Keywords: astroparticles, neutrinos, multi-messenger, high-energy, astrophysics, supernova, gravitational waves

Search for transient sources with the ANTARES and KM3NeT neutrino telescopes in the multi-messenger astronomy era

by Marta COLOMER MOLLA Two analyses are detailed in this thesis related to neutrino and multi-messenger astronomy with Cherenkov telescopes in the Mediterranean Sea.

The first analysis explores the capabilities of the KM3NeT neutrino telescopes to detect the signal from a Galactic core-collapse supernova (CCSN), as well as the physical constraints that could be extracted from such a detection. Together with the Sun, CCSNe are the only confirmed sources of astrophysical neutrinos. A search method for these astrophysical neutrino sources with KM3NeT has been developed during this thesis, based on the analysis of the first data which has allowed for a good characterisation of the background and the detector performance. The results show that the KM3NeT detector might be sensitive to this MeV neutrino flux, with a coverage at 5σ discovery potential of more than 95% of Galactic CCSN progenitors. Therefore, KM3NeT will contribute to the observation of the next Galactic explosion. The CCSN analysis has been implemented in a real-time trigger, that is active since summer 2019. Moreover, it has yielded the first KM3NeT real-time results with the follow-up of the unmodelled candidate gravitational-wave (GW) events. These results have allowed the KM3NeT experiment to join the SNEWS network, to which all detectors sensitive to CCSN neutrino send their alerts.

The second analysis exploits the data of the ANTARES neutrino telescope to search for high-energy neutrinos (TeV-PeV) in time and space coincidence with gravitational-wave sources and very-high energy gamma-ray bursts (GRBs). In fact, compact binary mergers and gamma-ray bursts have long been suggested as potential high-energy neutrino emitters. Typically, these searches look for muon neutrinos coming through the Earth (upgoing tracks). For the first time, all-flavors (including the so-called shower events) were included in this kind of searches. Moreover, these analyses have been applied to sources both below the ANTARES horizon (seen as upgoing events), and above the horizon of the ANTARES telescope (downgoing). This has lead to an improvement of sim15-30% for upgoing events and up to a 200% for searches above the horizon. The analyses carried out during the thesis yielded no neutrino in coincidence with any of the gravitational-wave sources from the first GW catalog, neither with the first GRBs detected at very high energies.

Résumé

Dans le présent manuscript s'expose le travail réalisé au sein de la Collaboration ANTARES-KM3NeT, dont le cadre général est l'astronomie multi-messagers avec des télescopes à neutrinos. Le travail a porté sur deux axes: la détection de neutrinos de supernova à effondrement de coeur à basse énergie avec KM3NeT (MeV), et la recherche de neutrinos de haute énergie (TeV-PeV) dans les données d'ANTARES associés à une source transitoire associée, détectée en ondes gravitationalles ou via le rayonement gamma de haute énergie.

Astronomie des neutrinos

L'astronomie de neutrinos est une discipline jeune qui mélange la physique des particules et l'astrophysique. Elle est née avec les observations des neutrinos provenants du Soleil ainsi que d'une explosion de supernova (SN1987A). Plus récemment, les premières détections de neutrinos cosmiques à haute énergie et les premières sources astrophysiques détectées simultanément à travers differents messagers cosmiques ont conduit à une nouvelle perception qui va au délà de l'astronomie conventionelle : l'astronomie multi-messagers.

Neutrinos, rayons cosmiques et rayons gamma peuvent être produits ensemble à proximité des sources astrophysiques où l'accelération de particules à très haute énergie est possible. Néanmoins, la production des rayons gamma peut aussi avoir lieu par des processus leptoniques. Pour cette raison, la détection des neutrinos provenant d'une source identifiée serait une preuve irréfutable d'un site d'acceleration hadronique.

