REF] assumes a GW and an electromagnetic (EM) detection and checks for their compatibility in time and sky. By contrast, in the analysis presented in [START_REF] Fletcher | A Joint Fermi-GBM and Swift-BAT Analysis of Gravitational-Wave Events from the GWTC-3 Catalog[END_REF], they start from the GW events from the GWTC-3 catalog, and they look for potential associations with Fermi/GBM and Swift-BAT data. Other analyses have been performed for specific events, such as Lindy Blackburn's method to search for GW150914 counterpart [START_REF] Blackburn | HIGH-ENERGY ELECTROMAG-NETIC OFFLINE FOLLOW-UP OF LIGO-VIRGO GRAVITATIONAL-WAVE BINARY COALESCENCE CANDIDATE EVENTS[END_REF]. The LIGO/Virgo O1 -Fermi/GBM [START_REF] Burns | A Fermi Gamma-ray Burst Monitor Search for Electromagnetic Signals Coincident with Gravitational-Wave Candidates in Advanced LIGO's First Observing Run[END_REF] analysis also computes a False Alarm Probability (FAP) assuming a GW detection and checking for a nearby GBM signal. Finally, during O2, a joint analysis calculates a p-value of the GW170817 and GRB 170817A association assuming a GW detection and a GBM detection and checking for compatibility in time and sky localization.

However, many of these searches have statistical or computational limitations that prevent their application to a large number of weak candidate events. For example, both X-pipeline and PyGRB require hours to days (running on a CPU cluster) to analyze the GW data around the time of a single GRB and start from the assumption that the GRB is a robust detection in the first place. With RAVEN the joint FAR of the foreground association is proportional to the single FAR in each channel following Eq. 4.1:

F AR c " F AR gw R grb ∆t I Ω (4.1)
where R grb is the rate of the unique GRB candidates given by all participating EM signal detectors, ∆t and I Ω are related to the time and sky overlap between the GW candidate and the GRB detection. This can lead to statistical limitations:

• In the case of accidental coincidences between GRBs and BBH signals: the numerator would be really small, and the accidental association should be suppressed by the denominator (I Ω ) that should be close to 0. However, with our current ground-based detectors the skymaps are quite large, so the sky overlap term I Ω between our current GW detectors and Fermi/GBM is approximately 1. Hence Eq. 4.1 cannot distinguish between the "two unrelated signals" hypothesis (called H SS below) and the "two signals from a common source" hypothesis (called H C below).

• In cases of sub-threshold events for which F AR gw would be quite high. However, recent versions of RAVEN can also deal with not particularly high confidence events [245] by changing its calculation of the joint FAR into:

F AR c " Z I Ω ˆ1 `lnp Z max Z q ˙(4.2)
where Z " F AR gw R grb ∆t and Z max are calculated using the maximum GW and GRB FAR thresholds. Motivated by the possibility that sGRBs come from CBCs and by the joint observation of GW170817 [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF] and GRB 170817A [START_REF] Goldstein | An ordinary short gamma-ray burst with extraordinary implications: Fermi-GBM detection of GRB 170817a[END_REF][START_REF] Savchenko | Integral detection of the first prompt gamma-ray signal coincident with the gravitational-wave event gw170817[END_REF] coming from a common BNS source, we develop a method to search for coincidences between transient events in the Fermi/GBM data and LIGO/Virgo CBC triggers, in order to increase the number of joint GW/GRB detections. This search is a deep search in the sense that it does not consider confident events only. Instead, in our approach we use the full list of Fermi/GBM triggers, and GW triggers from one specific observing run. The goal is to find the pairs of Fermi/GBM and GW triggers that could have a common origin, rank the pair thanks to a ranking statistic, and assign a FAR to them.

We first present how we generate the GW and gamma-ray candidates.

. GW and GBM trigger generation

The GW triggers used in the analysis are generated with matched-filtering pipelines described in Chapter 2. In addition, for each GW trigger, the posterior distribution for the sky location of the source is computed under the assumption that the trigger is of astrophysical origin. We use Bayestar [START_REF] Singer | Rapid bayesian position reconstruction for gravitational-wave transients[END_REF] due to its simplicity and low computational cost through the pycbc_make_skymap tool.

This analysis has been performed twice:

• In Sec. 4.3, we applied our deep analysis on PyCBC triggers coming from O2 to check the validity of our method against GW170817 -GRB 170817A.

• In Sec. 4.4, we use it on the GWTC-3 [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF] released (with a FAR ă 2/day) triggers from three pipelines: GstLAL, MBTA, and PyCBC. Here we handle the triggers from each pipeline independently rather than combining the results, which is easier to process and allows us to triple-check the joint analysis results.

Both for O2 and O3 analysis, on the GRB side, we use the result of the GBM targeted search for which the trigger generation is described in Sec. 4.1. The targeted search also gives us the sky localization of the GBM triggers with a sky grid resolution of 5 degrees. The resolution was initially set to 1 degree however, this value has been updated when the Targeted search extended the search to sub-threshold candidates [START_REF] Goldstein | Updates to the fermi gbm targeted sub-threshold search in preparation for the third observing run of ligo/virgo[END_REF]. The search produces maps of the posterior probability distribution P pΩ|D γ q, which quantifies the probability that the GBM trigger comes from a specific location Ω given the data D γ . We use the clustered GBM Targeted Search results in both analyses. It is justified by our desire to remove the correlation between the triggers and the expensive cost of dealing with the unfiltered triggers.

In 4.2.3, we describe the derivation of this ranking statistic and the different configurations we tested to compute the terms of this statistic and rank the associations.

. Ranking statistic

Addressing joint detections, there are many statistics to rank the potential associations. We first consider two simple ranking statistics:

• A Naive time statistic: a naive product of GW and GBM likelihoods, including the time overlap, and summarized by the following equation:

lnpΛq " ρ2 g 2 `LLR `lnpI ∆t q (4.3)
• A Naive time and sky statistic: a naive product of GW and GBM likelihoods, including the time and skymap overlaps and summarized by:

lnpΛq " ρ2 g 2 `LLR `lnpI ∆t q `lnpI Ω q (4.4)
Here ρg is the network reweighted SNR [START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF] described by Eq 4.5.

ρg "

d ÿ d ρ2 d (4.5)
where d represents the available GW detectors. I ∆t and I Ω are Bayes factors that quantify the overlap of the posterior distributions for the arrival times (time offset) and sky locations (skymap overlap) inferred separately from the GW and GBM data. The term ρ2 g 2 represents the log-likelihood ratio Ppdata|noise,signalq Ppdata|noiseq on the GW side, following the computation from [START_REF] Nitz | Detecting binary compact-object mergers with gravitational waves: Understanding and improving the sensitivity of the PyCBC search[END_REF]. These ranking statistics are really simple to implement, and we present the results using them in Sec. 4.3.2. We also justify our choice not to use them in this work and to compute the Bayesian ranking statistic described in the following paragraphs:

When searching for signals in GW and GBM data, the two simple possibilities of noise vs noise+signal become a complicated multi-messenger rainbow of mutually exclusive hypotheses:

1. (H N N ) hypothesis: Both GW and GBM data contain their respective noise only.

(H N S

) hypothesis: GW data contains noise and signal, and GBM contains only noise.

(H SN

) hypothesis: GW data contains noise, and GBM contains noise and signal.

4. (H SS ) hypothesis: Both GW and GBM contain noise and signal, but the signals are unrelated.

(H C

) hypothesis: Both GW and GBM contain noise and signal, and the signals come from the same source.

Here by "noise" in the GW data, we also consider the possibility of Gaussian noise with a glitch on top. To make a frequentist multi-messenger detection in the usual way, we combine cases 1-4 into a null hypothesis and then test hypothesis 5 vs null. As done in many astrophysical searches [START_REF] Piotrzkowski | A joint ranking statistic for multi-messenger astronomical searches with gravitational waves[END_REF], we then define a joint ranking statistic from the GW and GBM data, calculate the corresponding background distribution, and only then produce a p-value or FAR. Here hypotheses 1 to 4 in the list above can be defined as situations representing the "background". When ranking the different GW-GBM candidate combinations, we make the following considerations:

• A larger GW candidate significance corresponds to a more likely candidate in the GW channel.

• A larger GBM candidate significance corresponds to a more likely candidate in the GBM channel.

• The closer in time the GBM candidate is to the GW merger time, the more likely the association is.

• The closer the sky localizations are, the more confident the association is.

Going from the list of different hypotheses, and by a Bayesian derivation, we arrive at the association ranking statistic calculated in [START_REF] Stachie | Search for advanced ligo single interferometer compact binary coalescence signals in coincidence with gamma-ray events in fermi-gbm[END_REF] and derived from [START_REF] Ashton | Coincident detection significance in multimessenger astronomy[END_REF] that can be summarized with the following formula :

Λ " P pD g , D γ |H C q P pD g , D γ |H N N Ž H SN Ž H N S Ž H SS q (4.6)
where D g and D γ are the data sets from the GW and gamma-ray channel, (H i ) are the different hypotheses listed above.

Finally, if we assume complete ignorance about prior probabilities, this expression can be simplified as:

Λ " I ∆t I Ω 1 `Qg `Qγ `Qg Q γ (4.7)
where:

Q g " Q g pD g q " P pD g |noiseq P pD g |signalq (4.8)
and

Q γ " Q γ pD γ q " P pD γ |noiseq P pD γ |signalq (4.9)
are the single-instrument Bayes factors comparing the noise-only and noise-plussignal hypotheses in GW and GBM data, respectively. For the GW channel, the single-instrument means in fact all the available detectors. I ∆t and I Ω are Bayes factors that quantify the overlap of the posterior distributions for the arrival times (time offset) and sky locations (skymap overlap) inferred separately from the GW and GBM data. We discuss the calculation of each ranking statistic term from Sec. 4.2.3 to Sec. 4.2.3. Equation 4.7 has intuitive limits:

• If both signals are very marginal, deep into their noise distribution, then

Q g Q γ " Q g , Q γ "
1 and Λ « P pDg|H S q P pDg|H N q ˆPpDγ|H S q P pDγ |H N q ˆI∆t I Ω ! I ∆t I Ω . The association is suppressed by both single-instrument Bayes factors, and the parameter overlap must be exceptional for the association to be significant.

• If one signal is very significant (say the GW), then Q g ! 1 and Λ only depend on the significance in the other instrument (and the parameter overlap).

• If we have very significant signals in both GW and GBM data, then:

Q g Q γ ! Q g , Q γ ! 1
and Λ « I ∆t I Ω : the single-instrument significances become irrelevant, and the only thing that can prove the association between the triggers is the overlap in their inferred parameters.

GW Bayes Factor Q g

In addition, Bayestar also provides two Bayes Factor:

• BSN: Bayes Factor Signal versus Noise compares the probability for a trigger to be signal-like and noise-like. This Bayes Factor is qualitatively similar to an SNR and defined as:

P pD g |Signal `Gaussian noiseq P pD g |Gaussian noiseq (4.10)
• BCI: Bayes Factor Coherent versus Incoherent, compares the probability to be a coherent signal versus an incoherent signal. It is defined as

P pD g |C `Gaussian noiseq P pD g |I `Gaussian noiseq (4.11)
where C and I are respectively the coherent and incoherent signal.

Intuitively, we expect GW astrophysical signals to have both high log 10 pBSNq and log 10 pBCIq, Gaussian noise to have both small log 10 pBSNq and log 10 pBCIq and glitches to have a high log 10 pBSNq and a small log 10 pBCIq. Two configurations are tested to compute the GW Bayes Factor Q g . The first one is used in the analysis, and the second one has been investigated in Sec. 4.3.3.

1. We use the natural logarithm of the BCI, which is the result of a model comparison between a coherent GW signal in the entire network versus a signal that is not coherent (the most likely occurrence being a single-detector signal).

2. We compute a KDE-based GW Bayes Factor in the log 10 pBCIq ´log 10 pBSNq plane. We train the KDE on a positive sample composed of GW injections and a background sample made of GW triggers with a FAR above 2 per day; this is detailed in Sec. 4.3.3.

The BCI is robust to glitches contrary to the BSN, which is why we only extract the BCI from the skymaps in the main method here and we only explore a KDE-based method using both the BCI and the BSN in Appendix 4.3.3. Indeed a KDE requires a training sample, so GW injections skymaps should be generated in addition to skymaps for noise and glitches, which is much more complicated than considering only the BCI.

GBM Bayes Factor Q γ

Calculating Q γ accurately would, in principle, involve a complete parametric model for the photon flux of a sGRB, for the detailed response of GBM to that photon flux, and for the GBM background. This would then allow us to write a likelihood function and marginalize it over the relevant parameter space to compute the Bayes factor. Although attempts have been made to solve parts of this modeling task (see e.g. [START_REF] Hayashi | General-relativistic neutrino-radiation magnetohydrodynamic simulation of seconds-long black hole-neutron star mergers[END_REF]), this is clearly a major challenge at present. Instead, here we use an approximate phenomenological model based on a sample of sGRBs observed by GBM and confirmed by other γ-ray observatories and a sample of triggers unlikely to be associated with sGRBs.

Specifically, we approximate Q γ following a 2D KDE [START_REF] Weglarczyk | Kernel density estimation and its application[END_REF] in the log(Duration)log(LLR) space. The KDE is fitted on a sample of positive triggers: a sample of 61 GBM-triggered targeted search triggers within 3s of confirmed events (i.e. identified with the GBM untargeted search that has confirmation in other instruments like INTEGRAL SPI-ACS [START_REF] Rau | The 1st integral spi-acs gamma-ray burst catalogue[END_REF] or Swift [START_REF]The Swift Gamma-Ray Burst Mission[END_REF]) with T 90 ă 2s and above 90% probability of being a sGRB from O2, from O3 and between observing runs, and on a negative sample: conservatively, every non-positive trigger (including detector noise) is considered negative. The negative sample counts 1897956 triggers. Then the KDE is evaluated on the GBM triggers, and the ratio of the probability functions described in Eq 4.9 is computed. The resulting Q γ distribution is shown in the top panel of Fig. 4.2. We can observe that the signal-like region is associated with the highest LLR values. Moreover, at fixed LLR, triggers with a shorter duration have a smaller (i.e. signal-like) Q γ than longer duration triggers.

The right panel of the same figure compares the present approximation with an earlier study [START_REF] Stachie | Search for advanced ligo single interferometer compact binary coalescence signals in coincidence with gamma-ray events in fermi-gbm[END_REF], which used a simpler 1D KDE on the LLR only, coupled with some assumptions to extrapolate the distributions beyond the range of the available training set. The 2D KDE method described here produces a similar behavior, but the rapid oscillations in the Bayes Factor vs LLR curve, artifacts of the previous method, have disappeared. We can also see that most of the curves with the 2D KDE Bayes Factor are above the 1D KDE curve, meaning that with our 2D KDE-based Bayes factor, it is harder for a candidate to be signal-like.

Time offset term I ∆t

The goal of the time offset term I ∆t is to quantify how probable it is for a pair formed by a GW trigger and a GBM trigger to be separated by a certain amount of time ∆t = t GBMt GW , where t GW is the merger time of the GW candidate estimated by the GW searches, and t GBM is the central time of the GBM trigger with the maximum LLR.

Here we define the time term as:

I ∆t " " 1 ´|∆t| 30 if |∆t| ă 30s, 0 otherwise. (4.12)
It is similar to what has been used in [START_REF] Stachie | Search for advanced ligo single interferometer compact binary coalescence signals in coincidence with gamma-ray events in fermi-gbm[END_REF] under the same assumptions. The time delay between GW170817 -GRB 170817A was about 1.7 s, so we make the prior assumption that the closest in time the two messengers are, the most likely they are to come from the same source. Our prior extends to much larger delays than 1.7 s, and than the current GRB LVK searches [START_REF] Abbott | Search for gravitational waves associated with gamma-ray bursts during the first advanced LIGO observing run and implications for the origin of GRB 150906b[END_REF][START_REF] Sutton | X-pipeline: An analysis package for autonomous gravitational-wave burst searches[END_REF], which, although unlikely according to some prompt emission models, is large enough to allow us to detect so-far unconfirmed phenomena, like sGRB precursors [START_REF] Tsang | Resonant Shattering of Neutron Star Crusts[END_REF][START_REF] Stachie | Searches for Modulated γ-Ray Precursors to Compact Binary Mergers in Fermi-GBM Data[END_REF] However, for future analysis, we will need a more realistic and, thus, stricter time offset prior. Indeed, with the future generation of GW detectors, much more GW data are expected. In order to avoid dealing with an extremely large amount of GW triggers, a selection will be needed, and a stricter time offset prior can help us.

Sky overlap term I Ω

The general form of the Bayes factor of the sky proximity is given in [START_REF] Ashton | Coincident detection significance in multimessenger astronomy[END_REF] as:

I Ω " ż P pΩ|D g qP pΩ|D γ q P pΩq dΩ (4.13)
As shown in Fig. 4.3, from [START_REF] Ashton | Coincident detection significance in multimessenger astronomy[END_REF], the sky overlap Bayes factor I Ω is supposed to be high (strongly positive) when the GW trigger and GBM trigger are overlapping and both well localized (small uncertainty region). It will be close to 0 when the Chapter 4. Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 134

two triggers are localized far from each other. The sky overlap is I Ω « 1 even if the two triggers are overlapping, but the skymaps are uninformative (large uncertainty regions on both sides). In that case the posterior P pΩ|D i q (with i " g or γ) is almost equal to the prior P pΩq, in Eq. 4.13, leading to I Ω « 1. Moreover, when looking for a CBC producing coincident signals in GW data and Fermi/GBM, we know a priori that it cannot be located behind the Earth. Therefore, a more realistic prior (compared to a uniform prior on all-sky) for the sky location is zero over the Earth, and uniform over the portion of the sky not occulted by the Earth. This leads to the following:

P pΩq " " 1{ ş C dΩ " 1{f vis 4π if Ω R C 0 if Ω P C (4.14)
where

f vis " 1 4π ż C dΩ (4.15)
is the fraction of the sky not occulted by the Earth. Finally, one can rewrite Eq. 4.13 as

I EA Ω " 4πf vis ż C P pΩ|D g qP pΩ|D γ qdΩ (4.16)
In contrast to an all-sky prior, the Earth-avoiding prior systematically reduces the Bayes factor when the events being compared are well separated from the Earth, regardless of how much their skymaps overlap. In this case I EA Ω « f vis I AS Ω and for a satellite in a quasi-circular low-Earth orbit such as Fermi, f vis « 0.7.

When the sky localization of the association is most likely behind the Earth, the difference between the sky term with a prior avoiding the Earth and considering a uniform prior over all-sky (ignoring the presence of the Earth) becomes important. An example is shown in Fig. 4.4. Here, the GW trigger in question displayed in the spectrogram is a blip-shaped glitch (triggering the high mass templates, SNR « 73 and χ 2 « 259) and the GBM trigger has a probability of being on the top of the Earth of 83%. Hence, it is likely not a GRB but rather noise coming from behind the Earth or from the Earth itself (e.g. Terrestrial Gamma-Ray flashes [START_REF] Roberts | The First Fermi-GBM Terrestrial Gamma Ray Flash Catalog[END_REF]) triggering the detector. When we set to zero the probability behind the Earth, the Earth-avoiding sky term is I EA Ω « 3.08ˆ10 ´10 , which indicates that the association is more likely to be an accidental coincidence. On the contrary, with the all-sky prior, it becomes I Ω « 4.06. Since both triggers have most of their posterior distribution behind the Earth, the sky overlap term of the association should be strongly close to zero, which is the case with I EA Ω . Finally, it is important to mention that the limit on the sky localization in our method is given by the worst sky localization (between GBM and LIGO/Virgo). This means it does not matter if one of them has a good sky localization; if one skymap has a large uncertainty region, I EA Ω would be smaller than two candidates overlapping with precise sky localizations.

The discrete computation of the Earth-avoiding prior is detailed in the following section.

Discrete computation of overlaps of HEALPix skymaps

HEALPix [START_REF] Zonca | healpy: equal area pixelization and spherical harmonics transforms for data on the sphere in python[END_REF][START_REF] Górski | HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere[END_REF] stands for "Hierarchical Equal Area isoLatitude Pixelation" of a sphere. Within HEALPix, a spherical surface is subdivided into pixels that all cover the same area. Many features can be found in HEALPix package, among them, the pixel manipulation and the visualization of skymaps.

A discrete HEALPix localization array from Bayestar or Fermi/GBM, hpa, is normalized such that each pixel contains the probability for the source to be inside that pixel, which means that :

N ÿ i hparis " 1 (4.17)
where N is the number of pixels in the HEALPix array. We must compare this expression with the normalization of a continuous probability density,

ż P pΩ | hpaqdΩ " 1. (4.18)
Hence, to go from the continuous version to the discrete one, we need the following replacement:

ż Ñ N ÿ i (4.19) P pΩ | hpaqdΩ Ñ hparis (4.20)
The discrete form of Equation 4.13 is then, assuming we have three HEALPix arrays for the prior and posteriors,

I Ω " N ÿ i hpa_gwrishpa_gbmris hpa_priorris . (4.21)
With a uniform prior on the sky, Equation 4.13 becomes

I AS Ω " 4π ż P pΩ | D g qP pΩ | D γ qdΩ (4.22)
In the case of Equation 4.22, the dΩ's no longer cancel out: one remains at the denominator and needs to be replaced with the HEALPix pixel area ∆Ω. Therefore

I AS Ω " 4π ∆Ω N ÿ i hpa_gwrishpa_gbmris (4.23)
The case of Equation 4.16 is similar, but we can note that the sum must avoid the pixels covered by the Earth:

I EA Ω " 4π

. Calculation of the significance

Eventually, we want to assign a statistical significance to each foreground pair. To do it, we want to compare the foreground to the background to compute the significance of the foreground. The FAR (or the inverse false alarm rate, IFAR [yr]) of an event gives a quantitative idea of how likely it is for noise to generate an event. It is defined as the rate of background with ranking statistics equal to or higher than the one observed for the candidate in question [START_REF] Morrá | False alarms induced by gaussian noise in gravitational wave detectors[END_REF]. Therefore, it gives a physical meaning to the ranking statistic.

We want to generate the foreground sample, i.e. identify pairs of GW-GBM triggers that could come from a common astrophysical source, sort these pairs with our ranking statistic, and compute a joint FAR. A background sample is needed to assign it to each foreground event. The same set of triggers is used to generate both the foreground and the background. To compute the background sample, we use a time-slides method [START_REF] Michał Wą S | On the background estimation by time slides in a network of gravitational wave detectors[END_REF] in which we time-shift the GBM triggers by a predetermined offset, and we look for (fake) coincidences between the GW triggers and the time-shifted GBM triggers. This method can be summarized by Fig. 4.5. This method to compute the significance of a candidate is similar to what PyCBC does for GW data analysis (see Sec. 2.1.3 and Fig. 2

.5).

To choose an optimal background interval (i.e. the number of time slides and the time difference between two following time slides), we need to consider some requirements: First, keep the interval to a minimum to have "local" estimates of the background. Hence, the detector is in the same state during the background time interval to avoid bias. Second, the interval chosen should not be extremely large to avoid expensive computational costs. Third, the interval must be large enough to reach an interesting FAR (< 1/[1000 yr]) for claiming a discovery.