Puisque les neutrinos intéragissent très faiblement, leur détection contitue un défi, mais cette même propriété fait des neutrinos des messagers cosmiques très utiles. Leur détection apporte des éléments uniques sur les mécanismes astrophysiques en jeu dans les phénomènes explosifs de l'Univers. Jusqu'à present, une seule source de neutrinos de haute énergie a été identifiée : le blazar TXS 0506+056. A cela s'ajoute la détection d'un flux diffus de neutrinos cosmiques avec des énergies de l'ordre du TeV-PeV, qui se répartit de façon isotrope dans le ciel et dont l'origine est encore inconnue.

La détection des neutrinos se fait de façon indirecte. C'est à dire, à travers l'observation des particules produites lors de leur intéractions. Le principe de détection des telescopes à neutrinos est basée sur la détection des particules chargées produites lors que les neutrinos intéragissent avec la matière. Dans le cas des détecteurs ANTARES et KM3NeT, ces intéractions ont lieu dans l'eau saline et elles peuvent être observées en colectant la lumière de Tcherenkov induite par le passage d'une particule chargée à vitesse rélativiste grâce aux divers photomultiplicateurs (PMTs) qui constituent le décteur. Les PMTs sont disposés sur des lignes verticales pour former l'ensemble de l'instrument. En suivant la quantité de lumière déposée et le temps auquel les photons sont détectés dans les PMTs, la trajectoire Contents des particules peut être reconstruite.

Il existe trois sources de bruit de fond dans la mer pour ce type de décteurs Tcherenkov: la bioluminescence, les isotopes radioactifs présents dans l'eau de mer, et des leptons chargés qui sont produits dans des intéractions des rayons cosmiques dans l'atmosphère, qui arrivent dans l'eau et produissent de la lumière qui peut être observée. Dans ce dernier cas, on inclut les neutrinos et les muons atmospheriques.

KM3NeT est un teslescopes à neutrinos qui est en cours de deploiment dans la mer Meditérranée. Il est composée de deux détecteurs: ORCA et ARCA. Le premier (ORCA) est situé au large de la côte française (Toulon), et il a comme objectif l'étude des oscillations des neutrinos et la détermination de l'hierarchie de masse des neutrinos. Le deuxième (ARCA), est placé au large de la Sicile (Cappo Passero) et est consacré à la recherche des sources astrophysiques de neutrinos de haute énergie, comme son prédécesseur ANTARES et le détecteur plus grand de ce type qui existe actuellement, IceCube. La nouveauté des détecteurs KM3NeT réside dans le fait qu'ils sont formés par des sphères qui disposent de 31 PMTs chacune, appéllées DOMs, tandis qu'ANTARES et IceCube ont un seul PMT de grande photocathode. Ces détecteurs se situent à une profondeur d'environ 2500 m (ORCA, ANTARES) et 3500 m (ARCA). Ceci permet de reduir la quantité de bruit de fond atmospherique qui est détectée. ORCA est un détecteur plus dense avec 115 lignes instrumentés, contrairement à ARCA qui lui est plus grand (∼1 km 3 ), avec 230 lignes de détection.

Dans la suite, les analyses menées pendant cette thèse et les résultats obtenus sont résumés.

Detection des neutrinos de supernova avec KM3NeT

Dans une premier partie, le potentiel des télescopes KM3NeT pour observer un flux de neutrinos d'une explosion supernova est étudié. Les supernovae sont la deuxième source de neutrinos astrophysiques confirmée après le Soleil. La seule détection des neutrinos provenant d'un événément supernova a permis de consolider les bases théoriques du mecanisme astrophysique sous-jacent des explosions de supernova. Par contre, une seule détection n'a pas suffi pour contraindre tous les paramètres qui permettent de décrire en détail les différents phenomènes qui ont lieu au cours de l'explosion. Cela constitue une motivation forte pour réaliser ce type d'études pour une prochaine détection.