Hence, we have tried two background intervals to compute the FAR of the foreground. These background intervals are described in Sec. 4.3.

The time offset chosen to compute the background must be higher than twice the maximum time offset of 30 s considered in this analysis to be a nonphysical time delay between a CBC and any possible GRB emission resulting from it. In the first configurations, we use a ˘100 s offset and then reduce it to ˘70 s to accumulate background associations. We repeat this process multiple times, each with a different nonzero integer multiple of 100 s (and then 70 s), and accumulate the background distribution of Λ values as shown in Fig. 4.6. For the foreground, we rank the pairs with the same statistic, but without time-shifting the GBM triggers to find the potential GBM-GW candidate pairs.

In terms of computing, the analysis is run automatically thanks to Pegasus [START_REF] Deelman | Pegasus, a workflow management system for science automation[END_REF]. It enables the creation of a workflow, which is defined as a series of steps related to the processing of data. A workflow allows us to parallelize and automatize jobs in an analysis. Its flowchart is shown in Fig. 4.7. To gain time we first associate each GBM skymap to the time of the corresponding GBM trigger and save it in a dictionary. We also compute the GBM Bayes Factor Q γ . Then we start looking for possible associations: on one side, we compute the background associations that are stored in multiple HDF files, and on another side, we store the foreground associations in one single file. We then merge the background HDF files into one single file, and we use both the background and the foreground association file to compute the significance of the foreground. The foreground associations with their corresponding significances are stored in a new HDF file. Finally, tables and figures showing the results are generated, and examples of these plots will be shown in the following sections.

. Check the validity of the method against GW170817

Before applying our deep search on the LIGO/Virgo and Fermi/GBM data covering O3 duration (Section 4.4), the same analysis has been applied to the data coming from O2 (Section 4.3) to check the validity of our method against GW170817 -GRB 170817A, the only GW/GRB association we detected so far.

In this analysis, we focus on O2 PyCBC coincident triggers from the two LIGO detectors (LIGO Hanford (H1) and LIGO Livingston (L1)) in which potential BBH, BNS, and NSBH signals can be found. Although the search triggers are produced from LIGO data only, we also use Virgo data (when available) for the sky localization, as it can lead to significantly narrower posterior distributions.

In total, we deal with 780206 GBM triggers and 15270 GW triggers.

. Configurations

Several configurations are tested to maximize the significance of GW170817 -GRB 170817A. All the requirements described in the previous section lead us to start with a shorter time interval of +/-50,000 seconds ("27 hours around the GW trigger) in 100 seconds steps for testing and then use the larger interval of +/-180,000 seconds ("4 days around the GW trigger) in 70 seconds steps for final significance estimates. The non-symmetry between the lower and upper edge is only chosen for a computational reason.

Before the description of the configurations using the Bayesian ranking statistic, we first present, in Sec. 4.3.2, the results obtained using the naive time ranking statistic described in Sec.4.2.3 computing the background associations with time slides from -50000 to + 50000 with steps of 100 seconds.

We then focus on the main analysis of this paper using the Bayesian ranking statistic defined above, and we test five different configurations to maximize the significance of GW170817 -GRB 170817A:

1. We first present the results without using Virgo's contribution to the sky location. The background is computed with time slides from -50000 to + 50000 with steps of 100s (-50000:50000:100s). The significance of the foreground is computed by separating the associations by GBM spectral value and duration (configuration n ˝1). So we treat each different (spectral value -duration) pair as an independent search, and we apply a final trials factor to the FARs to account for the number of searches.

2. Then we include Virgo contribution, and the background is computed with time slides from -50000 to + 50000 with steps of 100s. The significance of the foreground is computed by separating the associations by GBM spectral value and duration (configuration n ˝2).

3. After that, we present the configuration n ˝3 in which we extend our background interval to -180070s to +180000s with a ˘70 s offset to accumulate background associations. The significance of the foreground is computed separating the associations by GBM spectral value and duration.

4. Fourth, we compute the significance of the foreground associations without the separation by GBM spectral value and GBM duration (configuration n ˝4).

5. Finally, we discuss the configuration n ˝5: no separation by GBM spectral value and GBM duration and application of a preliminary cut of the GW triggers based on the FAR. We remove the GW triggers with a GW FAR above 2 per day (threshold inspired from GWTC-3 [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]). This pre-selection is justified later. From configuration n ˝1 to n ˝3 we compute the significance of the foreground by separating the associations by GBM spectral value and GBM duration. By separating by spectral value and duration we compare GW170817 -GRB 170817A to associations with the same characteristics on the GBM trigger side. It prevents us from comparing GW170817 -GRB 170817A to loud associations whose properties correspond less to GRBs coming from NS mergers. We justify our choice to not use this separation in configurations 4 and 5 later in the chapter.

. Results

Naive statistic results

We first run this analysis on O2 data with the naive time and naive time and sky ranking statistics summarized by Eq. 4.3 and Eq. 4.4. Background associations are computed using time shifts going from -50000 to +50000s with a step of 100s. The results of the ranking statistic including only the time proximity and the one including the time and sky proximity are very similar so we only present the naive time ranking statistic. Figure 4.9 represents how the background behaves. The associations are shown separated by GBM spectral value (the three panels) and GBM duration. Here, the rate of some curves is an order of magnitude smaller than others. On the right panel of Fig. 4.9, the curve representing the associations containing an 8.192s -soft GBM trigger (lightest green curve) does not appear. The GBM Targeted Search intentionally removed such GBM triggers because they contaminate the background above all. These plots show that the background associations go to extremely high association rank values. Indeed, as shown in Table 4.1 and Fig. 4.8, these statistics are limited by random coincidences between actual bright short GRBs and random noise in the GW detectors. Moreover, we can see that adding the sky overlap here would not affect the results because of the extremely high values of association rank we get. Since the GBM LLR for bright events is several orders of magnitude larger than any of the other quantities in the ranking statistic, the ranking statistic just reduces to the LLR for bright GRBs, and the other properties become irrelevant. Therefore, naive statistics cannot be used unless the various quantities summed together have similar magnitudes.

Finally, if one computes Λ in the case of GW170817 -GRB 170817 with the naive time statistic, a value of lnpΛq « 580 is found, which will not give a significant FAR compared to the highest ranked background associations from Table 4.1 (with lnpΛq « 19856) that are contaminated by extremely loud triggers in the GBM channel.

Configuration 1: Bayesian ranking statistic without Virgo contribution and separation by GBM spectral value and duration

We now switch to the Bayesian statistic (Eq. 4.7) and present the background behavior, then focus on the highest-ranked background associations and the most significant foreground associations.

Here, we present the results without using Virgo's contribution to the GW skymaps. Figure 4.10 represents how the statistic behaves for the background associations. The associations are separated by GBM spectral value (the three panels) and duration. As for the naive time ranking statistic (Fig. 4.9), the rate of some curves is an order of magnitude smaller than others. It goes above one but for a low rate with a maximum association rank of "26 at a background rate of almost 10 ´3yr ´1, in other words, we would expect fake (background) associations to have such association rank 1 per 10 3 year. Otherwise, most of the background has an association rank smaller than 1.

Table 4.2 shows the properties of the first four top-ranked background associations, and Fig. 4.11 displays the first of these background associations. On the GW side, all the candidates in the four highest ranked background associations have a signal-like Q g but are more likely to be noise looking at the H1 and L1 spectrograms and considering that we did not find any GW confident events at the GPS time of these triggers. An example of the spectrograms of such GW candidates is presented in Fig. 4.11. On the GBM side, only the third association contains a GRB detection: GRB ˝509164689 [START_REF]GRB Coordinates Network[END_REF]. However, all the GBM candidates in Table 4.2 have signal-like GBM Bayes factor Q γ , and in the highest ranked background association, the two candidates are well localized and overlap each other. This explains the signal-like I EA Ω and thus the high association ranking statistic. More generally, the highest-ranked background associations comprise signal-like GBM candidates and GW candidates that are more likely to be noise. It is composed of very diverse GBM triggers, bright and less bright GBM triggers (large and small LLR), a large range of duration (going from 0.064 to 8.192 seconds), and all spectral values (hard, normal, and soft). This diversity is reassuring, and we do not see any reason (e.g. the search triggers only a specific type of GBM trigger which leads us to believe that there has been a problem with the code/analysis).

The FAR, defined by Eq. 2.18, is computed by counting the number of associations in the background with a higher association rank value than the foreground association in question. One can then build the cumulative rate as a function of the IFAR for the foreground associations as shown in Fig. 4.12. If we have a joint detection, we will see the foreground (blue curve) deviating from the expectation (orange region). Figure 4.12 has been plotted by separating the associations by pairs of GBM spectral value and GBM duration. We do not observe any deviation at more than 1σ of the foreground from the background here. Moreover, the beginning of the foreground curve deviates from the expectation computed with the background. This behavior is understood, and explanations are given in Sec. 4.3.3. Table 4.3 shows the first four most significant foreground associations with configuration 1. Here, we can see that the first ranked foreground association is related to GW170817 -GRB 170817A. This association has an IFAR of 1.102 yr which is not highly significant. The display of this association is shown in Fig. 4. [START_REF] Van Eerten | OFF-AXIS GAMMA-RAY BURST AFTERGLOW MODELING BASED ON a TWO-DIMENSIONAL AXISYMMETRIC HYDRODYNAMICS SIMULATION[END_REF]. We can see the chirp in both H1 and L1 spectrograms. Here, L1 spectrogram has been displayed using the data after the glitch subtraction. In Table 4.3, the next associations after GW170817 -GRB 170817A are more likely composed of noise in the GW channel despite their signal-like Q g . In the GBM channel, the candidates are more likely to be noise, except the fourth GBM trigger that might be associated with a long GRB [START_REF]GRB Coordinates Network[END_REF] that started "30 seconds before the MET of this candidate. These associations are not significant since they have a small IFAR, making them more likely to be accidental coincidences. In addition, the 2 nd and the 4 th most significant foreground association in Table 4.3 appear to have a negative delay meaning that the GBM trigger is detected before the GW trigger, so it would be surprising that they have a common origin when we put it in the context of astrophysics, in addition to the low IFAR of these associations and the poor significance of the candidate in at least one of the single (GW and/or GBM) channel.

We stop at the 4 th most significant foreground association because the rest of the table does not contain an association with IFAR large enough to be investigated.

However, we know from the literature that a soft tail has followed the prompt gamma-ray emission of GRB 170817A (see Chapter 1, Sec. 1.1.3) [START_REF] Pozanenko | Grb 170817a associated with gw170817: Multi-frequency observations and modeling of prompt gamma-ray emission[END_REF], one can wonder if we would detect an association of GW170817 with the soft-tail of GRB containing the properties of the fifth most significant foreground associations with configuration 1. This is GW170817, associated with the soft-tail of GRB 170817A. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank value.

170817A in our analysis. Table 4.4 shows that we do have a foreground association related to GRB 170817A soft-tail. However, it is in the fifth position with a poor significance.

Considering that we did not include Virgo's contribution to the sky localization of the GW triggers, one could intuitively expect that adding it would improve the sky localization and thus the sky overlap term of GW170817 -GRB 170817A, increasing its significance. In the following section, we explore the results of this configuration.

Configuration 2: Bayesian ranking statistic with Virgo contribution

The top-ranked background associations are mostly similar to those without Virgo contribution, so we present only the foreground results here. Figure 4.14 shows that the top-ranked foreground association is still not highly significant: it deviates from the background at less than 3σ, and its IFAR is > 11.017 yr. However, since we do not have high enough ranked background associations to compare this foreground association with, the IFAR of the most significant foreground association is now a limit, and the actual IFAR value of this association is higher than this. Table 4.5 shows that now the top 2 of the highest ranked foreground associations are related to GW170817 -GRB 170817A; in the first row of the table we can notice that the GBM candidate corresponds to the first peak of GRB 170817A and in the second row, the GBM candidate is the soft tail of GRB 170817A. We can see here that with Virgo's contribution to the sky location, the GW Bayes Factor of GW170817, which is directly extracted from the skymaps) is much better (an order of magnitude smaller) than previously, and the sky term I EA Ω is much higher ( compared to Table 4.3). Indeed, GW170817 has a much more precise sky localization with Virgo contribution, as shown in Fig. 4.15.

The next associations in the table are not significant enough to be investigated as astrophysical associations.

The results obtained here are better than the previous configuration. However, the significance of the joint detection is still not high enough. The fact that we only have a limit on the IFAR of GW170817 -GRB 170817 means that we do not have accumulated enough background. In the next part, we change the configuration to compute the background and use time shifts from -180070 to +180000 seconds by step of 70 s. 4.6 shows the properties of the first four top-ranked background associations. In the first row, in the GBM channel, the candidate has a signal-like Q γ . It is GRB n°510119909 [START_REF]GRB Coordinates Network[END_REF]. On the GW side, the candidate has a signal-like Q g , but it is more likely to be noise looking at the H1 and L1 spectrograms and considering that we did not find any GW confident event at the GPS time of this trigger. Hence, as previously, the highest-ranked background associations comprise associations with signal-like GBM candidates and GW candidates that are more likely to be noise. It is composed of very diverse GBM triggers, bright and less bright GBM triggers (large and small LLR), a large range of duration (going from 0.064s to 8.192s), and all spectral values (hard, normal, and soft). Again, this diversity reassures us. Figure 4.18 shows the cumulative rate of the foreground associations as a function of their IFAR. As for configurations 1 and 2, Fig. 4.18 has been plotted when computing the significance of the foreground by separating the associations by pairs of GBM spectral value and GBM duration. One association deviates at 3σ from the background with an IFAR " 28 yr. Table 4.7 shows the first four most significant foreground associations with configuration 3. Here, the top 2 are related to GW170817 -GRB 170817A. The second association corresponds to the soft tail of GRB 170817A [START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF][START_REF] Goldstein | An ordinary short gamma-ray burst with extraordinary implications: Fermi-GBM detection of GRB 170817a[END_REF]. The display of GW170817 -GRB 170817A with With configuration 3, GW170817 -GRB 170817A is discovered at barely 3σ, which is not highly significant.

In Table 4.7, the next associations after GW170817 -GRB 170817A are more likely composed of noise in both GBM and GW channels despite their signal-like Q γ and Q g . Their spectrograms, SNR time series, and the O2 confident GW events list have been checked. These associations are not significant since they have a small IFAR, making them more likely to be accidental coincidences. We stop at the 4 th most significant foreground association because the rest of the table does not contain an association with IFAR large enough to be investigated. One can also compute the significance of the foreground without separating by GBM spectral value and GBM duration. This enables us to compare GW170817 -GRB 170817A and, thus, increase its IFAR. The results without this separation are shown in Fig. 4.20. By comparing the joint associations GW170817 -GRB 170817A to many more background associations, all GBM spectral values, and GBM duration included, we still have a 3σ deviation from the expected background. However, we increase the IFAR of the joint detection going from "28 yr to "90 yr. Indeed when we compute the FAR by separating the associations and thus treat each search as an independent search, we need to multiply the significance by a trial factor to account for the number of searches. Removing this trial factor increased the value of the IFAR of GW170817 -GRB 170817A. Later we decide not to separate the associations by GBM spectral value and GBM duration.

GW properties GBM properties

Limitations of GW170817 -GRB 170817A significance

The poor significance of GW170817 -GRB 170817A presented above demonstrates that our configuration is not as satisfactory as it should be and investigations of what limits the joint detection significance show that some background associations have higher association rank value than GW170817 -GRB 170817A. containing the properties of the background association with the same GBM duration and spectral value as GRB 170817A that limits the significance of GW170817 -GRB 170817A in configuration 3. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank value.

value as GRB 170817A and a higher association rank. The GBM trigger in this association corresponds to a real GRB, and on the GW side, the IFAR of the GW trigger is about 4.265 ˆ10 ´5 yr which is noise-like. So in configuration n ˝3, when we separate the associations by GBM spectral hardness and duration, such association limits the significance of the joint detection. However, this association is more likely to be an accidental coincidence and should be suppressed by the FAR of its GW candidate. One can conclude that the poor significance of GW170817 -GRB 170817A is mainly due to the large amount of GW triggers we have to consider (mainly composed of noise), and to maximize the significance, we decide to apply a cut on the GW triggers based on their FAR value. We choose a threshold of 2 per day, inspired by the choices made in GWTC-3. The background comprises associations with signal-like GBM candidates and noise-like GW candidates. The table showing the highest-ranked background associations is not provided here to avoid redundancy, but together with Fig. 4.21, it shows a background composed of very diverse GBM triggers, a large range of LLR in the GBM trigger side, a large range of duration (going from 0.064s to 8.192s), all kinds of spectral values. As previously, this diverse background reassures us.

The behavior of the foreground is presented in Fig. 4. [START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF]. It shows that we now have a discovery at more than 4σ contrary to the results without pre-selecting the GW triggers. This joint association has an IFAR that is more significant than 1348 yr. This IFAR of the joint detection is a limit (as for configuration 2 in Sec. 4.3.2), and the actual IFAR value of this association is higher than this. Table 4.9 shows the first four most significant foreground associations. Now the top 3 are related to GW170817 -GRB 170817A. The pre-selection of the GW triggers has brought a 3 rd weak extra GBM trigger connected to GRB 170817A and coupled with GW170817. Figure 4.23 shows the 3 GBM triggers of GRB 170817A that correspond to the three most significant associations. The 4 th ranked foreground association does not contain significant candidates in both channels. Its Q γ is noise-like, and its Q g is signal-like, but we checked L1 and H1 data, and they do not show any excess power at the time of the GW trigger. But above all, its joint IFAR is also not extremely high, so this association is more likely to be accidental.

Discarding GW triggers highly likely to be noise before running this analysis allows us to remove loud background (time-shifted) associations containing noise in the GW channel and limiting the significance of GW170817 -GRB 170817A such as Table 4.8. We finally found an optimal configuration that enables us to maximize GW170817 -GRB 170817A significance. Eventually, Table 4.9 also demonstrates that GW170817 -GRB 170817A was the only GW-GRB association that has been observed in the GW and GBM data during O2 because the 4 th most significant foreground association does not have a sufficiently high IFAR to be investigated as an interesting association.

Discussion about O2 results

We presented a method to search for associations in a symmetric way between GW triggers from LIGO and Virgo interferometers and data from Fermi/GBM. We sorted the associations thanks to a ranking statistic introduced in [START_REF] Stachie | Search for advanced ligo single interferometer compact binary coalescence signals in coincidence with gamma-ray events in fermi-gbm[END_REF] based on the time and spatial overlap and the significance of the GW and the GBM candidates. The method described here has been applied to PyCBC and Fermi/GBM triggers from O2 to check its validity against GW170817 -GRB 170817A. Several configurations have been tested to maximize the significance of this joint association. Indeed, when we have to analyze a large amount of noise on the GW side, GW170817 -GRB 170817A is not highly significant. When we pre-select the GW triggers on their FAR to reduce their rate, we rediscovered GW170817 -GRB 170817A with the three most significant foreground associations related to this joint detection. The first two have an IFAR ą 1348 yr. Other configurations could be tested to increase the significance of the joint detection, such as removing the GW triggers with masses incompatible with neutron stars or using a more realistic time offset prior, since currently, we allow the GBM trigger to happen long before the GW trigger. In [START_REF] Zhang | The delay time of gravitational wave -gamma-ray burst associations[END_REF], the time delay between the GW and the GRB is written as a function of the time for the central engine to launch a relativistic jet ∆t jet , the time for the jet to penetrate through and break out from the surrounding medium ∆t bo and the time after breakout for the jet to reach the energy dissipation radius where the observed γ-rays are emitted ∆t GRB , thanks to the following formula: ∆t GW´GRB " p∆t jet `∆t bo `∆t GRB qp1 `zq. Starting from this review [START_REF] Zhang | The delay time of gravitational wave -gamma-ray burst associations[END_REF] and understanding the jet and GRB physics in BNS systems would lead to an estimation of ∆t GW´GRB that could be used as our time offset prior in future analysis. We are also considering improving the calculation of the GW Bayes factor. Thus, a new Q g calculation with a KDE is proposed in Sec. 4.3.3, and we may test it in future work. Finally, we did a search optimized for sGRBs since sGRBs are believed to be produced by neutron star mergers, contrary to long GRBs due to CCSNe. However, this classification is now questioned since Rastinejad et al. recently observed cases where a kilonova, the remnant of neutron stars mergers, might have been associated with a long GRB [START_REF] Rastinejad | A kilonova following a long-duration gamma-ray burst at 350 mpc[END_REF]. Another improvement would Chapter 4. Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 160

be extending the search to all types of GRBs by, for example, taking a sample of short and long GRBs as a signal training sample in the GBM Bayes factor calculation. Furthermore, since we see more noise than signals in both LIGO/Virgo and Fermi/GBM, and we see more unrelated signals than multi-messenger discoveries, our ranking statistic could be improved if we do not assume complete ignorance about prior probabilities anymore. Finally, our approach in this study is not limited to Fermi/GBM data. Other missions like the future instrument SVOM [START_REF] Atteia | The SVOM mission[END_REF] can use a similar approach if they produce their own form of GBM Bayes Factor Q γ and provide independent sky localizations. Thus, another potential improvement would be considering information from multiple GRB monitors.

. Investigations KDE-based method to compute Q g

The current GW Bayes factor does not allow us to discriminate correctly between noise and an astrophysical gravitational wave signal. For instance, Table 4.6 shows that the four highest-ranked background associations have signal-like GW Bayes factor (Q g ă 1). A new way to compute Q g should be investigated for future analysis to properly separate the noise-like GW triggers from the interesting GW candidate. The skymaps produced by Bayestar [START_REF] Singer | Rapid bayesian position reconstruction for gravitational-wave transients[END_REF] provide the BCI (the current Q g ) along with the BSN. Consequently, it should be possible to use a KDE-based method to compute Q G with a KDE trained in the log 10 pBCIq ´log 10 pBSNq plane. We also pre-process the data using the logarithm here to avoid dealing with values very different from each other. The expected behavior is summarised in the following list:

• Gaussian noise should have both small log 10 pBCIq and small log 10 pBSNq values.

• Glitches should have a small log 10 pBCIq value and a high log 10 pBSNq values.

• Astrophysical GW signals should in principle have both high log 10 pBCIq and high log 10 pBSNq values.

Thus, we construct a GW Bayes factor using these parameters. We build a signal sample with 1000 BNS injections and GW events from all runs. The background sample comprises 2000 O2 GW triggers with a FAR ą 2/day. The injections of the signal sample are done in Gaussian and stationary noise with the parameters summarised in Table 4.10. A cut on the optimal SNR has been applied: only signals with a network SNR above 8 and 5.5 in at least one of the interferometers were kept. The remaining signals are localized with Bayestar to generate the skymaps.