Les détecteurs KM3NeT ne sont pas optimisés pour détecter des neutrinos à basse énergie (MeV). Néanmoins, le signal supernova peut être identifiée comme une hausse du taux d'événéments détectés au dessus du bruit de fond. De fait, l'énorme quantité de neutrinos émise lors de l'explosion va produire une hausse pas seulement du taux d'événéments détectés, mais aussi du taux d'événéments détectés en coincidence par les différents PMTs du même DOM.

Les détecteurs KM3NeT sont principalement sensibles au flux de ν e qui intéragissent avec les protons présents dans l'eau. Le nombre de PMTs sur un même DOM qui détectent des photons en coincidence (multiplicité) est utilisé pour réduire de forme radicale le bruit de fond provenant de la bioluminescence et la radioactivité. D'autre part, les correlations spatio-temporelles sont exploitées pour filtrer des événéments de bruit de fond atmospherique, qui vont produire des signatures caractéristiques que l'on peut identifier. Ces techniques permettent d'optimiser le potentiel de KM3NeT pour la détection d'un flux de neutrinos au MeV.

Une simulation détaillée de la réponse des détecteurs KM3NeT à un flux de neutrinos de supernova a été développée pendant cette thèse, et elle a permis d'évaluer sa sensibilité. Avec cette simulation, la masse effective de KM3NeT pour des recherches à basse énergie a été estimée. Les 115 lignes d'un Contents 9 block de détection sont équivalentes à un détecteur de neutrinos au MeV de 50 kton. Avec la coupure en multiplicité optimisée pour la recherche de neutrinos de supernova, cette masse effective est réduite à ∼1 kton. Cette simulation a permis de caracteriser la réponse du détecteur à basse énergie, qui a été paramétrisée avec une courbe d'efficacité en fonction de l'énergie des neutrinos. Cette paramétrisation peut être appliquée directement pour la simulation de tout flux astrophysique de neutrinos avec des énergies entre 1 et 100 MeV.

La méthode de détection utilisant les coincidences a été optimisée pendant cette thèse et a été appliquée aux premières données de KM3NeT pour mesurer le bruit de fond. Avec ces estimations du bruit de fond et du signal attendu, la sensibilité de détection aux neutrinos de supernova avec KM3NeT a été évaluée. Les résultats obtenus indiquent que plus du 95% des supernovae galactiques pourront être détectées avec KM3NeT. Ces résultats demontrent que KM3NeT pourra contribuer à la détection de la prochaine explosion supernova galactique.

Premiers resultats en temps réel

La strategie adoptée pour l'analyse supernova a été mise en place dans le système de declenchement appliqué directement aux données qui sont procéssées en temps réel, et qui sélectione les événéments d'intérêt physique. La characterisation et rejection du bruit de fond atteints a permis à l'expérience KM3NeT de joindre le système d'alertes SNEWS, qui reçoit les alertes individuelles de tous les détecteurs sensibles aux neutrinos de supernova, et en déclenche une si deux experiences observent un signal supernova en coincidence.

A l'heure actuelle, KM3NeT est capable d'engendrer des alertes en combinant les données de ARCA et ORCA en temps réel, avec une latence qui est en dessous de 20 secondes. Avec six lignes qui prennent des données, ORCA peut observer des sources jusqu'à 6-9 kpc (en fonction de la masse du progeniteur) avec le seuil de significativité requis par SNEWS.

Un des objectifs de ces recherches en temps réel est de pouvoir identifier le signal dans des différents messagers (neutrinos, rayonement electromagnétique et ondes gravitationelles), et pouvoir déterminer quand et où a lieu l'explosion. De fait, les photons produits lors d'une supernova sont émis jusqu'à des heures après les neutrinos. De plus, les explosions de supernova sont une des sources dont on attend aussi une émission d'ondes gravitationelles. Ainsi, une détection prompte du flux de neutrinos faciliterait une observation electromagnétique et en ondes gravitationelles.