The results of the GW Bayes factor are presented in Fig. 4.24. Here we preprocess the data thanks to a quantile transform [START_REF]Scikit-learn: Machine learning in Python[END_REF] that flattens the distributions and moves them between 0 and 1. We can clearly see a separation between the signal-like and the noise-like region. We also check that this Bayes factor behaves Parameter Distribution Polarisation Upr0, 2πsq Phase at coalescence Upr0, 2πsq cos ι Upr´1, 1sq Position UpSp0, r40, 250sMpc)) Here, all the GW events from the validation sample are in the signal-like region with strongly negative lnpQ g q, which is consistent with the expectations. However, the lnpQ g q " 0 curve in Fig. 4.24 is almost vertical from log 10 (BSN) « -1.5 to log 10 (BSN) « 6.5, so except for very high BSN, Q g seems to only depend on the BCI. Indeed, as mentioned in Sec. 4.2.3, computing a KDE is complicated because some assumptions need to be made. We need to generate skymaps for GW injections, noise, and glitches. We also need to choose a bandwidth for the KDE computation, and results can be strongly bandwidth-dependent. Thus, using only the BCI might be an acceptable approximation and reduces the number of assumptions we need to make and the computational cost of Q g . Another method that could be investigated in the future consists in using the probability of astrophysical origin calculation, the p-astro, which is based on binary system rate densities. However, for now, the estimation of the BNS merger rate is not robust enough because we have not observed enough BNS events. Still, hopefully, we will be able to improve this estimation thanks to future GW observing runs.

Mass N pµ " 1.4M d , σ " 0.1M d q Spin N pµ " 0, σ " 0.01q

Modelling the curve of the cumulative rate as a function of the inverse false alarm rate

As mentioned in Sec. 4.3.2, Fig. 4.12 shows a rate turnover on the left of the plot. This is because each pair (GBM temporal or spectral value) does not have the same rate. For instance, GRBs with a short time scale are occurring more often due to their short duration. This behavior is explicit looking at Fig. 4.25, which is a zoomed-out version of Fig 4 .10, in which we can see that each curve does not start at the same rate. So when we separate the associations by GBM spectral value and GBM duration, each pair does not start contributing to the cumulative rate at the same IFAR. Investigations are made to model the expectation curve (in orange) to have the same turnover. We consider here the results from configuration n ˝3 (i.e. using Virgo, more time slides, separation by spectral value and duration, and no cut on GW triggers before applying the search). Figure 4.26 shows that when we sort by GBM duration, all the curves do not start at the same rate. One can create bins with edges defined by the dash lines in Fig. 4.26. Each bin is represented by its mean IFAR value. Then, one can weigh the bins by the cumulative number of triggers contributing to each bin. This can be summarized by the equations 4.25 and 4.26, where i represents each bin's index of the lower edge. R i " Ratep edgeris `edgeri `1s 2 q (4.25)

R i 1 " R i ˆři`1 0 nb_triggers ř 8 0 nb_triggers (4.26)
Here we have represented each bin by the IFAR value in its center, so we take only one value per bin to model the left of the curve.

To check the validity of this modeling, one can compute the significance of the foreground in configuration n ˝3 when we separate the analysis by GBM spectral value and duration. The results are represented in Fig. 4.27. To improve this modeling, one could define bins for each (spectral hardness -duration) pair (and not only duration as presented here) and apply weight for each of these bins. This could be something to investigate for future analysis. The method presented in Sec. 4.2.3 with the optimal configuration (configuration 5) found thanks to the O2 analysis (Section 4.3) has been used on the PyCBC, GstLAL, and MBTA GWTC-3 released triggers (with a FAR ă 2/day) and Fermi/GBM data from O3. We deal with 1101145 GBM triggers, 714 Gst-LAL triggers, 584 MBTA triggers, and 621 PyCBC triggers. Each pipeline also provides the inferred properties (chirp mass, total mass ...) and the p-astro of the GW triggers.

In this analysis, we use both LIGO and Virgo data which is an improvement compared to the analysis in O2 (Sec. 4.3) [START_REF] Pillas | Deep multimessenger search for compact binary mergers in ligo, virgo and fermi/gbm data from[END_REF] in which we use LIGO data and Virgo contribution to the sky localization when available. We cover single detector triggers as [START_REF] Stachie | Search for advanced ligo single interferometer compact binary coalescence signals in coincidence with gamma-ray events in fermi-gbm[END_REF] and include double and triple detector triggers and treat them the same way.

. Results

In this section, we explore the results obtained with the three pipelines. For each of them, we start by looking at the background cumulative rate versus association ranking statistic and the table of the highest-ranked background associations. Then we investigate the foreground results; we first show the cumulative rate versus IFAR for the foreground, and finally, we look more carefully at the most significant foreground associations. In the last part, we investigate a possible counterpart to S190816u, a GW signal that was too weak to belong to GWTC-3 [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]. Here, the associations are shown separated by GBM spectral value (the three panels) and GBM duration.

GstLAL

As for O2, most of the associations have an association rank close to 0. A few go above 1 with a maximum association rank going to Λ = 77.32 according to Table 4.11 showing the properties of the four highest ranked background associations, the inferred properties, and the astrophysical classification of their GW candidate. The four highest ranked background associations have the same GW candidate, GW200224_222234, a confident BBH detection from GWTC-3 [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]. In the first and second highest ranked associations, the GBM candidates belong to the long GRB°604213554 [261] that started around 200 s before the MET of the GBM candidate. In the third one, the MET of the GBM candidate corresponds to the first peak of the long GRB [261]. The 4 th still contains GW200224_222234 with the GW source properties inferred by GstLAL in Table 4.11 and associated with a signal-like GBM trigger according to this table. This GRB-like candidate has not been reported on the GCN. Figure 4.29 displays the highest-ranked background association with GstLAL triggers. We can recognize the chirp of GW200224_222234 in the spectrograms. The left-hand GBM waterfall plot shows a multi-peak GRB-like trigger. The two loudest peaks here are responsible for the two first-highest-ranked background associations with GstLAL.

GstLAL discovery plot, Fig. 4.31, shows no deviation of the foreground from the background, and the most significant foreground association with GstLAL has an IFAR of 2.481yr. Table 4.12 presents the properties of the four most significant foreground associations and Fig. 4.30 displays the first one. The first association contains a GW candidate which is the confident BBH event GW190915_235702 from GWTC-3 [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]. The inferred properties of this BBH event are described in Table 4.13. The IFAR of this association is not high enough to suspect that both candidates are real astrophysical events (only the GW event here) and come from the same astrophysical source. In addition, this GW event is associated with a noise-like GBM trigger (low LLR, Q γ ą 1 ) that has been detected 12.359 s before the GW event, and in the literature we do not expect any GRB counterpart to a BBH merger. Putting it all together, it would be very surprising that these two candidates are related when we put it in the context of astrophysics. The next associations have ranking statistics close to 0, and their IFARs are not high enough to be significant, so we will not describe them.

MBTA

The background behavior for MBTA presented in Fig. 4.32 appears similar to Gst-LAL. The maximum association rank goes up to 66 with a rate going to almost 10 ´3yr ´1. Table 4.14 describes the four highest-ranked background associations with MBTA triggers and the top three are similar to those with GstLAL triggers. The properties of the GW source inferred by MBTA for these associations can be found in Table 4.14 legend. Only the properties of the GW triggers in each background association change compared to GstLAL, and there are some variabilities in the skymaps. One can see that the GstLAL skymap overlaps better, leading to a lower association ranking statistic for MBTA than GstLAL. The GW trigger sky localization of the first association is represented in Fig. 4.33. The fourth highestranked background association also contains a confident GRB detection [START_REF]GCN/FERMI NOTICE 601984129[END_REF], and the GW candidate is more likely to be terrestrial according to its p terrestrial . Figure 4.34 shows no deviation of the foreground from the background and the most significant foreground association with MBTA pipeline has an IFAR of 1.608 yr. Table 4.15 and Table 4.16 confirm that the most significant foreground association for MBTA triggers is the same as for GstLAL. The display of this association is the same as in Fig. 4.30 except the GW sky localization represented in Fig. 4.35, which is different from the GstLAL trigger associated with GW190915_235702. The IFAR of this association is not high enough to suspect that both candidates are actual astrophysical events (only the GW event here) and come from the same astrophysical source. The three next associations have ranking statistics close to 0 and are not significant enough (IFAR close to 0), so we will not describe them. and come from the same source. The display of this association is the same as in Fig. 4.30 except for the GW sky localization represented in Fig. 4.39, which is different from the PyCBC trigger associated with GW190915_235702, and leading to a lower sky term as described in Table 4

PyCBC

S190816u

During O3, a sub-threshold GRB candidate has potentially been associated with S190816u [START_REF]Fermi GBM-190816: A subthreshold GRB candidate potentially associated with a subthreshold LIGO/Virgo compact binary merger candidate[END_REF][START_REF]Fermi GBM-190816: Updated localization of subthreshold GRB-GW candidate[END_REF], a sub-threshold LIGO/Virgo compact binary merger candidate identified by PyCBC Live [START_REF] Alexander | Distinguishing short duration noise transients in LIGO data to improve the PyCBC search for gravitational waves from high mass binary black hole mergers[END_REF], MBTAOnline [START_REF] Adams | Low-latency analysis pipeline for compact binary coalescences in the advanced gravitational wave detector era[END_REF], and GstLAL [START_REF] Cannon | Gstlal: A software framework for gravitational wave discovery[END_REF] analysis pipelines. This is a GW event that was too weak to belong to GWTC-3. Thus, it does not appear in our search. Investigations have been done to find possible counterparts to this sub-threshold event and in the results of the GBM targeted search a potential candidate has been found " 1s after the input time of the GW event. We look for possible coincidences between S190816u and the results of the GBM-targeted search. We run our deep analysis using only the GW trigger related to S190816u and all the Fermi/GBM data. Table 4.20 shows the three associations found with our analysis including S190816u. The third one contains the GBM trigger that has been identified as a possible counterpart for S190816u. This association is eliminated by the bad sky overlap value which is due to uninformative skymaps. The GBM trigger is also likely to be noise regarding its Q γ . We do not observe a significant association, but rather the event is ranked consistently with the noise distribution.

. Investigations: Separation of the associations by chirp mass

4.5.1 . Context and Method As seen in Sec. 4.3, when calculating the FAR of an association, we can compare the association with either the entire background sample or only with a subset of it and then apply a trial factor based on the number of "bins" into which we split the background sample. In the O2 joint analysis, we only considered splitting the background by GBM duration, GBM best spectrum, or both, as we show in Sec. 4.3.2. Because of trial factors, it is better not to divide by these quantities, at least using GW170817 as a reference. The O3 analysis suggests that astrophysical BBH signals hurt us because of their high rate and the GW and GBM skymaps are too large to suppress the corresponding false association rate. The chirp mass is a parameter provided by the CBC search without needing any complicated parameter estimation. One could imagine a split by chirp mass to separate the BNS-like triggers from the others. Equation 1.46 gives the formula of the chirp mass. If we consider that the maximum mass of a neutron star is around 3 M d , a (3;3) M d BNS system will have a chirp mass of M « 2.6M d . Choosing a separation at 2.6M d would delimit between BNS/some NSBH and BBH/NSBH. Entirely including NSBH-like signals by a chirp mass split is complicated, so we will not try it here for simplicity. 4.28, demonstrates that separating by chirp mass with GstLAL triggers reduces the background rate of about an order of magnitude for the associations with M ď 2.6M d compared to the associations with M ą 2.6M d . Moreover, Fig. 4.41 shows that the IFAR of the most significant foreground association with GstLAL is lower than without separation (Fig. 4.31). This association is the same as before, so it still contains the confident BBH event GW190915_235702. In the case of GstLAL, splitting seems beneficial.

. Results

For MBTA, the rate of some curves (the 0.064s curves) in the left panel of Fig. 4.42 seems higher than in the right panel. Moreover, Fig. 4.43 shows that the IFAR of the most significant foreground association (with GW190915_235702) is higher than without the splitting (Fig. 4.34), which is problematic since we want to reduce the significance of the associations containing BBH-like events. In the case of MBTA, splitting seems potentially harmful.

Finally, with PyCBC, the effect on the background seems very small (but positive), comparing the left to the right panel of Fig. 4.44 and the current IFAR of the most significant foreground association (Fig. 4.45) to the previous IFAR without the separation (Fig. 4.38).

Whether the background depends on the chirp mass seems to depend on quite a bit on the details of the CBC search. Further tests should be done to investigate properly these differences. One can explore for instance the chirp-mass dependence of the GW noise trigger rate and the chirp-mass dependence of the GW noise trigger skymaps. An injection study might be necessary to configure the analysis in O4 properly.

. Conclusion about O3 results and perspectives

We have presented a deep search for GW-GRB associations in LIGO/Virgo and Fermi/GBM O3 data. The ranking statistic used here has been presented in Sec. 4.2.3 and is described in the associated method paper [START_REF] Pillas | Deep multimessenger search for compact binary mergers in ligo, virgo and fermi/gbm data from[END_REF]. In this analysis, we have used GWTC-3-released triggers from PyCBC, GstLAL, and MBTA, and no GW-GBM pair has been identified as a true association coming from a common astrophysical source. The most significant foreground association with the triggers of each pipeline contains the confident BBH-like GW event GW190915_235702 associated with a noise-like GBM trigger. This foreground pair gets a FAR of " 1/[2 yr] with GstLAL. It seems highly unlikely that this foreground pair has a common astrophysical origin. The next most significant foreground associations have ranking statistics close to 0, so they are not significant enough to be investigated. These null results are consistent with other joint GW-GRB searches on O3 data that have been performed [START_REF]Search for gravitational waves associated with gamma-ray bursts detected by fermi and swift during the ligo-virgo run o3a[END_REF][START_REF] Abbott | Search for gravitational waves associated with gamma-ray bursts detected by fermi and swift during the LIGO-virgo run o3b[END_REF]. We also investigated a possible counterpart to S190816u sub-threshold event. We found an association with a GW trigger we got from the global search, ranked consistently with the noise distribution due to a really small sky overlap term in the ranking statistic. For future analysis, some improvements to this method could be considered. One shortcoming of our ranking statistic lies in the GW Bayes Factor which does not discriminate properly between noise and signal. For instance, Q g could be computed using both the BCI and the p astro which is computed in a Bayesian way. Our current computation of Q g ignores our knowledge about the population contrary to the p astro . However, the p astro calculation is currently not robust enough for NS signals compared to BBHs since we do not have detected enough BNS events yet. We also think of separating associations by M chirp to treat each type of merger (NS or BH mergers) independently and avoid loud BBH signals at the top of the most significant foreground associations.

With the improvement of the sensitivity of our detectors and the next generation of GW detectors, like Einstein Telescope, the rate of true detections will significantly increase, and thus the chance to have fake coincidences, for instance, a BBH signal close in time to a GRB. And in fact, we can already see it in O3 with our background being dominated by an association between GW200224_222234 and a signal-like GBM trigger. One way to prevent loud BBHs limiting the significance of true associations is to separate by M chirp . However, it implies multiplying by a trial factor to account for the number of independent searches, and we saw that in the case of GW170817 -GRB 170817A the best significance was reached by removing the separation by GBM spectral value and duration, mostly because of this trial factor. The same can be expected with a separation by M chirp . Also, further investigations should be done to understand the discrepancies between the results of the M chirp separation for each pipeline, and an injection study could be a relevant first step. Another way to prevent the contamination of the background by loud BBH signals is by having better sky localization. A good sky localization will remove accidental coincidences demonstrating that the two candidates are spatially unrelated, reducing the rate of H SS . Thus, these accidental coincidences will not contribute to the tail of the background and will be in the bulk of the background.

CHAPTER 5

PREPARING A TEMPLATE BANK FOR O4

Before the fourth GW Observing Run (O4) begins, the PyCBC search prepares its analysis (solve faced issues, write documentation, implement improvements in PyCBC codes..). One of the main steps in matched filtering is the generation of template banks. Indeed, the more accurate the templates, the higher the search sensitivity. Thus, the PyCBC group decided to explore the generation of a new template bank for O4 using waveform approximants that have been upgraded compared to the ones used in O3. This chapter presents investigations I performed on a new template bank for O4.

. IMRPhenomX family phenomenology

Waveform models play an essential role in GW data analysis; they are used for template bank generation or Bayesian GW parameter inference [START_REF] Christensen | Parameter estimation with gravitational waves[END_REF] by matchedfiltering pipelines. Thus, constructing waveform models as close as possible to the solutions of Einstein equations (Eq. 1.17 to Eq. 1.20), including as many effects as possible (spins, eccentricity, tidal disruption, higher-order modes...), is necessary to improve the sensitivity of the GW search and increase the number of detected CBCs.

Here, we present one of the waveform models that describe the dominant mode (for details on the GW harmonic modes, see Appendix C), the IMRPhenomXAS waveform [START_REF] Pratten | Setting the cornerstone for a family of models for gravitational waves from compact binaries: The dominant harmonic for nonprecessing quasicircular black holes[END_REF], a new model for non-precessing (aligned spins) quasi-circular BBHs.

Aligned-spin models, including the three parts (inspiral-merger-ringdown) of a BBH waveform, can be divided into two classes of models: the frequency-domain EOB models (there also are equivalent models in the time-domain), used, for instance, by PyCBC in O3 (see Sec. 2.1.3 from Chapter 2), that can be computationally expensive sometimes [START_REF] Husa | Frequency-domain gravitational waves from nonprecessing black-hole binaries. i. new numerical waveforms and anatomy of the signal[END_REF][START_REF] Field | Fast prediction and evaluation of gravitational waveforms using surrogate models[END_REF] and the phenomenological ("Phenom") frequency-domain models. IMRPhenomXAS is one of the latter. It is an extended version of IMRPhenomD [START_REF] Husa | Frequency-domain gravitational waves from nonprecessing black-hole binaries. i. new numerical waveforms and anatomy of the signal[END_REF][START_REF] Khan | Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. a phenomenological model for the advanced detector era[END_REF] that models the (2,2) harmonic modes of nonprecessing quasi-circular BBH systems. This waveform model is fully described in [START_REF] Pratten | Setting the cornerstone for a family of models for gravitational waves from compact binaries: The dominant harmonic for nonprecessing quasicircular black holes[END_REF]. To construct this model, the waveform is separated into two functions of the Fourier frequency: an amplitude and a phase. These two functions are described in three different regimes presented in Fig. 5.1. (1) At low frequency during the inspiral part (0.0026 ď M f ď 0.018, where M is the system total mass and f the frequency), the waveform is described with post-Newtonian theory. The amplitude and the phase here are based on the TaylorF2 model [START_REF] Messina | Quasi-5.5pn TaylorF2 approximant for compact binaries: Pointmass phasing and impact on the tidal polarizability inference[END_REF]. (2) The high-frequency regime where the waveform is characterized using BH perturbation theory and quasi-normal ringdown behavior [START_REF] Kokkotas | Quasi-normal modes of stars and black holes[END_REF]. A Lorentzian and a deformed Lorentzian describe the phase and the amplitude here. (3) An intermediate frequency regime describes the transition between the abovementioned regimes. Here, the amplitude depends on the frequency as the inverse of a fourth-order or fifthorder polynomial. The three regimes are then glued together to constitute the full amplitude and phase of the waveform.

IMRPhenomXAS model has been tuned and validated using 652 Numerical Relativistic (NR) waveforms described in [START_REF] Pratten | Setting the cornerstone for a family of models for gravitational waves from compact binaries: The dominant harmonic for nonprecessing quasicircular black holes[END_REF]. Figure 5.2 shows the mismatch 1 ´mpa, bq (see Eq. 2.16), or 1 ´M with the figure notations, of the IMRPhe-nomXAS waveforms against SEOBNRv4-NR hybrids. A similar simulation is done with IMRPhenomD approximant, presented in the same figure. There is a difference of an order of magnitude between the mismatch with IMRPhenomXAS and IMRPhenomD, representing a significant improvement.

Since IMRPhenomXAS is an updated version of IMRPhenomD, it presents some upgrades:

• The number of waveforms used to tune the model has increased from 19 (IMRPhenomD) to 652.

• According to [START_REF] Pratten | Setting the cornerstone for a family of models for gravitational waves from compact binaries: The dominant harmonic for nonprecessing quasicircular black holes[END_REF], the validity range of IMRPhenomXAS approximant goes up to mass ratio 1000 (with Teukolsky waveforms [START_REF] Harms | A new gravitational wave generation algorithm for particle perturbations of the kerr spacetime[END_REF]), compared to IMR-PhenomD that allows mass ratio up to 18 only.

• IMRPhenomXAS captures the full spin (still aligned) dependence of the waveform contrary to IMRPhenomD, which used a single effective spin to describe the spin dependence.

• IMRPhenomXAS models the 3-dimensional parameter space of mass ratio, and component spins (Mass ratio, effective spin parameterization of their choice, linear-in-spin difference) instead of the 2-dimensional space previously modeled by IMRPhenomD.

. O4 preparation: a new PyCBC template bank

. IMRPhenomXAS -SEOBNR battle royale

In the months leading up to the start of O4, the PyCBC group committed to preparing the analysis. One of the tasks was to create a new template bank for Py-CBC. New and improved models became available before O4: SEOBNRv5_ROM and IMRPhenomXAS. Thus, it is natural to consider their adoption for a new PyCBC template bank. Before generating the bank, to ensure we can use either IMRPhenomXAS or SEOBNRv5_ROM template bank in O4, basic tests of these approximants need to be completed. At the time of this project, only IM-RPhenomXAS approximant is available in LALSimulation [START_REF]LIGO Algorithm Library -LALSuite. free software[END_REF], the waveform generation package used in PyCBC. Thus, this chapter only presents the checks done for IMRPhenomXAS.

Two tests have been performed:

1. Faithfulness simulations: To ensure we can use IMRPhenomXAS in O4 we want to compare IMRPhenomXAS waveforms to those computed with the previous approximants (TaylorF2 and SEONRv4_ROM) used in O3 by Py-CBC. Since we detected a significant number of GW signals in O3 using these approximants, we do not expect a priori large differences between the old and new models, at least in the region of search space where signals were detected. This comparison results in a distribution of match values (Eq. 2.16) between IMRPhenomXAS and TaylorF2/SEONRv4_ROM waveforms in the injection parameter space to check if they are regions where the match is small (i.e. totally different waveforms).

Bank simulations:

We also want to create an IMRPhenomXAS template bank, generate waveforms using O3 approximants (injections), and try to recover the injections with the bank. This results in a fitting factor (FF) computation, defined in Eq. 2.15 (Chapter 2), that will tell us if the new template bank has recovered injections. However, a function computing the duration of the waveform template is needed in PyCBC. As mentioned in Chapter 2, the O3 search space is partly defined by a duration cut. Thus, a reliable duration estimate for IMRPhenomXAS templates is needed to generate a similar bank using this approximant. Unfortunately, no duration function was implemented at that time. Therefore, the opposite test is performed here: we use an O3 template bank, generate IMRPhenomXAS waveforms, and compute the FF.

Even if IMRPhenomXAS initially models BH mergers, it should be accurate for lower-mass systems. Indeed, low-mass binaries like BNS and NSBH are dominated (in the LIGO/Virgo/KAGRA sensitive band) by the inspiral part of their waveform. IMRPhenomXAS uses TaylorF2 to compute the inspiral. Thus, the model should be usable for low-mass systems.