Pendant la dernière période de prise de données par les détecteurs d'ondes gravitationelles, deux alertes ont été déclenchés pour des signaux qui pourraient provenir d'une supernova. À ce moment, quatre lignes d'ORCA étaient actives. Ces alertes ont été suivis avec les données d'ORCA, auxquelles l'analyse supernova a été appliquée. Il n'a pas été observé d'excèss dans les donnés correspondant à un potentiel signal de neutrinos au MeV. Avec cette non-détection, des limites sur une potentielle explosion supernova ont été placées, avec une distance minimale de 6-12 kpc (suivant la masse du progeniteur). De plus, les limites obtenues avec cette analyse ont pu rejetter l'hypothèse d'une explosion supernova avec une énergie total émisse en neutrinos plus grande que 3 × 10 53 erg, qui est l'énergie typique pour ces explosions. Cette analyse a permis mettre en place un premier suivi et ainsi de vérifier le functionement et validité de l'algorthme de déclenchement dans un cas réel, en prouvant une capacité de réponse rapide.

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Étude des propiétés du flux de neutrinos

Une autre partie du travail a été d'évaluer les performances de KM3NeT pour contraindre et distinguer entre les différents modèles de production des neutrinos. Pour ceci, il est crucial de déterminer quelle est la résolution temporelle, angulaire et en énergie du détecteur.

Pour méner des analyses qui impliquent des variations temporelles, il est nécessaire d'avoir une bonne résolution temporelle. En particulier, dans le cas d'un flux de neutrinos de basse énergie, l'idéal est une résolution à l'échelle de la milliseconde pour pouvoir étudier des changements rapides en temps et déterminer avec precision quand débute le signal. Pour ceci, l'instrument doit être capable de détecter une quantité de neutrinos élévée pour avoir de la statistique. Avec KM3NeT, ceci est possible seulement si on utilise toutes de coincidences. La coupure en multiplicité permet une diminution du bruit de fond plus grande et une meilleure sensibilité de détection, mais au dépend d'une grand perte d'événéments de signal.

L'analyse temporelle principale qui a été méne pendant cette thèse a été le développement d'une méthode pour combiner les courbes de lumière de neutrinos détectées par différents instruments. Le but est d'extraire avec cette combinaison le décalage temporelle du signal observé par les différents détecteurs, et de déterminer l'incertitude de cette mesure experimentale. Cette méthode permettra de mésurer ce décalage temporel de façon modèle indépendante. Pour ceci, on a considéré dans la simulation une paramétrisation simple qui modélise l'évolution temporelle du flux de neutrinos attendu, et une caractérisation simplifiée de la réponse des détecteurs à ce flux, en utilisant des données publiques. Les uncertitudes obtenues pour l'estimation de ce décalage temporelle sont en dessous de 1 ms pour le meilleur des cas, et jusqu'à ∼7 ms pour la combination des détecteurs la moins performante. Finalement, ces résultats ont été utilisés pour estimer la position de la source par triangulation du signal dans les différents détecteurs. La précision obtenue est une boîte d'erreur de ∼70 deg 2 pour la localisation de la supernova. Cette analyse a été conçue pour fournir une réponse rapide. La boîte d'erreur peut être réduite ensuite en combinant des informations et analyses supplementaires.

Recherche de neutrinos de haute énergie issus de sources transitoires d'ondes gravitationelles et de sursauts gamma détectés à haute énergie

Comme introduit au début de ce résumé, on s'attend à ce que l'origine des neutrinos cosmiques de haute énergie soit la même que celle des rayons cosmiques ultra énergétiques. L'émission de neutrinos pourrait aussi avoir lieu au même temps que le rayonement gamma de haute énergie et un signal gravitationnel. Pour cette raison, une partie du travail de cette thèse est consacrée à la recherche d'une émission de neutrinos de haute énergie associée à un signal electromagnetique ou gravitationnel d'une source confirmée. Une attraction particulière a été portée aux sources d'ondes gravitationelles (collision d'objects compacts dans des systèmes binaires), et à des sursauts gamma qui ont été détectés à des énergies autour du TeV par la première fois.