A PSD (Eq. 1.47) file or model must be specified to perform the faithfulness and the bank simulation. For the former, we tested the simulated PSD aLIGOZeroDetHighPower [START_REF]Advligo interferometer sensing and control conceptual design ligo[END_REF][START_REF]LIGO Algorithm Library -LALSuite. free software[END_REF], a popular model used by many studies and a simulated PSD O4DesignPSD corresponding to the expected sensitivity of LIGO in O4. Both are displayed in Fig. 5.3. The results are similar, so here, we only present the complete set of results with aLIGOZeroDetHighPower. For the bank simulation, we tested O4DesignPSD and the PSD of LIGO at the end of O3 (also provided in Fig. 5.3). Again, the results are similar with both PSDs. For BNS injections, we show results using O4DesignPSD; for the rest, we present the results for the LIGO PSD at the end of O3.

. Faithfulness simulation: Match between IMRPhenomXAS and O3 approximants Workflow generation and configuration of the simulation

At the time of the study, there was a workflow in PyCBC to perform the faithfulness simulation. However, it was outdated and difficult to use. As a consequence, the first step is to implement one. As for the joint LIGO/Virgo -Fermi/GBM analysis (Chapter 4), we use the Pegasus software to create the workflow. The Flowchart is presented in Fig. 5.4.

As shown at the top of the Flowchart, we first create a set of injections. Thus, the values of the injections parameters should be defined, i.e. the mass and spin ranges we want the injections to cover. Here we perform tests covering all types of CBC sources: one for BNS-like injections, one for NSBH-like, and three for BBH-like injections. Table 5.1 describes the configuration chosen for each test. These injections are created with IMRPhenomXAS model and in the parameter ranges given by the user. Then, these injections are stored in an xml file split into multiple smaller xml files to speed up further calculations. During the faithfulness simulation, PyCBC compares these injections to the waveforms constructed with the second model and creates multiple tables containing the parameters of each injection and the match between the two waveforms. The workflow merges all these tables and finally plots the distribution of the match values in the injection parameter space.

Results: BNS range

The inspiral regime is described by IMRPhenomXAS in the framework of the PN theory and is based on the TaylorF2 model. In PyCBC, BNS-like injections are generated with TaylorF2 since their long-duration inspiral part contributes the most to the waveform. Thus, it is natural to expect that the match between IMRPhenomXAS TaylorF2 will be close to 1 for waveforms in the mass and spin range corresponding to BNS signals. Figure 5.5 shows the distribution of the match for all the injections we consider over the m 1 ´m2 space (top) and the q ´χeff space (bottom). The effective spin is defined by Eq. 5.1, where χ 1z and χ 2z are the projections of the two spins along the orbital angular momentum.

χ eff " m 1 χ 1z `m2 χ 2z m 1 `m2 (5.1)
As expected, the match between the two approximants is close to 1 everywhere. Figure 5.6 shows the waveforms generated by the two approximants for the injection with the lowest match value. This lowest match value equals 0.985, and we can see that the two waveforms are similar. Thus, one can conclude that there is no particular problem with IMRPhenomXAS when dealing with BNS signals.

Results: NSBH range

For NSBH waveforms, we can see regions in the parameter space where the match is much lower than for BNS. According to Fig. 5.7, the high mass ratio -high effective spin region reaches match values close to 0.6.

These low match values imply differences between IMRPhenomXAS and SEONRv4_ROM at high mass ratio and effective spin. However, Fig. 5.7 alone cannot determine which of these two models better describes waveforms with high q -high χ eff .

Figure 5.8 shows the waveforms a and b generated by the two approximants for the injection with the lowest match value mpa, bq " 0.641. They have been generated with high mass ratio q « 85 and high effective spin χ eff « 0.98. The IMRPhe-nomXAS waveform (blue) does not seem physical compared to SEONRv4_ROM. We can see in the left figure that the strain increases until 0.4 s before the merger, then decreases, and finally increases again until the merger, which is not expected during the inspiral phase. A preliminary conclusion is that IMRPhenomXAS model seems inaccurate for high mass ratio -high effective spin signals.

Results: BBH range

Conclusion

We can first conclude that for BNS IMRPhenomXAS is similar to the O3 approximant (TaylorF2). When the two-component masses and spins of the source are in the same order of magnitude the difference between the approximants seems negligible. The discrepancy between the models becomes significant when we look at high spins and high mass ratio waveforms. When we approach mass ratios above 100, SEONRv4_ROM cannot produce waveforms, so the match is not calculated. On the contrary, IMRPhenomXAS can generate it, and an example with high spins and a mass ratio q « 150 is presented in Fig. 5.12. In the PyCBC search, we do not search for signals with q > 100 at the moment (because of computational, human, and statistical costs). However, it is important to know the behavior of our approximants at boundaries, and looking at Fig. 5.12, the waveform generated here does not look physical. These results have been presented to the waveform group of LIGO/Virgo/KAGRA, and these differences between the models and the odd behavior of IMRPhenomXAS at a high mass ratio are known by the group. The IMRPhenomXAS model usable in PyCBC is calibrated to NR for q ď 18. Hence, the recommendation from the waveform group (in agreement with the results presented here) is that the model should not be used for a mass ratio above 18.

. Bank simulation: Fitting Factor computation

The first test demonstrated discrepancies between IMRPhenomXAS and the approximants used in O3. However, this test does not tell us if an IMRPhenomXAS template bank can recover GW signals. The second test, the bank simulation that calculates the effectualness of a template bank, allows the user to investigate the construction of new template banks and perform a consistency check of the template bank generation placement. It ensures a bank is recovering signals at an acceptable match (" 97%). However, as mentioned in Sec. 5.2, we cannot generate an IMRPhenomXAS template bank because no IMRPhenomXAS duration function was provided in LalSimulation at that time. Thus, we proceed the opposite way, using an existing O3 template bank and trying to recover IMRPhe-nomXAS injections. We perform tests for simulated BNS, NSBH, BBH, and heavy BBH signals to cover all the parameter space. The mass and spin range covered by the injections are presented in Table 5.2. We first present the results of the bank simulation using 1000 BNS injections. Then, for the NSBH and BBH range, we increase the number of generated injections to 10000 to reduce the gap between injections in the parameter space.

The following section presents two different figures: (1) The "filtered" results. As mentioned in Chapter 2, Sec. 2.2.1, the PyCBC search does not include templates with a duration above 0.15 s. Thus, here we apply the same cut and filter the injections. Since we do not have a duration function implemented in LALSimulation for IMRPhenomXAS, we use the one from IMRPhenomD. It will give us an approximation to the duration computed with IMRPhenomXAS since the latter is an updated version of the former. (2) The "unfiltered" results show all the injections without any cut of the injection duration.

For injections in the BNS mass and spin range, we present the unfiltered results only, which are the same as the filtered injections since at low mass, the chirp duration is longer than 0.15 s. For NSBH and BBH injections, we present filtered results.

Results

Figure 5.13 shows the distribution of the recovered FF in the parameter space for BNS-like injections. According to the bottom panels, the minimum fitting factor is 0.92, and only three injections have a fitting factor below 0.96. These injections are in the low-mass region of the search space, and thus they are long-duration signals. These lower FF might be related to the configuration of the bank. Indeed, if the frequency resolution for the waveform generation is larger than 1/[waveform duration], it could result in a lower FF. Further investigations might be needed to check if the configuration we use is not optimal for low-mass templates or if there is a deeper issue with an approximant. Apart from that, we can conclude that most of the injections here fulfill the requirements of the PyCBC search to have a minimum FF of 0.965. Moreover, to precisely cover the whole parameter space in the future, we should increase the number of injections we generate.

Figure 5.14 shows the distribution of the recovered FF in the parameter space for NSBH-like injections. We present only the injections with a duration ą 0.15 seconds. Here, the recovered FF decreases to 0.80 in the high effective spin and mass ratio region. Considering the results obtained with the faithfulness simulation (Sec. 5.2.2), it was expected.

Results for the filtered BBH injections with m 1,2 P r3, 97s M d are provided in The recovered FF goes down to 0.80 in the high total mass region (m tot « 500M d ). Further investigations might be needed to precisely know if this is an artifact of the approximate duration cut we implemented, if this is due to a technical reason (for instance, the starting frequency being too high), or if there is some issue in the SEOBNRv4_ROM waveforms that do not well-describe this region of the mass space. However, this problematic region is well covered by cWB [START_REF] Drago | Coherent waveburst, a pipeline for unmodeled gravitational-wave data analysis[END_REF], so this is not an alarming problem.

. Conclusion

In conclusion, IMRPhenomXAS seems to behave pretty similarly to SEOB-NRv4_ROM at the corners of the search space with BNS injections and BBH injections with m 1,2 P r3, 97sM d . We saw some differences in the "extreme NSBH" space when the mass ratio becomes higher than a few tens, and the effective spin becomes larger than 0.5. The O3 PyCBC template bank was designed to have a minimum FF of 0.965, and here we found regions of the search space that go to smaller FF. With the faithfulness simulation, we found unphysical IMR-PhenomXAS waveforms in the high mass ratio -high spins region. Information provided downstream by the LVK waveform group made us understand that the model becomes unreliable for q > 18, which is a significant part of the search space targeted by PyCBC in O4. Indeed, the model is unreliable for these parameters since they're well out of the calibration region (NR simulations only up to q = 18).

In addition, the lack of duration function implemented in LALSimulation for IMRPhenomXAS at that time is problematic because this function is used in many PyCBC scripts. We wanted to ensure that IMRPhenomXAS duration function correctly works because the IMRPhenomD approximant gave us negative durations in the past when trying to calculate the duration with the difference between phase derivatives at the start frequency and a frequency near the merger for short duration signals:

T " 1 2π " δϕ δf ȷ f end fstart (5.2)
Given the simulations and considerations in this chapter, IMRPhenomXAS does not seem to represent a major improvement with respect to the TaylorF2 + SEOBNRv4_ROM combination used in O3. Future tests will be done for SEOB-NRv5_ROM, an updated version of SEOBNRv4_ROM used in O3 by PyCBC. Finally, additional investigations have been performed to compute the duration of the IMRPhenomXAS waveform "by hand". These investigations are described in Appendix D.

CHAPTER 6

STUDY OF THE EFFECT OF THE EARTH'S ROTATION ON BNS SIGNALS WITH THE NEXT GENERATION OF GW DETECTORS

In this last chapter, we look further into the future, particularly with Einstein Telescope (ET), with which we expect to detect " 7ˆ10 4 BNS signals per year [START_REF] Singh | Exploring compact binary populations with the Einstein Telescope[END_REF]. How to analyze its data is becoming an important question and is currently being investigated by the ET collaboration. There will be some important differences with respect to 2G detectors. For instance, studying the frequency dependence of the ET antenna pattern due to the much larger arm length than 2G detectors might be necessary (long-wavelength approximation [START_REF] Rakhmanov | High-frequency corrections to the detector response and their effect on searches for gravitational waves[END_REF] might no longer be valid). In our case, we decided to focus on the duration of BNS signals in the detector, which will significantly increase with ET compared to the 2G detectors. This chapter investigates how a longer signal duration will affect the BNS detections with ET.

. Third-generation GW detector: Einstein Telescope

Einstein Telescope (ET) has been introduced in Chapter 1 (1.2.3). As mentioned before, ET will be located a few hundred meters underground to reduce seismic noise and thus gain sensitivity. It also targets a broader range of frequencies ([1 Hz, 10 kHz]) with respect to the 2G detectors. One of the main designs investigated so far is a triangular shape detector composed of three interferometers with a 60-degree opening angle. This design is presented in Fig. 6.1, and we also show one of the three possible configurations in terms of sensitivity that are discussed for ET detectors, ET-D [START_REF] Hild | Sensitivity studies for third-generation gravitational wave observatories[END_REF], compared to aLIGOZeroDetHighPower, a popular model used for LIGO in Fig. 6

. Motivation for this work

The 2G GW detectors start having useful sensitivity at f start " 15 Hz. ET is expected to reach a lower start frequency (" 1 Hz in the most optimistic scenario). Thus, inspiral signals will spend a longer duration (hours to days, depending on the binary mass) in the detector bandwidth. Indeed, T chirp (Eq. 1.51) depends on the start frequency so, for instance, a GW170817-like signal would have lasted about one day in the ET detector bandwidth (with f start " 2 Hz). Until now, GW signals were observed in LIGO/Virgo only for a few seconds (for BBH), or minutes (for BNS), so we were considering the response of the 2G detectors (represented by their antenna patterns F `and F ˆ) constant in time, leading to Eq. 1.52 (Chapter 1). With ET, the Earth's rotation will not be negligible during the duration of the signal in the detector, and the approximation of the antenna patterns constant in time might no longer be valid. A priori, the BNS signals will be the most affected due to their low mass.

Different works [START_REF] Leong Chan | Binary neutron star mergers and third generation detectors: Localization and early warning[END_REF][START_REF] Zhao | Localization accuracy of compact binary coalescences detected by the third-generation gravitational-wave detectors and implication for cosmology[END_REF][START_REF] Singh | Constraining parameters of low mass merging compact binary systems with einstein telescope alone[END_REF] seem to indicate that considering the Earth's rotation might be necessary for constraining the BNS parameters and localizing the source accurately with ET; however, we do not know if the approximation of F `and F ˆconstant in time with ET will significantly impact the sensitivity of the search and affect the number of detected BNS signals. To investigate the effect of the Earth's rotation on BNS signals with ET, we need to quantify the loss of SNR due to the approximation. We can first simulate BNS signals coming from different sky locations with and without the approximation of the antenna patterns constant in time and then compute the match (Eq. 2.16) between the two waveforms. This can be easily done with the PyCBC code. However, it is computationally expensive and memory intensive, and it takes days to generate a thousand waveforms to compute a map of the match distribution over the right ascension-declination space. Here to reduce the computational cost, our approach consists of deriving an analytical calculation of the match between the waveforms with and without the approximation but using functions implemented in PyCBC to compute the ET antenna patterns, for instance. We can characterize our method as a semi-analytical approach. We first consider only one of the three ET detectors. Thus, in the following sections, F `and F ˆare the antenna patterns of one ET detector. Then, we start from Eq. 1.48 and 1.49 that gives us h `ptq and h ˆptq as follow:

. Analytic approach

h `ptq " Aptq p1 `cos 2 pıqq cospΦptqq (6.2) Using Eq. 1.50, the waveform with the approximation of the antenna patterns constant in time becomes:

h
h const ptq " Aptq b F 2 `p1
`cos 2 pıqq 2 `F 2 ˆ4 cos 2 pıq cospΦptq `ϕ0 q (6.7)

" Aptq B cospΦptq `ϕ0 q (6.8) with B and ϕ 0 constants equal to:

B " b F 2 `p1 `cos 2 pıqq 2 `F 2 ˆ4 cos 2 pıq (6.9) and ϕ 0 " arctan ˆ´F ˆ2 cospıq F `p1 `cos 2 pıqq ˙(6.10)

Here, F `and F ˆare the antenna patterns of ET that do not depend on the time and are computed at the coalescence time.

Computing the waveform in the frequency domain requires the Stationary phase approximation (SPA) [START_REF] Droz | Gravitational waves from inspiraling compact binaries: Validity of the stationaryphase approximation to the fourier transform[END_REF]. In the case of a (non-precessing, quasicircular, quadrupole-only) inspiral signal, the chirp gives a monotonic correspondence between time and frequency, and any slowly-varying function of time that acts as a multiplicative factor for the time-domain waveform amplitude (in our case, the antenna pattern) ends up multiplying the frequency-domain amplitude as well, after being evaluated at the time corresponding to the Fourier frequency.

Applied to our case, the SPA claims that:

hconst pf q " B ż dt Aptq cospΦptq `ϕ0 qe 2πif t (6.11)

» B ? π 2
Aptpf qqe ´iϕ 0 ˜2 :

Φptpf qq ¸1{2 e iΨpf q (6.12) 207 6.3. Analytic approach with Ψpf q " 2πf tpf q ´Φptpf qq ´π 4 (6.13) and t(f) tpf q " t c ´5 256 ˆGM c 3 ˙´5{3 pπf q ´8{3 (6.14)

We then need to derive the waveform considering time-dependent antenna patterns. Here F `,ˆp tq " F `,ˆp α, δ, ψ, tq. Since we make the approximation in one case and in the other, we do not, the maximum overlap might happen not at the true coalescence time and phase but at slightly different ones. In other words, using the approximated response might, in principle, lead to a bias in the coalescence time and phase. Thus, we now need to work with t 1 c " t c `∆t c and ϕ 1 c " ϕ c `∆ϕ c , which are the coalescence time and phase of the waveform without the approximation. h rot ptq " F `ptqh `ptq `Fˆp tqh ˆptq (6.15) Since the antenna patterns now depend on time, we can no longer bring the antenna patterns outside the Fourier integral as for hconst pf q, but we can divide hrot pf q into two integrals: We can still use the SPA in the case of hrot since we expect a slow variation of F ànd F ˆ. Then, we use the SPA for the two terms X and Y: with t rot pf q " tpt c `∆t c ; f q and Ψ rot pf q is computed at t rot pf q.

hrot pf q " ż tc
X » ? π 2

. Computation of the match

We know have explicit formulas for hrot and hconst . We then need to inject them into the match formula from Eq. 2.16 (Chapter 2) that can be written as: mph rot , h const q " max ∆tc,∆ϕc O (6.25

)
where O is the overlap between the two waveforms. In our case, the overlap is written as:

O " ℜ ´ş hrotpf q hconstpf q ‹ Snpf q df c´ş hrotpf q hrotpf q ‹ Snpf q df ¯´ş hconstpf q hconstpf q ‹ Snpf q df ¯(6.26)

" Z 1 ?
Z 2 Z 3 (6.27)

We simplify Z 1 , Z 2 and Z 3 separately. We first introduce the following notation:

P pt rot pf qq `iQpt rot pf qq " F `pt rot pf qqp1 `cos 2 pıqq `iF ˆpt rot pf qq2cospıq (6.28)

One can show that: Apt rot pf qq " Aptpf qq and ϕpt rot pf qq " ϕptpf qq Thus, Z 1 becomes: Finally, we maximize over ∆t c and ∆ϕ c . We numerically maximize over the coalescence time by searching in a ˘5 s window around t c , assuming that the difference ∆t c should be small. The maximization over ∆ϕ c is done following [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF].

Z 1 " π 4
We must also replace F `ptq and F ˆptq by their explicit formula. Since they depend on time, we can no longer use Eq. 1.52. Indeed Eq. 1.52 is specific to a coordinate system defined by the detector, not in equatorial coordinates where the detector is at an arbitrary and time-dependent orientation with respect to the coordinate axes. Thus, here we call a PyCBC function to evaluate the antenna patterns for a specific detector which allows us to add a time dependency.

. Results of the semi-analytical approach

h `and h ˆdepend on the inclination of the source. For example, the optimal orientation where the signal in the strongest is a face-on binary with an inclination ı " 0 ˝or a face-away with ı " 180 ˝. On the contrary, as mentioned in Chapter 1, Sec. 1.2.3, if ı " 90 ˝, only h `remains and h ˆis suppressed. Thus, we can suppose that the distribution of the match will depend on this inclination. As a consequence, we present here several maps for different values of ı (face-on: ı " 0 ˝and edge-on: ı " 90 ˝). The match is also PSD dependent, so we use the ET curve from [START_REF] Hild | Sensitivity studies for third-generation gravitational wave observatories[END_REF] presented in Fig. 6.2. For simplicity here we set ψ " 0.

In fig 6.3 and fig. 6.4, the top panel shows the map of the mismatch (1 ḿph rot , h const q) and we provide the map of the antenna pattern of the corresponding detector (ET or LIGO) in the bottom panel.

The Earth's rotation should not have a significant effect on the 2G detectors. Thus, as a check, fig. 6.3 shows the mismatch distribution of sources with inclination ı " 0 ˝using the LIGO PSD Model and starting at f low " 10 Hz. As expected, the mismatch is close to 0 over all sky except for the four blind spots of the detector. With ET (using ET PSD with f low " 2 Hz) in the top panel of Fig. 6.4, the regions with high mismatch are larger than for the 2G detectors and are following the behavior of the ET antenna patterns (bottom panel of Fig. 6.4). The effect of the Earth's rotation might play a role in high mismatch spread, but also we consider only one ET detector here, with the two arms separated by 60 The top panel in Fig. 6.5 provides the mismatch distribution for a source with ı " 90 ˝seen in ET. The high mismatch region follows four vertical curves. We find the same pattern in the bottom figure that shows the match map for 2G detectors. This behavior is explained by the antenna patterns of the detector (E1, for example, in Fig. 6.6) assuming that all the sources are edge-on ı " 90 ˝. In this case, only h `remains, and only F `matters. |F `| is presented in Fig. 6.6 in which we can see a similar behaviour. As a comparison, we provide the mismatch distribution of edge-on sources for H1 on the bottom panel in Fig. 6.5. Similar behavior is visible, but the vertical curves of high mismatch are thinner.

In conclusion, Fig. 6.4 and 6.5 show regions of the sky where the match between the signal with and without the approximation of F `and F ˆconstant in time is small. These low-match regions seem to follow the blind spots of the ET antenna patterns. To understand what happens in these regions, we represent the waveforms with ı " 0 ˝and ψ " 0 with the lowest match (m « 0.3) in Fig. 6.7. This figure shows the difference in the amplitude and phase of the two waveforms. The discrepancy in amplitude is pretty dramatic, and it happens at a frequency where the SNR integrand is very large (i.e. where the SNR is accumulated; for a better visualization see

. BNS population simulation

We saw regions of the sky where the match is small however, we still do not know if it will degrade the sensitivity of the search and how many signals we could miss because of the approximation. To answer this question, further investigations should be done. The idea is to simulate a population of BNS in the sky; for each BNS signal, we compute the SNR seen in ET with a template that models the Earth's rotation and a template that neglects it. Using a threshold on those SNRs, one can estimate the fraction of signal we lose, making the approximation.

We want to simulate a population of BNS, including the cosmological effect of the redshift. Indeed, the stars are not uniformly distributed in the Universe, so we need to generate a redshift distribution. We start from the hypothesis that the number of BNS at a specific redshift follows the star formation rate (SFR) density as a function of the redshift presented in Fig. 6.8. The top panel shows the SFR provided by the Madau-Dickinson function [START_REF] Madau | Cosmic star-formation history[END_REF] and the bottom panel shows the distribution from Schneider+ 2001 (older) [START_REF] Zhao | Determination of dark energy by the einstein telescope: Comparing with CMB, BAO, and SNIa observations[END_REF][START_REF] Cai | Estimating cosmological parameters by the simulated data of gravitational waves from the einstein telescope[END_REF][START_REF] Wang | Calibration of gamma-ray burst luminosity correlations using gravitational waves as standard sirens[END_REF]. If we want to use the Madau-Dickinson SFR, which is a more recent result than the Schneider distribution we need to notice that the SFR presented in the top panel of Fig. 6.8 is in M d yr ´1 Mpc ´3 so to estimate the number of sources as a function of the redshift, we need to consider the co-moving effect of the number of sources.