Les correlations temporelles et spatiales entre les photons détectés aident à identifier des topologies d'événéments caractéristiques des intéractions des particules chargées dans l'eau. Un cône de lumière qui traverse le détecteur est caratéristique du passage d'un lepton chargé ("trace"): muons atmosphériques ou muons issu de l'intéraction par courant chargé d'un neutrino électronique. Un point brillant (sphère lumineuse en expansion) dans le détecteur, indique la présence d'une gerbe hadronique ou electomagnétique produite par des intéractions par courant neutre ou par courant chargé dans le cas d'un neutrino électronique ("cascades"). Les corrélations causales permettent d'identifier ces topologies et de rejeter des événéments de bruit de fond. Ainsi, à haute énergie, la composante de bruit de fond qui domine sera constituée de muons et neutrinos atmosphériques.

La méthode habituelle pour rejeter la composante de bruit de fond atmosphérique est de garder les événéments qui arrivent au détecteur en ayant traversé la Terre (montants), puisque seuls les neutrinos peuvent la traverser. Par ailleurs, les neutrinos atmospheriques présentent un spectre en énergie différent de celui des neutrinos cosmiques. Aussi, une sélection des neutrinos plus énergétiques permet de discriminer statistiquement les neutrinos atmospheriques traversant la Terre et les neutrinos d'origine cosmique.

Une autre possibilité est de réaliser une analyse où on cherche des coincidences spatio-temporelles avec une détection confirmée d'une source transitoire. Une région du ciel petite et une fenêtre temporelle courte où rechercher le signal permettent de réduire le bruit de fond et augmenter le potentiel de découverte. En fait, le bruit de fond peut être diminué tellement qu'il est possible e3 chercher des sources qui sont au dessus de l'horizon d'ANTARES, vues comme événéments descendants qui sont plus probablement des muons. De cette façon, la recherche peut être étendue à tout le ciel et toutes les saveurs de neutrinos (traces et cascades).

Une partie du travail présenté dans ce manuscript a été consacrée au développement d'un critère de sélection pour des événéments de type cascade qui soit applicable dans ces recherches multi-messagers. Cette sélection, comme pour les traces, se base sur une méthode qui consiste à trouver les coupures dans les parametres de qualité de la réconstruction de sorte qu'un événément qui passe les coupures dans la fenêtre de la recherche et a une position compatible avec celle de la source, mène à une détection à 3σ de niveau de confiance. Cette stratégie offre un bon compromis entre une bonne sensibilité (limites plus contraignantes) et un bon potentiel de découverte.

Cette analyse a été appliqué aux données d'ANTARES dans deux contextes différents: la recherche de neutrinos en coincidence avec les signaux d'ondes gravitationelles du catalogue O2, et la recherche de neutrinos associés avec une émission de photons gamma de très haute énergie O(TeV) provenant de sursauts gamma longs. Pour la première fois, les cascades ont été inclues dans ce type d'analyse, ce qui a abouti à une amélioration de la sensibilité d'un 15-30% pour des sources dans l'horizon d'ANTARES et jusqu'un 200% pour des recherches d'événéments descendants.

Mots clés: astroparticules, neutrinos, astrophysique, haute énergie, astronomie, multi-messagers, supernova, ondes gravitationnelles

Part I

Neutrino astronomy

Chapter 1

An introduction to neutrino astronomy

This chapter is a short introduction to the current knowledge in the field of neutrino astrophysics. The scientific motivations for a neutrino astronomy are summarised, insisting on the role that neutrinos could play in different scenarios and pointing out the interesting known and potential candidate astrophysical sources. The interaction properties of neutrinos place them as potentially unique astronomical messengers in the information they carry. A special focus is thus given to multi-messenger astronomy, which aims at exploiting the synergy between the multiple messengers emitted by these astrophysical sources, presenting their respective advantages.