We start with the Schneider distribution as a first approach since, as explained, the Maudau-Dickinson function requires additional computations to be changed into a redshift distribution. However, we expect close results with both distributions. Thus, we construct a redshift distribution following the Schneider model defined as [START_REF] Cai | Estimating cosmological parameters by the simulated data of gravitational waves from the einstein telescope[END_REF], which already considers the co-moving effect of the number of sources density: We generate a random variable following the Schneider distribution and create a redshift distribution. Then, to construct a mass distribution, we recall that the masses seen in the detector (see Eq. 1.1, Chapter 1) are redshift dependent, leading to a higher mass in the detector than the mass in the source frame. Hence, according to Eq. 1.51 (Chapter 1), the duration of the signal in the detector is reduced. Thus, the Earth's rotation effect might be smaller than expected at first sight. Furthermore, ET will observe sources at higher redshift than LIGO/Virgo (z Á 1) due to its gain in sensitivity, so we cannot approximate the luminosity distance d L with H 0 d L " cz anymore. d L now depends on additional cosmological parameters, and the relation between the redshift and the luminosity distance becomes:

d L pzq " cp1 `zq H 0 ż z 0 dz 1 rΩ m p1 `z1 q 3 `ΩΛ p1 `z1 q 3p1`ωpz 1 qq s 1{2 (6.37

)
where ωpzq is related to the dark energy, and Ω m and Ω Λ are density parameters describing the matter density and the vacuum energy density, respectively. We build our distance distribution following the cosmological model from [START_REF]Planck 2018 results -vi. cosmological parameters[END_REF] (Planck 2018 cosmological parameters). Finally, we use uniform distribution between 0 and 2π over the right ascension and the polarization. The inclination follows a arccos Ur´1, 1s distribution and the declination follows a arcsin Ur´1, 1s distribution. We choose a uniform distribution between 1 and 3 M d over the source masses. We draw our BNS population by randomly choosing points in these distributions.

Eventually, we want to compare two quantities:

• The optimal SNR (see Eq. 2.12) taking into account the Earth's rotation:

ρ rot opt " d 4 ż 8 0 | hrot | 2
S n pf q df (6.38)

• The "approximated" SNR that would be seen (on average) using a template with the correct intrinsic parameters but neglecting the Earth's rotation:

ρ approx "

˙2

S n pf q df (6.41) By injecting tpf q (Eq. 6.14), Aptpf qq (Eq. 6.4), ϕptpf qq (Eq. 6.6) in Eq. 6.41 we get:

ρ 2 opt « 5π 24 π ´7{3 c 2 D 2 ˆGM c 3 ˙5{3 ż fmax f min f ´7{3 pF 2
`pt rot pf qqp1 `cos 2 pıqq 2 `F 2 ˆpt rot pf qq4cos 2 pıqq S n pf q df (6.42) Finally, we compute the square root of Eq. 6.42, which is the optimal SNR taking into account the Earth's rotation:

ρ opt « ˜5π 24 π ´7{3 c 2 D 2 ˆGM c 3 ˙5{3 ż fmax f min f ´7{3 pF 2
`pt rot pf qqp1 `cos 2 pıqq 2 `F 2 ˆpt rot pf qq4cos 2 pıqq S n pf q df ¸1{2 (6.43) We assume the GW is detected above an optimal SNR of 8 [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF][START_REF] Petrov | Data-driven expectations for electromagnetic counterpart searches based on LIGO/virgo public alerts[END_REF], which is a popular choice, and the signal is missed below that threshold. Drawing the cumulative rate of signals as a function of the optimal SNR will tell us how many signals will be missed making the approximation that would not have been missed without it. This is presented in Fig. 6.9. Here 1475 signals will be detected with the approximation compared to 1481 detected over 15000 without the approximation.

To check the validity of our computation, we represent ρ approx in the redshift -total mass space in Fig. 6.10. The sources with the highest ρ approx have low redshift, meaning they are close to us. This is expected since the closer the source, the higher the chance of detecting it. The small number of missed signals due to the approximation is directly visible in the bottom panel of Fig. 6.10. These missed signals are weak and have a ρ opt " 8; thus, even with a high match, it leads to a ρ approx À 8, explaining why they have been missed.

Considering these results, we can make two main observations:

• The difference in the number of detected signals with and without the approximation is very small. Moreover, the few missed signals with the approximation are weak signals with an optimal SNR close to our threshold.

• At first sight, one surprising observation is the poor number of detected sources, independently of the approximation. We simulated 15000 BNS sources, and we managed to detect only " 10% of them. One reason for the latter observation is that in our simulation, we only consider one of the three ET detectors (see Fig. 6.1). We expect to improve our results considering the three detectors. Moreover, each ET detector has its two arms separated by 60 ˝, compared to 90 ˝for LIGO/Virgo detectors, which lower the detector sensitivity if only one is considered. Indeed since ET will be composed of three detectors, it increases its sensitivity by ? 3 compared to a single detector, but the sensitivity of one single ET detector is smaller by a factor of sinp60 ˝q " ? 3{2 compared to an L-shaped detector [285]. Hence in the next section, we consider ET as a network of three detectors. We compute a coherent SNR following:

ρ 2 opt,tot " 3 ÿ A"1 ρ 2 opt,A (6.44)
where A represents each detector. By estimating the match for the three detectors, we can compute ρ 2 approx,tot similarly. The ET combined antenna pattern function is presented in Fig. 6.11. Contrary to LIGO/Virgo pattern or a single ET detector, there is no blind spot anymore. Hence, if the match distribution between the waveforms with and without the approximation still follows the antenna patterns, we expect to see a difference between the number of detected sources with and without the approximation that has not drastically changed compared to our previous results. However, to perform a more realistic simulation, we redo the simulation using the three ET detectors. Finally, even if we are looking for a ratio of detected sources with and without the approximation, we should increase the number of sources included in our population to be more accurate. 6.5 . ET as a network of three detectors 6.5.1 . Results The results considering the three detectors are presented in Fig. 6.12. Over 45000 injected sources, 14437 have an SNR above eight without the approximation against 14397 with the approximation. The sources not detected with the approximation but that would have been detected without the approximation are weak and have their ρ approx,tot close to 8, which is similar to the previous simulation when we consider only one ET detector. This leads to a ρ approx,tot close but below 8. Figure 6.12 first indicates that the Earth's rotation effect is negligible since we only miss a few signals using the approximation of the antenna patterns constant in time. Considering a source located in a region where the match is small and that has a very high ρ opt,tot , then, even with a small match, the source will probably be detected with the approximation. Similarly, if its optimal ρ opt,tot is very small, regardless of the value of the match, the BNS signal will not be detected.

. Discussion

Even if the effect of the Earth's rotation seems negligible from the point of view of the recovered SNR, there are still sources for which the match between the waveforms with and without the approximation is small. This can be problematic for the CBC pipeline consistency test. Indeed, we saw in Chapter 2 that CBC pipelines such as PyCBC perform a χ 2 (and compute a reduced-χ 2 (χ 2 r )) and reweight the SNR of the candidates depending on their χ 2 r value, following Eq. 2.17. The χ 2 r of a trigger is related to its SNR value [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF][START_REF] Gareth | Establishing significance of gravitational-wave signals from a single observatory in the pycbc offline search[END_REF]. Specifically, it depends on the match between the signal and the template waveform. The higher the match, the smaller the χ 2 . Therefore, χ 2 r will be close to one for signals that strongly match their template waveform. When the match between the template waveform (for which the Earth's rotation effect is not included) and the signal is small, it can lead to χ 2 r higher than 1. This effect is studied in [START_REF] Allen | FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries[END_REF]. A high mismatch can lead to a bad value of the χ 2 , resulting in a down-weighted SNR. Coming back to our simulation, even if the optimal SNR of the source is high (ρ opt,tot " 10 2 ), leading to ρ approx,tot ě 8, if the match is small, the χ 2 test can discard the candidate by down-weighting its SNR. Hence, our current CBC pipelines can be used for ET, and for now, the effect of the Earth's rotation seems to be negligible; however, further investigations will need to consider if our consistency tests can still be used as they are or if some changes are necessary to ensure we do not accidentally reject signals. In [START_REF] Singh | Exploring compact binary populations with the einstein telescope[END_REF], a solution proposed to avoid considering the Earth's rotation consists in analyzing the signal every five minutes, so the change in the antenna patterns due to the rotation of Earth is negligible for such duration.

CHAPTER 7

SUMMARY AND PERSPECTIVES

GW170817 -GRB 17081A paved the way for multi-messenger astronomy. This joint detection definitely connected sGRBs and NS mergers. However, fundamental questions remain, among others: are the properties of GW170817 common to all NS mergers or do they represent an exceptional case? What is the fraction of short GRBs associated with NS mergers? Can long GRBs also be associated with BNS mergers? Hence, more joint GW/GRB detections are needed to answer these questions, and for this purpose, we set up a deep analysis to search symmetrically for GW/GRB associations in LIGO/Virgo and Fermi/GBM data. Our method is based on Bayesian statistics and considers equally the GW and GBM candidate significance and the time and sky proximity between them. To ensure its validity, we first evaluated it on data covering O2 and found GW170817 -GRB 170817A with a satisfying joint significance (IFAR ą 1300 yr). By applying the method to O3 data, we did not find any significant associations that could originate from a common astrophysical source. The analysis is the deepest search we could implement so far. We used the state of the art of Fermi/GBM and GW data. Our method is inspired by Bayesian model selection which is understood and widely used. The background is computed with time slides which is also widely used and robust. The loudest association contains a confident BBH detection in the GW channel and a GBM trigger that likely corresponds to noise, which raises the problem of loud BBH signals altering the highest-ranked associations. Although we do not expect such a counterpart to BBH mergers, we did not want to miss interesting physics, and thus we have been entirely agnostic on the type of CBC we search for. With the next generation of GW detectors and the increase in detection rate, accidental coincidences between BBHs and GRBs will be much more frequent. One way to prevent loud BBH from limiting the significance of true associations is to separate by M chirp . Thus, instead of applying a strict cut on the masses, we have discussed the separation of the associations by chirp mass. This seems to impact differently the results of each considered CBC pipeline. This should be investigated in O4 since we expect more GW detections than in the previous runs. We have also discussed another way to prevent the contamination of the background by loud BBH signals, which consists in improving the sky localization. Indeed, it will remove accidental coincidences demonstrating that the two candidates are spatially unrelated and avoid applying a trial factor to account for the number of independent searches. Other improvements can be explored to reduce the number of accidental coincidences we expect in the future observing runs, and in particular, a more realistic time offset prior. We suggest using the calculation proposed in [START_REF] Zhang | The delay time of gravitational wave -gamma-ray burst associations[END_REF], where the time delay between the GW and the GRB is written as a function of the time for the central engine to launch a relativistic jet, the time for the jet to penetrate through and break out from the surrounding medium, and the time after breakout for the jet to reach the energy dissipation radius where the observed γ-rays are emitted. Finally, a new calculation of the GW Bayes factor can be investigated, and in particular, we could use the p astro of the candidates.

To explore the potential improvement of the GW search sensitivity, I have been involved in the GW data analysis within the PyCBC group. I first gained expertise by participating in the PyCBC standard CBC and the SSM search during O3. I analyzed segments of data called chunk 39 and chunk 8, respectively for the PyCBC offline and sub-solar mass search. Regarding the PyCBC offline analysis, a confident triple-detector BBH event has been found in the chunk. The event is now part of the GWTC-3 catalog [START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF] and has also been used to estimate the Hubble constant together with seven other selected GW events. In terms of subsolar mass search, no significant candidate has been found neither in chunk 8 nor in all chunks allowing to put constraints on the fraction of DM formed with PBH.

We also explored the generation of a new template bank for O4 PyCBC offline analysis. Having accurate waveforms is crucial to reach a satisfying search sensitivity. For this purpose, we investigated IMRPhenomXAS approximant behavior over the PyCBC search parameter space. We found odd behavior at high mass ratio and high effective spins. This result, together with other investigations, led us not to choose IMRPhenomXAS for O4 but SEOBNRv5_ROM approximant, an upgraded version of SEOBNRv4_ROM, the approximant used in O3. On a computational level, we contributed to the PyCBC code development by creating a workflow that compares two approximants evaluated on a set of injections.

Furthermore, we presented a project aiming to discriminate glitches from astrophysical signals. We obtained mixed results: the metric is powerful for heavy mass systems and inefficient for low mass signals. We have ideas for improvement, such as computing the metric only for the tiles in a predetermined window around the coalescence time of the PyCBC trigger. Once these changes have been made and their effectiveness tested, the metric could become a powerful indicator of the trigger's astrophysical or instrumental/environmental origin. Thus, it could be used in the GW Bayes factor calculation within the deep GW/GRB search we performed.

Furthermore, we have been interested in the next generation of GW detectors to NS mergers. Einstein Telescope expects more than 10 4 BNS detections per year, taking multi-messenger astronomy to a new level. Until now, we considered the detector response of a signal constant in time due to the short duration spent by a GW in the detector bandwidth. Thus, we always neglected the effect of the Earth's rotation, considering the antenna pattern of the detector constant in time. We have shown that this approximation can still be made with Einstein Telescope. We first used only one of the three ET detectors and then considered ET as a network of three detectors. We have drawn a BNS population, including the cosmological effect of the redshift. We computed the match between the waveforms and the optimal SNR with and without the approximation. We found that the number of signals missed due to the approximation seems negligible, considering the number of BNS signals that Einstein Telescope expects to detect. However, small matches between the waveform with and without the approximation can result in bad χ 2 values that will accidentally reject signals. Further computations should be done before concluding on the need to take into account the effect of the Earth's rotation.

Titre:

  Exploration de la physique des fusions d'étoiles à neutrons avec les ondes gravitationnelles et les sursauts gamma.................................................................................................................. Mots clés: Fusion d'étoiles à neutrons, ondes gravitationnelles, sursaut gamma, Fermi/GBM, LIGO, Virgo

Title:

  Exploring the physics of neutron star mergers with gravitational waves and gamma-ray bursts.................................................................................................................. Keywords: Neutron star mergers, gravitational waves, gamma-ray burst, Fermi/GBM, LIGO, Virgo

Introduction 1

 1 Gravitational waves and Gamma-ray Bursts in the Era of multi-messenger Astronomy 1.1 August 17 th , 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 An emblematic history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 GW170817 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 The γ-ray counterpart: GRB 170817A . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Other counterparts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.5 Implication for fundamental science . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.6 How lucky were we to detect GW170817? . . . . . . . . . . . . . . . . . . . . . 1.2 Gravitational waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 General relativity and gravitational waves . . . . . . . . . . . . . . . . . . . . . 1.2.2 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Detection of gravitational waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Gamma-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 History and model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Characteristics of GRBs and pieces of evidence for two different progenitors . . 1.3.3 GRB Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Open questions about GRBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 The purpose of GW-GRB joint searches . . . . . . . . . . . . . . . . . . . . . . . . . .

0. 3 .Figure 1 :

 31 Figure 1: Rapport de sensibilités (VT) de l'analyse PyCBC sur le segment de données chunk 2 avec (numérateur) et sans repondération du SNR avec les triggers Omicron (dénominateur) pour trois choix de seuil le taux inverse de fausse alarme, IFAR [yr].Le taux de fausse alarme FAR (ou inverse FAR, IFAR) d'un candidat donne une idée quantitative de la fréquence à laquelle le bruit génère un candidat. Il est défini comme le taux de bruit de fond dont la statistique de classement est égale ou supérieure à celle observée pour le candidat en question[START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF][START_REF] Morrá | False alarms induced by gaussian noise in gravitational wave detectors[END_REF]. Elle donne donc une interprétation fréquentiste à la statistique de classement.

Figure 2 :

 2 Figure 2: Taux cumulé en fonction de l'IFAR (en années) pour les coïncidences sans décalage temporel (en trait plein).

0. 3 .

 3 Nouvelles détections OG/GRB conjointes? -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 Time [seconds] from 2019-09-15 23:57:02.7 UTC (1252627040.7)

Figure 3 :

 3 Figure 3: Haut: Spectrogramme montrant GW190915_235702. Taux cumulé en fonction de l'IFAR (en années) pour les coïncidences sans décalage temporel (en trait plein) pour les candidats GstLAL (milieu gauche), MBTA (bas) et PyCBC (milieu droite).

Figure 4 :

 4 Figure 4: Gauche : Carte du décalage entre les formes d'onde avec l'approximation du diagramme d'antenne constant dans le temps et les formes d'onde sans approximation, dans le plan d'ascension droite -déclinaison, lorsque la source est face à l'observateur (ı " 0 ˝) avec le télescope d'Einstein commençant l'observation à 2Hz. Droite: Résultats finaux comparant le SNR optimal du signal avec et sans l'approximation des diagrammes d'antenne constants dans le temps et en considérant l'ET comme un réseau de trois détecteurs. Fraction cumulative en fonction du SNR optimal pour une population BNS de " 45000 signaux.

Figure 1 . 1 :

 11 Figure 1.1: GW170817 seen from the LIGO Hanford, LIGO Livingston, and Advanced Virgo detectors. Left panel: Top: Spectrogram of L1 data with the blip glitch overlapping the chirp. Bottom: glitch subtraction. Right panel: Spectrogram showing H1, L1, and V1 data. The GW170817 signal is visible in both LIGO detectors, and one can notice scattered light glitches above 150 Hz in Virgo data. Figures extracted from [7].

Figure 1 . 2 :

 12 Figure 1.2: Top panel: Map showing the reconstructed LIGO/Virgo sky location of GW170817. Bottom right panel: the a posteriori luminosity distance distribution from three GW localization analyses: one using H1 and L1 (blue) and two using the H1, L1, and V1 (light and dark green). Figure extracted from [7].

1. 1 .Figure 1 . 3 :

 113 Figure 1.3: Display of the joint detection of GW170817 and GRB 170817A. The three top panels show the light curve of GRB 170817A in different energy bands with Fermi/GBM and INTEGRAL/SPI-ACS. The bottom panel represents the spectrogram of GW170817 with combined L1 and H1 data. Extracted from [7].

1. 1 .Figure 1 . 4 :

 114 Figure 1.4: Joint sky localization of GW170817 and GRB 170817A using the three GW detectors, Fermi/GBM, and INTEGRAL observations. The two right panels show the images of the Swope and DLT40 telescopes that led to the discovery of the optical signal [48].

Figure 1 . 5 : 1 . 1 .

 1511 Figure 1.5: Summary of the 170817 observations. The upper panels: the combined spectrogram of GW170817 in the GW detectors (left); GW170817A light curves from Fermi/GBM and INTEGRAL (middle); spectrum from different optical ground-based spectrographs (right). The middle panel: timelines of observations. The bottom panels: optical images of AT2017gfo. On the right are the images of the X-ray counterpart detection (upper) and the radio afterglow (bottom).Figure extracted from [49].

Figure 1 . 6 :

 16 Figure 1.6: Three possible outflow structures attempting to explain the observed properties of GRB 170817A, taken from [47].

1. 1 .Figure 1 . 7 :

 117 Figure 1.7: Kilonova light curve from AT2017gfo and the best-fit model of three components (blue-red-purple). Figure taken from [67].

1. 1 .Figure 1 . 8 :

 118 Figure 1.8: Multi-messenger matrix showing the relation between the range of expected EM counterparts of BNS mergers (vertical axis) and the GW-measured chirp mass. Extracted from [71].

Figure 1 . 9 :

 19 Figure1.9: Posterior distribution for H 0 inferred thanks to the kilonova KN170817 detection in coincidence with GW170817. The dashed vertical line represents the 68% interval, and the dotted one the 95% interval, taken from[START_REF] Bp | A gravitational-wave standard siren measurement of the hubble constant[END_REF].

1. 2 .

 2 Figure 1.10: Top: Sketch of a monochromatic GW of pulsation ω = 2π/T propagating along the z direction. Bottom: the effects of the + and ˆpolarizations on a ring of freely falling particles (plane orthogonal to the z-direction) in a local inertial frame. Figure from [82].

  is shown in Appendix A, Fig. A.1.

Figure 1 . 11 :

 111 Figure 1.11: Sketch showing the three stages of a compact binary merger: the inspiral, the merger, and the ringdown. The bottom panel represents the expected waveform of the GW signal during the inspiral part.

Fig. 1 . 11 .

 111 An example of the time evolution of the GW frequency is given in the right-hand figure of Fig. 1.1, where the spectrogram of GW170817 signal in the two LIGO detectors is provided.

Chapter 1 . 52 Figure 1 . 13 :

 152113 Figure 1.13: Optical scheme of GW interferometers.

  1.13) in Virgo setup.

1. 2 .

 2 Figure 1.14: Sensitivity curve of LIGO Hanford, LIGO Livingston, and Advanced Virgo during O3b. The black curve represents the PSD model.

Figure 1 . 2 ``F 2

 122 Figure 1.15: GW antenna pattern function for Advanced Virgo detector plotted at the end of O3b (2020-03-09 03:01:21) and setting the polarization to 0. The color map here represents the root mean square of the antenna pattern, F unpolarized " b F 2 ``F 2 ˆover

Figure 1 . 16 :

 116 Figure 1.16: Current plan of observations for the LIGO-Virgo-KAGRA collaboration.Here the BNS range is estimated for O4 and O5.

Figure 1 . 17 :

 117 Figure 1.17: Schematic description of the fireball model of GRBs (taken from [125] and modified).

Chapter 1 . 60 Figure 1 . 18 :

 160118 Figure 1.18: An overview of the expected GW and EM signatures from minutes before until years after the merger (taken from [130]).

Figure 1 . 19 :

 119 Figure 1.19: Light curves of 6 bright gamma-ray bursts detected by BATSE (Modified but extracted from[START_REF] Asaf Pe'er | Physics of gamma-ray bursts prompt emission[END_REF]). This sample of light curves shows short and long GRB events.

Figure 2 .

 2 Figure 2. from GRB 170817A Associated with GW170817: Multi-frequency Observations and Modeling of Prompt Gamma-Ray Emission null 2018 APJL 852 L30 doi:10.3847/2041-8213/aaa2f6 https://dx.doi.org/10.3847/2041-8213/aaa2f6 © 2018. The American Astronomical Society. All rights reserved.

Figure 2 .

 2 Figure 2. from GRB 170817A Associated with GW170817: Multi-frequency Observations and Modeling of Prompt Gamma-Ray Emission null 2018 APJL 852 L30 doi:10.3847/2041-8213/aaa2f6 https://dx.doi.org/10.3847/2041-8213/aaa2f6 © 2018. The American Astronomical Society. All rights reserved.

Figure 3 .

 3 Figure 3. from GRB 170817A Associated with GW170817: Multi-frequency Observations and Modeling of Prompt Gamma-Ray Emission null 2018 APJL 852 L30 doi:10.3847/2041-8213/aaa2f6 https://dx.doi.org/10.3847/2041-8213/aaa2f6 © 2018. The American Astronomical Society. All rights reserved.

Figure 3 .

 3 Figure 3. from GRB 170817A Associated with GW170817: Multi-frequency Observations and Modeling of Prompt Gamma-Ray Emission null 2018 APJL 852 L30 doi:10.3847/2041-8213/aaa2f6 https://dx.doi.org/10.3847/2041-8213/aaa2f6 © 2018. The American Astronomical Society. All rights reserved.

Figure 1 . 20 :

 120 Figure 1.20: Photo spectrum GRB 170817A (modified but extracted from [142]). Left figure: first pulse; Right figure: Second pulse.

Figure 1 . 21 :

 121 Figure 1.21: Schematic view of the distribution of 227 long and short GBM GRBs and their corresponding BATSE GRBs in the E obs peak -Fluence, E obs peak -Peak Flux planes.Horizontal blue dashed line: lower limit for the GBM instrument. Horizontal red dashed line at "50 keV: lower limit for the BATSE instrument. Horizontal red dashed line at "1 MeV: upper limit for BATSE (for the GBM, there is no upper limit in this plane). The vertical dashed line (left panel): an example of fluence selection. Dashed curve (right panel): photon flux selection criterion adopted by BATSE. Extracted from[START_REF] Nava | Spectral properties of long and short gamma-ray bursts: comparison between batse and fermi bursts[END_REF]

Figure 1 . 22 :

 122 Figure 1.22: Classification of 1966 BATSE GRBs. This distribution shows a bimodality in the spectral peak energy -observed duration plane.

Figure 1 . 23 :

 123 Figure 1.23: Spectrally separated waterfall plots for GRB 130502A (top) and GRB 170111B (bottom) produced by the GBM Targeted Search. Each time window is colored with the log-likelihood ratio (LLR). Extracted from [162].

Chapter 1 .Figure 1 . 24 :

 1124 Figure 1.24: Overview of several mission instruments. Left: Fermi Gamma-ray Space Telescope. Middle-top: SVOM space-based instrument. Middle-bottom: Neil Gehrels Swift Observatory. Right: High Energy Stereoscopic System.

Figure 1 .

 1 Figure 1.25: Left: Swift/BAT (a) and Fermi/GBM (b) gamma-ray light curves of GRB 211211A. Right: Fermi/GBM catalog (c): duration versus hardness distribution (taken from [21])

Figure 2 . 1 :

 21 Figure 2.1: Flowchart summarizing the different steps of the matched filtering in PyCBC.Extracted from[START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF].

Figure 2 . 2 :

 22 Figure 2.2: Masses (top) and spins (bottom) covered by the PyCBC template bank PyCBC in O3.

Figure 2 . 3 :

 23 Figure 2.3: Spectrograms showing different glitch morphologies encountered in GW data.Extracted from[START_REF] Aasi | The characterization of virgo data and its impact on gravitational-wave searches[END_REF].

Figure 2 . 4 :

 24 Figure 2.4: Example showing a time series of GW data in the vicinity of a glitch. In red, the time series has been gated around the time of the glitch. In blue, the data has not been gated. Extracted from [22].

Figure 2 . 5 :

 25 Figure 2.5: Sketch showing the method based on time slides between the three GW detectors used to estimate the background. Here, L1 and V1 data are fixed (dotted rectangle), and H1 data are shifted. Taken from [205] and modified.

Figure 2 . 6 :

 26 Figure 2.6: Ratio of search sensitivities (VT) comparing the three-detector HLV analysis and two-detector HL analysis in colored Gaussian noise, for four choices of inverse falsealarm rate (IFAR) threshold. Here the injections used to estimate sensitivity have been split into BNS and BBH bins. Taken from [205].

Figure 2 . 7 :

 27 Figure 2.7: Spectrogram around a single-detector trigger in L1 data from chunk 39. This trigger is likely due to scattered light.

Figure 2 . 8 :

 28 Figure 2.8: Spectrogram around a single-detector trigger in H1 data from chunk 39.This trigger is likely due to a blip glitch. This is the loudest single-detector trigger with a blip shape with a duration of ă 0.6 s.

Figure 2 . 9 :

 29 Figure 2.9: Spectrogram around a single-detector trigger in V1 data from chunk 39. This trigger is likely due to repeated blip glitches.

Figure 2 . 10 :

 210 Figure 2.10: Spectrogram around single-detector triggers in V1 data from chunk 39 that have a chirpy morphology.

Figure 2 .

 2 Figure 2.11: Top-Left: BBH missed (red crosses) and found injections (from yellow to blue dots) distribution in the chirp mass -optimal SNR plane. Top-Right & Bottom: spectrograms of the loudest (in terms of optimal SNR) BBH missed injections. There are repeated blips on top of the injection.

Figure 2 . 12 :

 212 Figure 2.12: Cumulative histogram of the IFAR (yr) that compares the foreground (blue triangles) to the expected background (dashed line) in chunk 39. GW200311_115853, the most significant foreground association, is represented by the purple triangle.

Figure 2 . 13 :

 213 Figure 2.13: Spectrograms showing GW200311_115853 in all available detectors at the trigger time. Top: H1 data. Middle: L1 data. Bottom: V1 data.

Figure 2 . 14 :

 214 Figure 2.14: Sky localization of GW200311_115853 inferred with Bayestar.

ă m 1 ă 10 • 1 • 1 •

 1011 Primary mass [M d ]: 0.2 Secondary mass [M d ]: 0.2 ă m 1 ă Mass ratio: 0.1 ă q ă Spin: -0.1 ă χ k ă 0.1 if m k ă 0.5 M d and -0.9 ă χ k ă 0.9 if m k ą 0.5 M d • Source uniform in comoving volume • Isotropically distributed on the sphere • Randomly oriented During the beginning of my PhD I have been involved in the O3 SSM search using the PyCBC pipeline and, like the previous work on chunk 39, I analyzed one segment of data, chunk 8, that lasted 7.240 days during the first part of O3 (O3a), from UTC 2019-05-29 10:35:24 to 2019-06-05 16:21:36. As previously, to look at the results, we first check the closed box (single-detector triggers and missed injections), and then we can open the box and look at the foreground results.

Figure 2 . 15 :

 215 Figure 2.15: Cumulative histogram of the IFAR (yr) that compares the foreground (blue triangles) to the expected background (dashed line) in chunk 8 of the sub-solar mass search.

Figure 2 . 16 :

 216 Figure 2.16: Spectrograms showing the most significant foreground association of chunk 8 for the sub-solar mass search in all available detectors at the time of the trigger. Topleft: H1 data. Top-right: L1 data. Bottom: V1 data.

Figure 2 . 17 :

 217 Figure 2.17: Constraints on the fraction of dark matter in PBHs using the full O3. The horizontal axis shows the source frame mass of the black hole. Extracted from [224].

Figure 3 . 1 :

 31 Figure 3.1: Example showing tiled time-frequency planes for two values Q = 4 (left) and Q = 20 (right), extracted from [24].

Figure 3 . 2 :X 8 ´8

 328 Figure 3.2: Omicron scan showing a glitch in L1. Only the tiles with ρ ą 5 have been kept. Figure from Florent Robinet.

Figure 3 . 3 :

 33 Figure 3.3: Distribution of a sample of GW signals and a sample of background (singledetector triggers) in the log 10 pDuration rssq ´log 10 pMetric rssq plane.

Figure 3 . 5 :

 35 Figure 3.4: Top: Spectrogram showing the PyCBC template (white) of GW200311_115853 and the associated Omicron triggers (from yellow to red tiles). Bottom: Distribution of the time-distance d t for GW200311_115853. In the legend, the duration [s] is the template duration. The metric σ and the mean M are in seconds.

Figure 3 . 6 :

 36 Figure 3.6: Sketch showing choices we made about the metric computation: (1) Discard the tiles with a frequency below the f low of the PyCBC waveform. (2) Extend the CBC track to the infinite. (3) Consider only the Omicron triggers in which at least one tile overlaps the track.

Fig. 3 .Figure 3 . 7 :

 337 Fig. 3.8 compares the metric distribution for single-detector triggers and injections. Here we show together the BNS, BBH, and NSBH simulated signals that have been injected in chunk 39 data (see Chapter 2, Sec. 2.2.1). Although most

Figure 3 . 8 :

 38 Figure 3.8: Comparison of the distribution of the injections and the data of chunk 39 in the Metric [s] -Duration [s] plane.

Figure 3 . 9 :Figure 3 . 10 :

 39310 Figure 3.9: Ratio of the search sensitivities (VT) comparing the PyCBC analysis of chunk 39 with and without the metric application for three choices of IFAR threshold.

Chapter 3 .

 3 Improvement of the search sensitivity to gravitational waves 112

Figure 3 . 11 :

 311 Figure 3.11: Spectrogram showing one loud PyCBC BNS injection in L1 and its corresponding tiles.

Figure 3 .

 3 Figure 3.14 shows the ratio of the VT before and after the reweighting. The method still seems powerful for heavy mass injections. However, for injections within[20,

Figure 3 . 12 :

 312 Figure 3.12: Training of the KDE with several chunks in the logpDuration rssq ĺogpMetric rssq plane. Top: background distribution (chunk 33-34-36-36-38) (left); associated probability density function (PDF) (right). Middle: injections distribution (chunk 38) (left); associated PDF (right). Bottom: ratio of the PDFs (weights) in the logpDuration rssq ´logpMetric rssq plane.

Figure 3 . 13 :

 313 Figure 3.13: Evaluation of the KDE: weight distribution of L1 chunk 39 single-detector triggers (left) and injections (right) in the log(Metric)-log(Duration).

Figure 3 . 14 :

 314 Figure 3.14: Ratio of the search sensitivities (VT) comparing the PyCBC analysis of chunk 39 with and without the reweighting for three choices of IFAR threshold.

Figure 3 . 15 :

 315 Figure 3.15: Spectrogram showing a glitch that has not been gated by the search overlapping an NSBH injection causing a large metric value. This injection stands in the background region (in blue) in the bottom panel of Fig. 3.12.

3. 4 .Figure 3 . 16 :

 4316 Figure 3.16: Evaluation of the KDE: weight distribution of L1 chunk 2 single-detector triggers (left) and injections (right) in the log(Metric)-log(Duration).

Figure 3 . 17 :

 317 Figure 3.17: Spectrogram showing scattered light glitches from chunk 2 standing in the noise-like region in Fig. 3.16.

Figure 3 . 18 :

 318 Figure 3.18: Ratio of the search sensitivities (VT) comparing the PyCBC analysis of chunk 2 with and without the reweighting for three choices of IFAR threshold.

3. 5 .

 5 Investigations of the noise-like region at low metric value and template duration «3 s metric application is not particularly useful for BNS and NSBH signals, mainly because of glitches overlapping the long-duration injections, as visible in Fig.3.15.

  3.14). Indeed, about "2000 chunk 39 L1 (BBH and NSBH) injections with m tot P[START_REF] Pierre | The pierre auger cosmic ray observatory[END_REF][START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF] M d stand in the circle region of Fig 3.12.

Figure 3 . 19 :

 319 Figure 3.19: Bottom panel of Fig. 3.12 where we circle an odd noise-like region.

  3.19. The training removing the data around GW200202_154313 is visible in Fig. 3.21. The blue region at low metric and duration «3 s has disappeared. When we evaluate the KDE on chunk 39 single-detector and injections (Fig. 3.22), the injections in this region are no longer down-weighted. The same change is visible in chunk 2 reweighted, but we have not provided the figure here since it is similar to chunk 39.Because of computational reasons, we have not yet explored the improvement of PyCBC search sensitivity removing the data around GW200202. Together with the application of a ˘1 s window around the time of the PyCBC trigger (see previous section 3.4) will be the subsequent investigations.

121 3. 5 .

 1215 Investigations of the noise-like region at low metric value and template duration «

Figure 3 . 20 :

 320 Figure 3.20: Top: Spectrogram around GW200202_154313 showing the trigger responsible for the circled noise-like region in Fig. 3.19. Bottom: Spectrogram around GW200202_154313 showing the CBC track and the corresponding Omicron tiles.

Figure 3 . 21 : 3 . 5 . 3 sFigure 3 . 22 : 4 SEARCHING

 3213533224 Figure 3.21: Training of the KDE with several chunks in the logpDuration rssq ĺogpMetric rssq plane removing data around GW200202_154313. Top: background distribution (chunk 33-34-36-36-38) (left); associated probability density function (PDF) (right). Middle: injections distribution (chunk 38) (left); associated PDF (right). Bottom: ratio of the PDFs (weights) in the logpDuration rssq ´logpMetric rssq plane.

Chapter 4 .

 4 Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 126

Figure 4 . 1 :

 41 Figure 4.1: Waterfall plots displaying GRB 170817A. Top: full triggers. Bottom: Result of the clustering.

Chapter 4 .

 4 Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 128

Chapter 4 .

 4 Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 130

  at Duration [s]=0.064 2D KDE method at Duration [s]=0.256 2D KDE method at Duration [s]=1.024 2D KDE method at Duration [s]=2.048 2D KDE method at Duration [s]=8.192 previous 1D KDE method

Figure 4 . 2 :

 42 Figure 4.2: GBM Bayes factor computed with a 2D KDE training with real data over the LLR and GBM duration [s]. Left: Behaviour of the GBM Bayes Factor Q γ computed with a 2D KDE fitted with real data. Right: Comparison between the GBM Bayes Factor Q γ computed with the 2D KDE (solid lines) and the 1D KDE trained on LLR and used in [240] (dashed line).

Figure 4 . 3 :

 43 Figure 4.3: Examples of the spatial overlap I Ω for an all-sky prior (Eq. 4.13). Extracted from [248].

Chapter 4 . 136 - 4

 41364 Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data

Figure 4 . 4 :

 44 Figure 4.4: Example of a GW-GBM association strongly suppressed by the Earth-Avoiding prior. Top: sky localization of the GW trigger. Middle: sky localization of the GBM trigger. The solid grey line represents the Galactic Plane and the yellow star in the GBM skymap represents the Sun. The blue region is the Earth's location. The three contour levels represent the 3σ, 2σ, and 1σ credible regions. Bottom: spectrogram of L1 data around the GW trigger.

Chapter 4 .Figure 4 . 5 :

 445 Figure 4.5: Description of the association computation, no time shifting for the foreground (left) and time shifting the GBM triggers for the background (right).

4. 3 .

 3 Check the validity of the method against GW170817

Figure 4 . 6 :

 46 Figure 4.6: Background associations computation. In the final analysis, STEP=70 s and time shifts go from -180070 to 180000. In the first tests, STEP=100 s and time shifts go from -50000 to 50 000 s.

Figure 4 . 7 :

 47 Figure 4.7: Flowchart of the workflow that searches for GW-GRB associations in LIGO/Virgo and Fermi/GBM data. The GW livetimes mean the available observing time of the GW triggers here.

4. 3 .

 3 Check the validity of the method against GW170817 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Time [seconds] from 2017-01-27 06:47:17.804 UTC (1169534855.804) ] from 2017-01-27 06:47:17.804 UTC (1169534855.804)

Figure 4 . 8 :

 48 Figure 4.8: Display of the 1 st highest ranked background association with the naive time statistic. The GBM trigger here is related to GRB 170127C, and no GW confident event has been found at the GPS time of the GW trigger. Top Left: Spectrogram representing the GW trigger in H1 detector. Top Right: Spectrogram representing the GW trigger in L1 detector. Bottom: Waterfall plot representing the GBM trigger.

Chapter 4 .

 4 Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 144

Figure 4 . 9 :

 49 Figure 4.9: Background rate as a function of the naive time ranking statistic. Left: associations with a hard GBM spectrum. Middle: associations with a normal GBM spectrum. Right: associations with a soft GBM spectrum. The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

Figure 4 . 10 :

 410 Figure 4.10: Background rate as a function of the Bayesian ranking statistic with configuration n ˝1. Left: associations with a hard GBM spectrum. Middle: associations with a normal GBM spectrum. Right: associations with a soft GBM spectrum. The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

Figure 4 . 12 :

 412 Figure 4.12: Cumulative rate as a function of the IFAR [yr] for the foreground (in solid line) with configuration 1. The foreground represents associations between Fermi/GBM candidates and LIGO candidates with no time shift.

Chapter 4 .

 4 Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 150

Figure 4 . 14 :

 414 Figure 4.14: Cumulative rate as a function of the IFAR [yr] for the foreground (in solid line) with configuration 2 (adding Virgo contribution). The foreground represents associations between Fermi/GBM candidates and LIGO candidates with no time shift.

Figure 4 . 15 :

 415 Figure 4.15: Skymaps of GW170817-GRB 170817A adding Virgo contribution. Left: GBM sky localization. Right: GW sky localization. The grey solid line represents the Galactic Plane and the yellow star in the GBM skymap represents the Sun. The blue region is the Earth's location. The three contour levels represent the 3σ, 2σ, and 1σ credible regions.

Figure 4 . 16 :Configuration 3 :

 4163 Figure 4.16: Background rate as a function of the Bayesian ranking statistic (configuration 3), zoom on the right edge of the curve. Left: associations with a hard GBM spectrum. Middle: associations with a normal GBM spectrum. Right: associations with a soft GBM spectrum. The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

Figure 4 .

 4 Figure 4.16 represents how the statistic behaves for the background associations with configuration 3. The behavior of the background is pretty similar to the previous configurations (Fig. 4.10), and most of the background has an association rank smaller than 1. Table4.6 shows the properties of the first four top-ranked background associations. In the first row, in the GBM channel, the candidate has a signal-like Q γ . It is GRB n°510119909[START_REF]GRB Coordinates Network[END_REF]. On the GW side, the candidate has a signal-like Q g , but it is more likely to be noise looking at the H1 and L1 spectrograms and considering that we did not find any GW confident event at the GPS time of this trigger. Hence, as previously, the highest-ranked background associations comprise associations with signal-like GBM candidates and GW candidates that are more likely to be noise. It is composed of very diverse GBM triggers, bright and less bright GBM triggers (large and small LLR), a large range of duration (going from 0.064s to 8.192s), and all spectral values (hard, normal, and soft). Again, this diversity reassures us.Figure4.18 shows the cumulative rate of the foreground associations as a function of their IFAR. As for configurations 1 and 2, Fig.4.18 has been plotted when computing the significance of the foreground by separating the associations by pairs of GBM spectral value and GBM duration. One association deviates at 3σ from the background with an IFAR " 28 yr. Table4.7 shows the first four most significant foreground associations with configuration 3. Here, the top 2 are related to GW170817 -GRB 170817A. The second association corresponds to the soft tail of GRB 170817A[START_REF] Abbott | Observation of gravitational waves from a binary neutron star inspiral[END_REF][START_REF] Goldstein | An ordinary short gamma-ray burst with extraordinary implications: Fermi-GBM detection of GRB 170817a[END_REF]. The display of GW170817 -GRB 170817A with

  ratio -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Time [seconds] from 2017-02-28 14:34:24.418 UTC (1172327682.418) 3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Time [seconds] from 2017-02-28 14:34:24.418 UTC (1172327682.418)

Figure 4 . 17 :

 417 Figure 4.17: Display of the highest ranked background association with configuration 3. Top: GBM trigger display (Left: Waterfall plot of the GBM trigger, Right: Waterfall plot of the clustered GBM trigger). Middle: GW trigger display (Left: H1 spectrogram, Right: L1 spectrogram) Bottom: Sky localization of the association (Left: GBM trigger, Right: GW trigger). The grey solid line represents the Galactic Plane and the yellow star in the GBM skymap represents the Sun. The blue region is the Earth's location. The three contour levels represent the 3σ, 2σ, and 1σ credible regions.

Figure 4 . 18 :

 418 Figure 4.18: Cumulative rate as a function of the IFAR [yr] for the foreground (in solid line) with configuration 3. The foreground represents associations between Fermi/GBM candidates and LIGO candidates with no time shift.

Figure 4 . 19 :

 419 Figure 4.19: Display of the most significant foreground association with configuration 3 corresponding to GW170817 -GRB 170817A. Top: GBM trigger display (Left: Waterfall plot of the GBM trigger, Right: Waterfall plot of the clustered GBM trigger). Middle: GW trigger display (Left: H1 spectrogram, Right: L1 spectrogram after the glitch subtraction.) Bottom: Sky localization of the association (Left: GBM trigger, Right: GW trigger). The grey solid line represents the Galactic Plane and the yellow star in the GBM skymap represents the Sun. The blue region is the Earth's location. The three contour levels represent the 3σ, 2σ, and 1σ credible regions.

Figure 4 . 20 :

 420 Figure 4.20: Cumulative rate as a function of the IFAR [yr] for the foreground (in solid line). The foreground represents associations between Fermi/GBM candidates and LIGO triggers with no time shift. Here the significance is computed with configuration 4: without separating the associations by pairs of GBM spectral value and GBM duration.

Configuration 4 :

 4 Bayesian ranking statistic removing the separation by GBM spectral value and duration

Configuration 5 :

 5 Bayesian ranking statistic and pre-selection of GW triggers based on their FAR

Figure 4 .

 4 Figure 4.21 shows a lower maximum association rank value than Fig.4.[START_REF] Wang | GRB 190829a-a showcase of binary late evolution[END_REF]. The background comprises associations with signal-like GBM candidates and noise-like GW candidates. The table showing the highest-ranked background associations is not provided here to avoid redundancy, but together with Fig.4.21, it shows a background composed of very diverse GBM triggers, a large range of LLR in the GBM trigger side, a large range of duration (going from 0.064s to 8.192s), all kinds of spectral values. As previously, this diverse background reassures us.The behavior of the foreground is presented in Fig.4.[START_REF] Samantha A Usman | The PyCBC search for gravitational waves from compact binary coalescence[END_REF]. It shows that we now have a discovery at more than 4σ contrary to the results without pre-selecting the GW triggers. This joint association has an IFAR that is more significant than 1348 yr. This IFAR of the joint detection is a limit (as for configuration 2 in Sec. 4.3.2), and the actual IFAR value of this association is higher than this. Table4.9 shows the first four most significant foreground associations. Now the top 3 are related to GW170817 -GRB 170817A. The pre-selection of the GW triggers has brought a 3 rd weak extra GBM trigger connected to GRB 170817A and coupled with GW170817. Figure4.23 shows the 3 GBM triggers of GRB 170817A that correspond to the three most significant associations. The 4 th ranked foreground association does not contain significant candidates in both channels. Its Q γ is noise-like, and its Q g is signal-like, but we checked L1 and H1 data, and

Figure 4 . 21 :

 421 Figure 4.21:Background association, when we cut the GW, triggers on their FAR before the analysis (configuration 5). Background rate as a function of the Bayesian ranking statistic, zooms on the curve's right edge. Left: associations with a hard GBM spectrum. Middle: associations with a normal GBM spectrum. Right: associations with a soft GBM spectrum. The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

Figure 4 . 22 :

 422 Figure 4.22: Cumulative rate as a function of the IFAR [yr] for the foreground (in solid line). The foreground represents associations between Fermi/GBM candidates and LIGO triggers with no time. Here the GW triggers are preliminary cut based on their FAR (configuration 5).

Chapter

Figure 4 . 23 :

 423 Figure 4.23: Waterfall plot showing GRB 170817A. The three rectangles at three different timescales are the results of the clustering that produced three GBM triggers for these events. They are the three first most significant foreground associations of Table 4.9.

  Figure 4.23: Waterfall plot showing GRB 170817A. The three rectangles at three different timescales are the results of the clustering that produced three GBM triggers for these events. They are the three first most significant foreground associations of Table 4.9.

  Figure 4.23: Waterfall plot showing GRB 170817A. The three rectangles at three different timescales are the results of the clustering that produced three GBM triggers for these events. They are the three first most significant foreground associations of Table 4.9.

Table 4 . 10 :

 410 Injection parameters for the positive sample used to train the KDE. The ι parameter corresponds to the inclination of the binary. The position of the simulated signals is generated uniformly in a shell S with an inner radius of 40 Mpc and an outer radius 250 Mpc. as expected by applying the KDE on a validation sample (stars in the bottom figure of Fig. 4.24).

Chapter 4 .

 4 Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 162

Figure 4 . 24 :

 424 Figure 4.24: Summary of the KDE training and evaluation on a simulated sample. The signal-like region corresponds to a Q g close to 0. Top left: on the negative sample: O2 GW triggers with a FAR ą 2/day. Top right: on the positive sample: O3 injections and confident GW events from O2 and O3. Bottom: Bayes factor distribution in the log 10 pBCIq ´log 10 pBSNq plane. Here the stars are a validation sample composed of four GW events that were not included in the positive sample.

Figure 4 . 25 :

 425 Figure 4.25: Cumulative rate versus association ranking statistics for the background in configuration 1. Zoomed-out version of Fig 4.10. The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

4. 4 .

 4 O3 joint LIGO/Virgo and Fermi/GBM analysis 4.4.1 . What is new compared to O2?

Figure 4 . 26 :

 426 Figure 4.26: Cumulative rate as a function of IFAR [yr] for different GBM durations. The grey dash lines show how to bin the curve depending on the duration of the GBM triggers.

Figure 4 . 27 :

 427 Figure 4.27: Modelling the turnover of the curve of the cumulative rate as a function of the IFAR in configuration n ˝3 when we separate the associations by GBM spectral hardness and duration value.

Figure 4 .

 4 Figure 4.28 shows the behavior of the background (time-shifted) associations.Here, the associations are shown separated by GBM spectral value (the three panels) and GBM duration.As for O2, most of the associations have an association rank close to 0. A few go above 1 with a maximum association rank going to Λ = 77.32 according to Table4.11 showing the properties of the four highest ranked background associations, the inferred properties, and the astrophysical classification of their GW candidate. The four highest ranked background associations have the same GW candidate, GW200224_222234, a confident BBH detection from GWTC-3[START_REF]Gwtc-3: Compact binary coalescences observed by ligo and virgo during the second part of the third observing run[END_REF]. In the first and second highest ranked associations, the GBM candidates belong to the long GRB°604213554[261] that started around 200 s before the MET of the GBM candidate. In the third one, the MET of the GBM candidate corresponds to the first peak of the long GRB[261]. The 4 th still contains GW200224_222234 with the GW source properties inferred by GstLAL in Table4.11 and associated with a signal-like GBM trigger according to this table. This GRB-like candidate has not been reported on the GCN. Figure4.29 displays the highest-ranked background association with GstLAL triggers. We can recognize the chirp of GW200224_222234 in the spectrograms. The left-hand GBM waterfall plot shows a multi-peak GRB-like trigger. The two loudest peaks here are responsible for the two first-highest-ranked background associations with GstLAL.GstLAL discovery plot, Fig.4.31, shows no deviation of the foreground from the background, and the most significant foreground association with GstLAL has an IFAR of 2.481yr. Table4.12 presents the properties of the four most significant

Chapter 4 .

 4 Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 166

Figure 4 . 28 :

 428 Figure 4.28: Background rate as a function of the ranking statistic. The left of the tail has been cut here. Results for GstLAL triggers. Left: Background associations containing a GBM candidate with a hard spectrum. Middle: Background associations containing a GBM candidate with a normal spectrum. Right: Background associations containing a GBM candidate with a soft spectrum. The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

  3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 Time [seconds] from 2020-02-24 22:22:34.4 UTC (1266618172.4)

Figure 4 . 29 :Figure 4 . 30 :

 429430 Figure 4.29: Display of the highest ranked background association for GstLAL triggers. Top: GBM trigger display (Left: Waterfall plot of the GBM trigger, Right: Waterfall plot of the clustered GBM trigger, showing only the windows with the highest LLR). The GBM trigger belongs to a confident GRB starting before the MET of this trigger. 2 nd row: Sky localization of the association (Left: GBM trigger, Right: GW trigger). The grey solid line represents the Galactic Plane and the yellow star in the GBM skymap represents the Sun. The blue region is the Earth's location. The three contour levels represent the 3σ, 2σ, and 1σ credible regions. 3 rd and 4 th rows: GW trigger display (Left: H1 spectrogram, Right: L1 spectrogram, Bottom: V1 spectrogram). Here the GPS time of the input GW trigger corresponds to GW200224_222234.

Figure 4 . 31 :

 431 Figure 4.31: Cumulative rate as a function of the IFAR for foreground (in solid line) for GstLAL triggers. The foreground represents associations between Fermi/GBM candidates and LIGO/Virgo candidates with no time shift.

Figure 4 . 32 :

 432 Figure 4.32: Background rate as a function of the ranking statistic. The left of the tail has been cut here. Results for MBTA triggers. Left: Background associations containing a GBM candidate with a hard spectrum. Middle: Background associations containing a GBM candidate with a normal spectrum. Right: Background associations containing a GBM candidate with a soft spectrum. The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

Figure 4 . 33 :

 433 Figure 4.33: Top: GW sky localization for MBTA highest ranked background association. Bottom: GBM sky localization of highest ranked background association. For the rest of the display, refer to Fig 4.29. The grey solid line represents the Galactic Plane and the yellow star in the GBM skymap represents the Sun. The blue region is the Earth's location. The three contour levels represent the 3σ, 2σ, and 1σ credible regions.

Figure 4 . 34 :

 434 Figure 4.34: Cumulative rate as a function of the IFAR for the foreground (in solid line) for MBTA triggers. The foreground represents associations between Fermi/GBM candidates and LIGO/Virgo candidates with no time shift.

Figure 4 .

 4 Figure 4.36 represents the behavior of the background (time-shifted) associations for PyCBC. As previously, the associations are shown separated by GBM spectral value and GBM duration, and most associations have an association ranking statistic close to 0; a few go above 1 with a maximum association rank of 38.05. Table4.17 shows the properties of the four highest-ranked background associations. They are the same as MBTA results. The display of the highest ranked

Figure 4 . 40 :

 440 Figure 4.40: Background rate as a function of the ranking statistic. The left of the tail has been cut here. Results for GstLAL triggers. Left: Background associations containing a GW candidate with M chirp ď 2.6 M d . Right: Background associations containing a GW candidate with M chirp ą 2.6 M d . The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

Figures 4. 40

 40

  , 4.42 and 4.44 shows how the background behaves for GstLAL, MBTA, and PyCBC respectively, separated by chirp mass. The left panel shows the associations containing a GW trigger with M ď 2.6M d , and the right panel the ones with M ą 2.6M d . Figure 4.40, compared to Fig.

Figure 4 . 41 :

 441 Figure 4.41: Cumulative rate as a function of the IFAR for the foreground (in solid line) for GstLAL triggers when we separate the association by chirp mass. The foreground represents associations between Fermi/GBM candidates and LIGO/Virgo candidates with no time shift.

Chapter 4 . 180 Figure 4 . 42 :

 4180442 Figure 4.42: Background rate as a function of the ranking statistic. The left of the tail has been cut here. Results for MBTA triggers. Left: Background associations containing a GW candidate with M chirp ď 2.6 M d . Right: Background associations containing a GW candidate with M chirp ą 2.6 M d . The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

Figure 4 . 43 :

 443 Figure 4.43: Cumulative rate as a function of the IFAR for the foreground (in solid line) for MBTA triggers when we separate the association by chirp mass. The foreground represents associations between Fermi/GBM candidates and LIGO/Virgo candidates with no time shift.

Figure 4 . 44 :

 444 Figure 4.44: Background rate as a function of the ranking statistic. The left of the tail has been cut here. Results for PyCBC triggers. Left: Background associations containing a GW candidate with M chirp ď 2.6 M d . Right: Background associations containing a GW candidate with M chirp ą 2.6 M d . The black curve represents all the associations regardless of the duration and spectral hardness of their GBM triggers.

Figure 4 . 45 :

 445 Figure 4.45: Cumulative rate as a function of the IFAR for the foreground (in solid line) for PyCBC triggers when we separate the association by chirp mass. The foreground represents associations between Fermi/GBM candidates and LIGO/Virgo candidates with no time shift.

Figure 5 . 1 :

 51 Figure 5.1: Transition region for the amplitude: the inspiral (purple), the intermediate (green), and the ringdown region (blue). Extracted from [265].

Figure 5 . 2 :

 52 Figure 5.2: Mismatches for IMRPhenomXAS (blue) and IMRPhenomD (grey) against all SXS NR hybrids. The Advanced LIGO design sensitivity PSD is used with a lower frequency cutoff of 20Hz. Figure extracted from [265].

Figure 5 . 3 :

 53 Figure 5.3: Sensitivity curves showing aLIGOZeroDetHighPower a PSD Model for LIGO, O4DesignPSD an O4 simulated PSD and the PSD of L1 at the end of O3. The former and the second are used in the faithfulness simulation. The second and the latter are used in the bank simulation.

Figure 5 . 4 :

 54 Figure 5.4: Flowchart of the workflow implemented in the PyCBC search to perform the faithfulness simulations.

Figure 5 . 5 :

 55 Figure 5.5: Match distribution of IMRPhenomXAS against TaylorF2 in the m 1 ´m2 space (top) and mass ratio-effective spin space, q ´χeff , (bottom) for BNS-like injections.

Figure 5 . 6 :

 56 Figure 5.6: Waveform comparison between IMRPhenomXAS and TaylorF2 approximant for the BNS injection with the lowest match. Left: In the time domain. Right: In the frequency domain (top: amplitude, bottom: phase).

Figure 5 .

 5 Figure 5.9 presents the distribution of the match for (1) BBHs with m 1,2 P r3, 97sM d (top) and (2) BBHs with m 1,2 P r100, 300sM d (bottom). The results are presented together because, except for a few waveforms, the models are pretty similar.However, for BBHs with m 1 P r100, 200sM d and m 2 P r3, 97sM d , Fig.5.10 and Fig.5.11 show that some waveforms are strongly different and the lowest match goes to 0.623, for a waveform with q « 30 and χ eff « 0.98. This low match seems consistent with what we already found in the NSBH results above.

Chapter 5 .Figure 5 . 7 :

 557 Figure 5.7: Match distribution of IMRPhenomXAS against SEOBNRv4_ROM in the m 1 ´m2 space (top) and q ´χeff space (bottom) for NSBH-like injections.

Figure 5 . 8 :

 58 Figure 5.8: Waveform comparison between IMRPhenomXAS and SEOBNRv4_ROM approximant for the NSBH injection with the lowest match. Left: In the time domain. Right: In the frequency domain (top: amplitude, bottom: phase).

Figure 5 . 9 :Figure 5 . 10 :

 59510 Figure 5.9: Match distribution of IMRPhenomXAS against SEOBNRv4_ROM in the m 1 ´m2 space (left) and mass ratio -effective spin space (right) for BBH injections with m 1,2 P [3,97] M d (top) and heavy BBH injections with m 1,2 P [100,300] M d (bottom).

Figure 5 . 11 :

 511 Figure 5.11: Waveform comparison between IMRPhenomXAS and SEOBNRv4_ROM approximant for the BBH injection with m 1 P [100,200]M d and m 2 P [3,97]M d with the lowest match. Left: In the time domain. Right: In the frequency domain (top: amplitude, bottom: phase).

Figure 5 . 12 :

 512 Figure 5.12: Waveform produced with IMRPhenomXAS for an NSBH injection with high mass ratio and high spins.

Figure 5 . 13 :

 513 Figure 5.13: Results of the bank simulation in the BNS range (IMRPhenomXAS -Tay-lorF2). Top-middle: Recovered fitting factor in the parameter spaces (top-left: spin1z -spin2z, top-right: mass ratio -effective spin, bottom-left: mass1 -mass2, bottom-right: total mass -effective spin). Bottom: Number (left) and cumulative fraction (right) of injections versus the recovered fitting factor. The total mass, mass1 and mass2 are in M d .

Figure 5 . 14 :

 514 Figure 5.14: Results of the bank simulation in the NSBH range (IMRPhenomXAS -SEONBRv4_ROM). Top-middle: Recovered fitting factor in the parameter spaces (topleft: spin1z -spin2z, top-right: mass ratio -effective spin, bottom-left: mass1 -mass2, bottom-right: total mass -effective spin). Bottom: Number (left) and cumulative fraction (right) of injections versus the recovered fitting factor. The total mass, mass1, and mass2 are in M d .

Figure 5 . 15 :Fig. 5 . 15 .

 515515 Figure 5.15: Results of the bank simulation in the BBH range with m 1,2 P[3,100]M d (IMRPhenomXAS -SEONBRv4_ROM). Top-middle: Recovered fitting factor in the parameter spaces (top-left: spin1z -spin2z, top-right: mass ratio -effective spin, bottomleft: mass1 -mass2, bottom-right: total mass -effective spin). Bottom: Number (left) and cumulative fraction (right) of injections versus the recovered fitting factor. The total mass, mass1 and mass2 are in M d .

Figure 5 . 16 :

 516 Figure 5.16: Results of the bank simulation in the heavy BBH range. Top-middle: Recovered fitting factor in the parameter spaces (top-left: spin1z -spin2z, top-right: mass ratio -effective spin, bottom-left: mass1 -mass2, bottom-right: total masseffective spin). Bottom: Number (left) and cumulative fraction (right) of injections versus the recovered fitting factor. The masses are in M d .

. 2 . 1 Chapter 6 . 1 Figure 6 . 1 :

 216161 Figure 6.1: One of the possible configurations for ET: A Triangular topology, in which each arm of length L is used twice to form three detectors with a 60-degree opening angle.Reproduced from[START_REF] Sathyaprakash | Scientific objectives of einstein telescope[END_REF].

Figure 6 . 2 :

 62 Figure 6.2: ET sensitivity model curve, ET-D, starting at f flow " 2 Hz, and the model used for LIGO detectors, aLIGOZeroDetHighPower starting at f flow " 10 Hz.

205 6. 2 .

 2052 Motivation for this work

6. 3 . 1 .

 31 Gravitational waveform under the Stationary phase approximation (SPA)To analytically derive a formula of the match, we explicitly write both waveforms in the frequency domain. Here we work with Newtonian inspirals only. We define the Fourier transform of the waveform:hpf q " ż tc ´8 hptqe 2iπf t dt (6.1) Chapter 6. Study of the effect of the Earth's rotation on BNS signals with the next generation of GW detectors 206

  ˝for 2G detectors, lowering the sensitivity. As a check of our semi-analytical calculation, we provide the map of the mismatch obtained thanks to a full calculation with PyCBC in Appendix A, Fig. B.3, which gives us similar results.

Chapter 6 .

 6 Study of the effect of the Earth's rotation on BNS signals with the next generation of GW detectors 210

Figure 6 . 3 : 2 ``F 2 ˆover

 6322 Figure 6.3: Top: Mismatch distribution between the waveforms with the approximation of the antenna patterns constant in time and the waveforms without, in the right ascension -declination plane with LIGO-Hanford with f low =10 Hz, when the source is face-on (ı " 0 ˝). Bottom: GW antenna pattern function for LIGO Hanford detector plotted at 2021-03-17 07:06:22 UTC. The color map here represents the mean root square of the antenna patterns, F unpolarized " b F 2 ``F 2 ˆover the sky localization angles (right ascension, declination).

Figure 6 . 4 : 2 ``F 2 ˆover 212 Figure 6 . 5 :

 642221265 Figure 6.4: Top: Map of the mismatch between the waveforms with the approximation of the antenna patterns constant in time and the waveforms without, in the right ascension -declination plane, when the source is face-on (ı " 0 ˝) with ET starting observation at f low " 2 Hz. Bottom: GW antenna pattern function for ET (configuration E1) plotted at 2021-03-17 07:06:22 UTC. The color map here represents the root mean square of the antenna patterns, F unpolarized " b F 2 ``F 2 ˆover the sky localization angles (right ascension, declination).

  Fig. B.1, Appendix B). The dephasing is also pretty large. We provide another example in Appendix B.

Figure 6 . 6 :

 66 Figure 6.6: Antenna patterns computed assuming all sources are edge-on and thus only |F `| matters.

Chapter 6 .

 6 Study of the effect of the Earth's rotation on BNS signals with the next generation of GW detectors 214

Figure 6 . 7 :

 67 Figure 6.7: Comparison of the waveforms in the frequency domain with (orange) and without the approximation (blue) of ET antenna patterns constant in time, for ı " 0 and ψ " 0 with the lowest match (match « 0.3), starting at f low "2 Hz. Top: Amplitude. Second row: Ratio of the amplitude. Third row: Phase. Bottom: Difference of the phase.

Figure 6 . 8 :Chapter 6 .z ď 1 3 4 p5 ´zq 1 ď z ă 5 0 z ě 5 ( 6

 686356 Figure 6.8: Top: Star formation rate density versus redshift using Madau-Dickinson distribution[START_REF] Madau | Cosmic star-formation history[END_REF]. Bottom: using Schneider distribution (blue) and assuming the sources are distributed uniformly between z P r0, 2s (constant comoving number density), in this case, Rpzq " 1 in Eq. 6.35 (orange)[START_REF] Zhao | Determination of dark energy by the einstein telescope: Comparing with CMB, BAO, and SNIa observations[END_REF][START_REF] Cai | Estimating cosmological parameters by the simulated data of gravitational waves from the einstein telescope[END_REF][START_REF] Wang | Calibration of gamma-ray burst luminosity correlations using gravitational waves as standard sirens[END_REF].

Figure 6 . 9 :

 69 Figure 6.9: Cumulative fraction versus optimal SNR for a BNS population of " 15000 signals.

Figure 6 . 220 Figure 6 . 11 :

 6220611 Figure 6.10: ρ approx distribution in z -M tot [M d ] space. Here the M tot is computed in the source frame. Top: colored by ρ approx . Bottom: using a three-color code.

Figure 6 . 12 :

 612 Figure 6.12: Final results comparing the optimal SNR of the signal with and without the approximation of the antenna patterns constant in time and considering ET as a network of three detectors. Top-left: Cumulative fraction versus optimal SNR for a BNS population of " 45000 signals. Top-right: ρ approx distribution in z -M tot [M d ] space using a three-color code. Bottom: Histogram showing the number of detected sources as a function of the redshift with and without the approximation.

Figure A. 5 :

 5 Figure A.5: Spatial distribution of 2704 GRBs registered by BATSE. Figure from [288].

Figure D. 1 :

 1 Figure D.1: Sketch of a new method to compute the waveform duration.

Figure D. 2 :

 2 Figure D.2: Example of waveform with a frequency artifact at the chirp beginning due to the inverse Fourier transform from the frequency domain to the time domain.

  Figure D.3: Control plot of the new duration function. The amplitude of the waveform versus time. t chirp « 63.42 seconds, with our method duration« 63.98 seconds. Here: m 1 " 1.5M d , m 2 " 1.5M d , s 1z " 0, s 2z " 0 and f low " 27.

2

  Gravitational wave data analysis 2.1 CBC searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Modeled searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Finding a signal hidden in the data: Matched-filtering . . . . . . . . . . . . . . 2.1.3 PyCBC search pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 PyCBC Offline analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Chunk 39 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Improvement of the search sensitivity to gravitational waves 3.1 Omicron algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Motivations and method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Omicron derived metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Trigger selection based on their metric value . . . . . . . . . . . . . . . . . . . . 3.3.2 Reweighting of chunk 39 PyCBC triggers . . . . . . . . . . . . . . . . . . . . . 3.3.3 Reweighting of chunk 2 PyCBC triggers . . . . . . . . . . . . . . . . . . . . . . 3.4 Discussion and perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Investigations of the noise-like region at low metric value and template duration «3 s . 6 Study of the effect of the Earth's rotation on BNS signals with the next generation of GW detectors 6.1 Third-generation GW detector: Einstein Telescope . . . . . . . . . . . . . . . . . . . . 6.2 Motivation for this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Analytic approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Gravitational waveform under the Stationary phase approximation (SPA) . . . 6.3.2 Computation of the match . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Results of the semi-analytical approach . . . . . . . . . . . . . . . . . . . . . . 6.4 BNS population simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 ET as a network of three detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	SYNTHÈSE
	0.1 . Introduction
	7 Summary and perspectives
	A Additional figures from Chapter 1
	B Additional figures from Chapter 6
	C Gravitational-wave harmonic modes
	D Investigations: A new duration function
	9

2.2.2 PyCBC Subsolar Mass Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

Table 1 .

 1 2: Comparison of GRB170817A signal in Fermi/GBM and in the INTE-GRAL instrument. The fluence here is averaged in the (10 -1000 keV) interval.

	Parameter		Instrument
		Fermi/GBM	SPI-ACS
	Event Time T 0 [s]	T GW 0	+ 1.74 ˘0.05	T GW 0	+ 1.88
	Fluence S	(1.4 ˘0.3)ˆ10 ´7 (1.4 ˘0.4)ˆ10 ´7
	rerg cm ´2s	in (10 -1000 keV) in (75 -2000 keV)
	GRB Significance	>5σ (in 3 NaI)	SNR=4.6
	GW170817-GRB 170817A		5.3σ	3.2σ
	Significance

Theory of General Relativity Chapel Hill conference Michelson Interferometric design Binary Pulsars LIGO's construction Virgo's construction 1st GW Observing Run (O1) and first GW detection O2 and first EM- GW detection O3 and first detection of NSBH mergers Beginning of the 4th GW Observing Run

										1.2. Gravitational waves
	2015 2019	Ended in 2017. First detection	of a BNS merger: GW170817	with GRB counterpart Will last 18 months	+ 2 months of	engineering run	LIGO KAGRA (H1 & L1) joined in 2020 detectors only Virgo (V1) joined in 2017 2023 Start with H1 & L1 only	Ended in 2016. Ended in 2017. First	First detection: detection of NSBH:	GW150914 GW200115 &	2016 GW200105
	1915 1960 2000	First demonstration of First indirect GW End of the	the measurability of evidence from construction	GW by experiment binary pulsars of Virgo (2G)				1957 1974 2004 of Gravitational Waves Pustovoit by Gertsenshtein and predicted the existence Michelson Interferometer 1916: Einstein First idea of using of Construction of the second generation (2G) of GW (Initial LIGO or interferometers: LIGO	iLIGO)

Figure

1

.12: Timeline presenting 100 years of search for GW, from the birth of GR to the fourth GW Observing Run (O4).

Table 2 .

 2 1: Table showing the set of parameters describing the CBC-like GW signal. tering techniques employed by the modeled searches to discriminate the GW signals from the noise. These techniques are described in the next section (Sec. 2.1.2).

	˙(2.2)
	1 `cos 2 piq

is the effective distance of the source. The other parameters have already been defined in Chapter 1, Sec. 1.2.2. Equation

2

.1 gives the waveform model used as a template for the matched fil-

Table 2 .

 2 2: Table showing the False Alarm Rate reached by GW200311_115853 in different GW pipelines.

	Parameter	Inferred value
	χ eff	´0.02 `0.16 ´0.20
	Chirp mass source M d	26.6 `2.4 ´2.0
	Luminosity Distance (Mpc)	1170 `280 ´400
	Mass1 M d	34.2 `6.4 ´3.8
	Mass2 M d	27.7 `4.1 ´5.9
	Network SNR	17.8 `0.2 ´0.2
	Redshift	0.23 `0.05 ´0.07
	Sky area (deg 2 )	35

Table 2 .

 2 3: Table containing the inferred parameters of GW200311_115853.

in Table

2

.2.

  Chapter 4. Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 140

	GW skymaps	GW livetimes	GBM triggers	GBM skymaps
		Create KDE	MET Skymap
	GBM Bayes Factor	MET skymap dict.
		GW-GBM
		association
	Background associations 0 Background associations 1 Background associations Background associations 2	Foreground associations
	3000	…
	Merge background assoc.	GW-GBM significance
	Background associations	Significance foreground
	HTML page	Background plot	HTML page	Foreground plot
	Background HTML page	Background cumulative rate VS ranking	Foreground HTML page	Foreground cumulative rate VS IFAR
			Legend:
					GBM
			Python Script	GW
			File		GBM-GW

Table 4 .

 4 1: Table containing the properties of the first four highest-ranked background associations with the naive time statistic (preliminary results). ρg : Network reweighted SNR. ∆t: time delay between the GBM and the GW trigger. ln(Λ): natural logarithm of the association rank value.

Table 4 .

 4 2: Table containing the properties of the first four highest ranked background associations with configuration 1. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank value.

		GW properties	GBM properties			Joint properties
	Rank	Merger time	Qg	Duration [s] -Spectrum	LLR	Qγ	∆t [s]	I EA Ω	Time shift [s]	Λ
	1	1181618716.304	0.329	2.048-soft	46.155	1.35ˆ10 ´2	-0.608	35.6	37500	25.9
	2	1169635035.712	0.573	0.512-soft	21.070	4.92ˆ10 ´2	-0.888	31.4	6600	18.5
	3	1171486002.071	0.058	1.024-normal	177.482	1.50ˆ10 ´3	0.793	18.0	-21100	16.5
	4	1169901594.667	0.161	4.096-soft	28.821	4.80ˆ10 ´2	-3.323	18.0	-18200	13.1

Table 4 .

 4 3: Table containing the properties of the first four most significant foreground associations with configuration 1. Q

		GW properties	GBM properties		Joint properties
	Rank	Merger time	Qg	Duration [s] -Spectrum	LLR	Qγ	∆t [s]	I EA Ω	Λ	IFAR [yr]
	5	1187008882.445	5.92ˆ10 ´5	4.096-soft	15.381	8.67ˆ10 ´1	2.72	8.62	4.20 0.095

g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank value.

Table 4 .

 4

4: Table

Table 4 .

 4 5: Table containing the properties of the first four most significant foreground associations with configuration 2 (adding Virgo contribution). Q

		Hard spectrum	Normal spectrum	Soft spectrum
	Rate [yr 1 ]	10 0 10 2 10 4	10 0 10 2 10 4	10 0 10 2 10 4	Duration: 0.064 s 0.128 s 0.256 s 0.512 s 1.024 s 2.048 s 4.096 s 8.192 s all
		10 2	10 2	10 2
		Association ranking statistic	10 3 10 2 10 1 10 0 10 1 Association ranking statistic	10 3 10 2 10 1 10 0 10 1 Association ranking statistic

g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank value.

Table 4 .

 4 6: Table containing the properties of the first four highest ranked background associations with configuration 1. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA

		GW properties	GBM properties		Joint properties
	Rank	Merger time	Qg	Duration [s] -Spectrum	LLR	Qγ	∆t [s]	I EA Ω	Time shift [s]	Λ
	1	1172327682.418	7.47 ˆ10 ´1	2.048-soft	328.1	1.84 ˆ10 ´3	0.158	48.4	-134640	27.5
	2	1177306450.914	1.13 ˆ10 ´1	0.256-soft	1595.4	2.15 ˆ10 ´4	13.854 55.4	22650	26.8
	3	1165069774.280	2.05 ˆ10 ´1	8.192-normal	64.28	1.53 ˆ10 ´2	1.216	28.8	-104540	22.6
	4	1165070949.873	1.63 ˆ10 ´1	4.096-soft	27.66	5.23 ˆ10 ´2	0.679	25.2	-16410	20.1

Ω : sky overlap value. Λ: association rank value.

Table 4 .

 4 7: Table containing the properties of the first four most significant foreground associations with configuration 3. The two first associations correspond to GW170817 -GRB 170817A and its soft tail. Q Chapter 4. Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 154

	0.064 0.128 0.256 0.512 1.024 2.048 4.096 8.192 Timescale [s]	10	5 Time from 524666471.464 [s] 0 5 GBM trigger display	10	0 20 40 60 Marginal log likelihood ratio	0.064 0.128 0.256 0.512 1.024 Timescale [s] 2.048 4.096 8.192	10	5 Time from 524666471.464 [s] 0 5 GBM trigger display	10

g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank value.

Table 4 .

 4 8 describes a background association with the same GBM duration and spectralChapter 4. Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 156

		GW properties	GBM properties	Joint properties
	Rank	Merger time	Qg	Duration [s] -Spectrum	LLR	Qγ	∆t [s]	I EA Ω	Λ
	1	1176213122.254	2.98 ˆ10 ´1	0.512-normal	176.6	1.05 ˆ10 ´3	-6.78	17.2	17.8

Table 4 .

 4

8: Table

Table 4 .

 4 [START_REF] Piran | The electromagnetic signals of compact binary mergers[END_REF]. Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 158 9: Tablecontainingthe properties of the first four most significant foreground associations with configuration 5. The top 3 contain GW170817 -GRB 170817A. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank value.

		GW properties	GBM properties		Joint properties
	Rank	Merger time	Qg	Duration [s] -Spectrum	LLR	Qγ	∆t [s]	I EA Ω	Λ	IFAR [yr]
	1	1187008882.445	6.31 ˆ10 ´6	0.512-normal	72.51	1.91 ˆ10 ´3	2.02	17.2	16.0 ą1348
	2	1187008882.445	6.31 ˆ10 ´6	4.096-soft	15.38	8.67 ˆ10 ´1	2.72	27.9	13.6 ą1348
	3	1187008882.445	6.31 ˆ10 ´6	0.064-hard	14.32	9.20 ˆ10 ´1	1.86	2.86	1.40 2.474
	4	1185284217.254	1.18 ˆ10 ´2	0.064-normal	9.457	10.0	12.71 5.05	0.261 0.142

  Chapter 4. Searching for Gravitational waves / Gamma-Ray Bursts associations in LIGO/Virgo and Fermi/GBM data 164

	Cumulative rate [yr 1 ]	10 2 10 3 10 4					Duration [s]: 0.064 0.128 0.256 0.512 1.024 2.048 4.096 8.192
		10 1
		10 5	10 4	10 3 Inverse FAR [yr] 10 2	10 1	10 0	10 1

Table 4 .

 4 11: Table containing the properties of the first four highest-ranked background associations with GstLAL triggers. All four contain GW200224_222234. Inferred total mass: 87.8 M d and p BBH « 1. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank.

	0.064 0.128 0.256 0.512 1.024 2.048 4.096 8.192 Timescale [s]	10	5 Time from 604213767.528 [s] 0 5 GBM trigger display	10	0 200 400 600 Marginal log likelihood ratio	0.064 0.128 0.256 0.512 1.024 8.192 4.096 2.048 Timescale [s]	10	5 Time from 604213767.528 [s] 0 5	10

Table 4 .

 4 12: Table containing the properties of the first four most significant foreground associations with GstLAL triggers. Q g : GW Bayes Factor. The first one contains GW190915_235702. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank.

		GW properties	GBM properties			Joint properties
	Rank	Merger time	Qg	Duration [s] -Spectrum	LLR	Qγ	∆t [s]	I EA Ω	Λ	IFAR [yr]
	1	1252627040.695	1.352 ˆ10 ´4	0.128-soft		12.148	3.004	-12.359	10.19	1.496	2.481
	2	1261972327.082	1.710 ˆ10 ´3	8.192-normal	13.301	1.786	-10.586	2.545	0.5904 0.476
	3	1250367605.166	1.082 ˆ10 ´1	0.064-hard		16.670	0.2920	-6.654	0.6434	0.3496 0.187
	4	1261701271.853	5.913 ˆ10 ´2	4.096-soft		14.588	1.208	-5.661	0.8049	0.2792 0.126
			Rank M tot [M d ] Astrophysical origin
			1	77.62	Astro (BBH) « 1
			2	46.63	Terrestrial « 1
			3	76.08	Terrestrial « 1
			4	9.792	Terrestrial « 1

Table 4 .

 4 [START_REF] Van Eerten | OFF-AXIS GAMMA-RAY BURST AFTERGLOW MODELING BASED ON a TWO-DIMENSIONAL AXISYMMETRIC HYDRODYNAMICS SIMULATION[END_REF]: Inferred properties of the GW candidate belonging to the most significant foreground associations in GstLAL.

Table 4 .

 4 14: Table containing the properties of the first four highestranked background associations with MBTA triggers. The top three contain GW200224_222234 with inferred M tot « 99.68 M d and p BBH «1. The fourth association has an inferred M tot « 2.222 M d and p Terrestrial «1. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank.

		Hard spectrum	Normal spectrum	Soft spectrum
	Rate [yr 1 ]	10 1 10 0 10 1 10 2 10 3		Duration: 0.064 s 0.128 s 0.256 s 0.512 s 1.024 s 2.048 s 4.096 s 8.192 s all
		10 2
		10 3
		Association ranking statistic	10 3 10 2 10 1 10 0 10 1 Association ranking statistic	10 3 10 2 10 1 10 0 10 1 Association ranking statistic

Table 4 .

 4 [START_REF] Eichler | Nucleosynthesis, Neutrino Bursts and Gamma-Rays from Coalescing Neutron Stars[END_REF] shows the properties of the four highest-ranked background associations. They are the same as MBTA results. The display of the highest ranked

		GW properties	GBM properties			Joint properties
	Rank	Merger time	Qg	Duration [s] -Spectrum	LLR	Qγ	∆t [s]	I EA Ω	Λ	IFAR [yr]
	1	1252627040.726	2.033 ˆ10 ´4	0.128-soft	12.148	3.004	-12.39	8.134	1.192	1.608
	2	1242429942.963	1.392 ˆ10 ´3	8.192-normal	14.726	1.003	-9.603	1.665	0.5644 0.436
	3	1239392783.772	8.960 ˆ10 ´3	0.064-normal	8.862	12.923	0.212	7.721	0.5461 0.414
	4	1256748315.377	5.090 ˆ10 ´4	4.096-normal	11.012	5.675	16.447	5.540	0.3746 0.212

Table 4 .

 4 15: Table containing the properties of the first four most significant foreground associations with MBTA triggers. The first one contains GW190915_235702. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank.

		GW properties	GBM properties	Joint properties
	Rank	Merger time	Qg	Duration [s] -Spectrum	LLR	Qγ	∆t [s]	I EA Ω	Λ
	1	1266618172.403	7.428 ˆ10 ´9	4.096-normal	704.152	1.816 ˆ10 ´3	-1.875	40.65	38.05
	2	1266618172.403	7.428 ˆ10 ´9	0.512-hard	100.155	1.343 ˆ10 ´3	-1.939	31.38	29.28
	3	1266618172.403	7.428 ˆ10 ´9	8.192-hard	115.839	7.439 ˆ10 ´3	-5.667	30.08	24.22
	4	1264309638.620	7.436 ˆ10 ´4	0.128-hard	366.849	9.722 ˆ10 ´4	3.572	21.72	19.09

Table 4 .

 4 17: Table containing the properties of the first four highest-ranked background associations with PyCBC triggers. The top three contain GW200224_222234. The top three contain GW200224_222234 with inferred M tot « 92.91 M d and p BBH «1. The fourth association has an inferred M tot « 2.219 M d and p Terrestrial «1. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank

		GW properties	GBM properties			Joint properties
	Rank	Merger time	Qg	Duration [s] -Spectrum	LLR	Qγ	∆t [s]	I EA Ω	Λ	IFAR [yr]
	1	1252627040.696	1.031 ˆ10 ´4	0.128-soft	12.15	3.004	-12.360	8.423	1.236	1.664
	2	1257949332.689	3.415 ˆ10 ´2	0.128-normal	7.707	21.85	11.15	0.255	0.468	0.321
	3	1244562730.749	1.648 ˆ10 ´4	0.064-hard	10.659	5.743	2.765	-3.085	0.368	0.212
	4	1253922585.373	1.126 ˆ10 ´3	0.512-normal	10.933	6.931	-0.685	2.447	0.302	0.149

Table 4 .

 4 18: Table containing the properties of the first four most significant foreground associations with PyCBC triggers. The first one contains GW190915_235702. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank

Table 4 .

 4 .[START_REF] Aartsen | The IceCube neutrino observatory: instrumentation and online systems[END_REF]. The next associations have ranking statistics close to 0 and are not significant enough (small IFAR) to be investigated as interesting associations. 19: Inferred properties of the GW candidate belonging to the most significant foreground associations in PyCBC.

	Rank M tot [M d ] Astrophysical origin
	1	74.59	Astro (BBH) « 1
	2	23.23	Terrestrial « 1
	3	6.779	Terrestrial « 1
	4	3.797	Terrestrial « 1

Table 4 .

 4 20: Table containing the properties of the foreground associations, including S190816u. Q g : GW Bayes Factor. Q γ : GBM Bayes Factor. ∆t: time delay between the GBM and the GW trigger. I EA Ω : sky overlap value. Λ: association rank.

Table 5 .

 5 1: Summary of the different parameter spaces and approximants covered by the faithfulness simulations.

Table 5 .

 5

2: Summary of the different parameter spaces and approximants covered by the bank simulations.

  ˆptq " Aptq 2 cospıq sinpΦptqq (6.3) with A(t) and ϕptq defined as:

	Aptq "	4 D	ˆGM c 2	˙5{3 ˆπf gw ptq c	˙2{3	(6.4)
	with
	f gw pt c ´tq "	1 π	ˆGM c 3	˙´5{8 ˆ5 256	1 pt c ´tq	˙3{8	(6.5)
	and
	Φptq "	´2 ˆ5GM c 3	˙´5{8	pt c ´tq 5{8 `ϕc	(6.6)

  ˆ1 `cos 2 pıq 2 ˙F`p t rot pf qqApt rot pf qq ˜2 : Chapter 6. Study of the effect of the Earth's rotation on BNS signals with the next generation of GW detectors 208

								¸1{2
						Φpt rot pf qq	e iΨrotpf q (6.22)
	and
	Y »	´?π 2	Apt rot pf qqF ˆpt rot pf qq2cospıqe ´iπ{2	˜2 : ϕpt rot pf qq	¸1{2	e iψrotpf q	(6.23)
	»	`i ? π 2	Apt rot pf qqF ˆpt rot pf qq2cospıq	˜2 : ϕpt rot pf qq	¸1{2	e iψrotpf q	(6.24)

  Bż pP pt rot pf qq `iQpt rot pf qqqAptpf qq 2 ´2 : p|P pt rot pf qq| 2 `|Qpt rot pf qq| 2 qAptpf qq 2 ´2 :Finally, by explicitly writing Aptpf qq and : ϕptpf qq and pΨ rot pf q ´Ψpf qq the match becomes:mph rot , h const q " max ∆tc,∆ϕc ℜ ş f ´7{3 |Bptrotpfqq|e ´iθpt rot pf qq e ip2πf ∆tc´∆ϕcqe iϕ 0 `pt rot pf qqp1 `cos 2 pıqq 2 `F 2 ˆpt rot pf qq 4 cos 2 pıq (6.33) arctan ˆ´F ˆpt rot pf qq 2 cospıq F `pt rot pf qqp1 `cos 2 pıqq ˙(6.34)

	209							6.3. Analytic approach
	and
	θptpf qq "
							S n pf q	ϕptpf qq	¯eipΨrotpfq´Ψpfqq e iϕ 0	df
								(6.29)
	Z 2 becomes:
								Sn
	Z 2 "	π 4	ż ϕptpf qq pf q	df	(6.30)
	and Z 3 :			Z 3 "	π 4	B 2	ż Aptpf qq 2 pf q ´2 : ϕptpf qq	Sn df	(6.31)
							Snpf q ş f ´7{3 |Bptrotpf qq| 2 b Snpf q	df	Snpf q df ş f ´7{3	df	(6.32)
	With:
			b
	Bptpf qq "	F 2

  ρ rot opt ˆmax ∆tc,∆ϕc ă h rot |h const ą a ă h rot |h rot ąă h const |h const ą loooooooooooooooooooooooomoooooooooooooooooooooooonTo compute ρ rot opt (just called ρ opt in the following equations) analytically, we start from Eq. 6.21-6.24. We first express | hrot pf q| removing the imaginary part of hrot pf q: `pt rot pf qqp1 `cos 2 pıqq 2 `F 2 ˆpt rot pf qq4cos 2 pıq (6.40) The square of the optimal SNR is written as follows: Apt rot pf qq ´2 : `pt rot pf qqp1 `cos 2 pıqq 2 `F 2 ˆpt rot pf qq4cos 2 pıq

	| hrot pf q| «	? π 2	Apt rot pf qq	˜2 : ϕpt rot pf qq	¸1{2	b	F 2
			ˆ?π
	opt « 4 ρ 2	ż fmax	2 ϕptrotpf qq	¯1{2 a F 2
		f min
								(6.39)
								match

Fermi uses the mission elapsed time (MET), a NASA time format, to define the trigger time.

1.3. Gamma-Ray Bursts

There is not only the χ

in the consistency test and additional tests can be included in the ranking statistic (e.g. the sine-Gaussian χ 2 ), and in fact, Chapter

proposes a new one.

2.2. PyCBC Offline analysis

4.2. A deep joint analysis: Context and Method

5.2. O4 preparation: a new PyCBC template bank

6.4. BNS population simulation

 [START_REF] Aasi | Advanced ligo. Classical and Quantum Gravity[END_REF]We first wanted to use EinsteinTelescopeP1600143 [275] a PSD Model provided by LALSimulation and implemented in PyCBC. However, we can notice important differences between EinsteinTelescopeP1600143 and ET-D curve [274]. It is probably due to the txt file from which LALSimulation extracts ET sensitivity that starts at 5 Hz, although we can ask EinsteinTelescopeP1600143 to start at 1 Hz. An extrapolation might have been done to get a sensitivity below 5 Hz, which leads to discrepancies between EinsteinTelescopeP1600143 and ET-D configuration.

 4.18 and Table 4.19 describe the properties of the most significant foreground associations with PyCBC triggers. The first one is the same as Table 4.12 and Table 4.15 with the confident BBH event GW190915_235702. As for the two other pipelines, the IFAR of this association is not high enough to suspect that both candidates are actual astrophysical events

ADDITIONAL FIGURES FROM CHAP-TER 1

In this appendix and in the following one (AppendixB), we provide additional figures to which we have referred in the main text. These figures are not necessary to understand the content of the chapters, although they are useful and give extra details.

APPENDIX C

GRAVITATIONAL-WAVE HARMONIC MODES

We have referred to the GW harmonic modes in Chapter 2 and Chapter 5. A whole section dedicated to GW harmonic modes and the higher-order modes is not crucial for the understanding of the thesis, however, we provide here details on this subject to facilitate the comprehension of some concepts mentioned in the thesis.

As the two binary components approach each other, the system loses energy by gravitational radiation. During this inspiral phase, these GW are emitted predominantly at twice the orbital frequency, but a fraction of the energy is converted to higher harmonics due to the scattering of emitted GWs off of the gravitational field around the system, which modifies the waveforms [START_REF] Ronald | The information content of gravitational wave harmonics in compact binary inspiral[END_REF].

Thus, the GW signal can be decomposed as a sum of spin-weighed spherical harmonics instead of being expressed with a single harmonic. This decomposition is written as Eq. C.1.

where l is the azimuthal number, m the polar number, Y ´2 lm spin-weighted spherical harmonics and:

θ " tm i , ⃗ χ i , e, Ωu i"1,2 (C.2) contains the parameters that describe the compact binary system. Most of these parameters are listed in Table 2.1 (Chapter 2). For BBHs, the harmonic that dominates the gravitational radiation is usually the l " 2 , m " ˘2 harmonic (however, it depends on the mass ratio and the viewing angle), called (2,2) mode. However, sub-dominant modes also contribute to the gravitational radiation, such as (2,1), [START_REF] Metzger | What is the Most Promising Electromagnetic Counterpart of a Neutron Star Binary Merger[END_REF][START_REF] Metzger | What is the Most Promising Electromagnetic Counterpart of a Neutron Star Binary Merger[END_REF] or (4,4) harmonic [START_REF] Mills | Measuring gravitational-wave higherorder multipoles[END_REF][START_REF] Kidder | Using full information when computing modes of postnewtonian waveforms from inspiralling compact binaries in circular orbit[END_REF][START_REF] Kant Mishra | Ready-to-use post-newtonian gravitational waveforms for binary black holes with nonprecessing spins: An update[END_REF]. This is presented in Fig

For the (2,2) mode, the spin-weighted spherical harmonic Y ´2 2˘2 is defined by Eq. C.3:

p1 ˘cos ϑq 2 e ˘2iφ (C.3) with the spherical coordinate system: x " r cos φ cos ϑ, y " r sin φ cos ϑ, z " r cos ϑ.

APPENDIX D

INVESTIGATIONS: A NEW DURA-TION FUNCTION

Depending on the f end chosen in Eq. 5.2 we might end with negative duration if ϕpf end q is lower than ϕpf start q. Thus, a new method to ensure a positive duration can be investigated. This method is summarized by Fig. D.1. Since IM-RPhenomXAS models the inspiral-merger-ringdown waveform, we cannot simply use T chirp (Eq. 1.51) as the duration of the waveform. We must also consider the duration t end ´tmerger , with t merger defined as the time of maximum amplitude. So here, we compute the duration as T " pt end ´tmerger q `pt merger ´tstart q. For lowmass signal, the inspiral part prevails in duration over the merger-ringdown, so our method should give durations approximately equal to T chirp . This is no longer true for high-mass signals in which the inspiral part can be extremely short, and thus the duration of the merger-ringdown part should also be considered.

Within this method, the only difficult part is computational. We need to find the start time t start of the waveform giving the start frequency f start , but when switching from frequency to time domain in waveform computation, we can face cases where there is a peak in frequency at the beginning of the waveform, as shown in Fig. D.2. This part should not be considered when finding t start . To solve this problem, we define t start as the time corresponding to the first frequency equal to f start starting from t merger and going back to the beginning of the waveform.

The ringdown phase of the amplitude can be approximated with a decreasing exponential. Thus, we define t end as the time of the half-maximum amplitude after the merger.

For comparison, we provide the results for a low-mass BNS system in Fig. For low-mass systems, our method gives results similar to the computation of T chirp , which is expected because the duration of the ringdown is negligible compared to the duration of the inspiral part. For heavy BBH binary, the duration of the inspiral becomes less important, and including the ringdown is necessary here.

This method requires the explicit calculation of the waveform and a Fourier transform and therefore is significantly more expensive than the approach in Eq 5.2. However, even for a low mass binary (i.e. a long duration signal) of m 1,2 " 1M d , the duration is calculated in " 0.2 seconds. Moreover, since it will never result in a negative duration, it could be worth implementing this function in PyCBC. Further investigations to check the accuracy of this duration function should be done.