Historical introduction

When talking about neutrino astronomy, one has to keep in mind that we are facing a relatively newborn field. It has been almost one century since a new fundamental particle called neutrino was proposed by Pauli in order to explain the missing energy observed in radioactive decays [START_REF] Pauli | Dear radioactive ladies and gentlemen[END_REF]. Moreover, already 60 years have passed since the initial idea and the basis of high-energy neutrino telescopes appeared. Neutrino astronomy was born in the 1960's with the first observation of neutrinos from the Sun [START_REF] Barnothy | Solar neutrino puzzle[END_REF]. This detection brought the discovery of neutrino oscillations and revealed the fact that neutrinos are massive particles, which was not predicted by the Standard Model (SM). The nature of neutrinos (Dirac or Majorana [START_REF] Czakon | Are neutrinos Dirac or Majorana particles?[END_REF] 1 ), their mass and the mechanism that makes them massive still remain unknown as well as many other mysteries involving these enigmatic particles. In particular, three flavours of neutrinos are observed (ν e , ν µ and ν τ ) but additional neutrinos (so-called sterile neutrinos) are hypothesised in order to explain the different experimental data.

From 1911, Victor Hess performed a set of observations of the dischargement of an electroscope at different altitudes with balloon flights [START_REF] Hess | Über beobachtungen der durchdringenden strahlung bei sieben freiballonfahrten[END_REF]. He measured an increase of this dischargement up to 4 km high, later reproduced at higher altitudes, which could only be due to a cosmic origin. This was how he was attributed the discovery of a flux of charged particles coming from outside the Earth, since then referred to as cosmic rays (CR). Their discovery had an immediate impact on particle physics, with the study of CR interactions and their products allowing for the discovery of a large number of new particles, such as positrons, muons, kaons and pions.

It was not until the 20th century that multi-wavelength astronomy appeared, with observations of the Universe using other wavelengths than visible light. This led to a set of important discoveries in astronomy such as the first observations of pulsars, gamma-ray bursts and fast radio bursts among Chapter 1. An introduction to neutrino astronomy others. Since then, the full electromagnetic (EM) spectrum has been covered. But the connection of the EM emission with cosmic-ray acceleration and neutrino production is still to be made.

The first detection of neutrinos from outside the Solar System dates back also to the 20th century, with the explosion of the supernova SN1987A, in the Large Magellanic Cloud. Their detection made possible to confirm the basic theoretical picture of massive stars explosion at the final stage of their evolution. The energy of the detected neutrinos from that source was at the MeV scale. It is, historically, the first extra-solar multi-messenger (MM) detection, with an electromagnetic signal and astrophysical neutrinos observed. The question of the detection capability with neutrino telescopes is the subject of Part II of this manuscript.

In 2013, the first detection of cosmic neutrinos at very high energies (above tens of TeV) was reported by the IceCube Collaboration [START_REF]Evidence for high-energy extraterrestrial neutrinos at the icecube detector[END_REF][START_REF]Observation of high-energy astrophysical neutrinos in three years of icecube data[END_REF]. The discovery of a diffuse high-energy neutrino flux has been confirmed with the growing statistics of high-energy neutrino (HEN) events detected, whose angular and energy distribution is consistent with an extra-galactic origin. These first observations constitute a revolution inside the field, but even after these observations many questions regarding their exact origin remain open.

The beginning of gravitational-wave (GW) astronomy with the first observation of a signal in 2015 by the LIGO interferometers [START_REF]Observation of gravitational waves from a binary black hole merger[END_REF] marked the next important step for the community, with new probe for observing the Universe and the confirmation of General Relativity prediction for their existence. This event represents also the first observation of the coalescence of two black holes in a binary system.

The detection of cosmic neutrinos and GW marked a major step in the development of multimessenger astronomy. In the MM era, constraining possible scenarios of cosmic neutrino production at different sources is made possible by combining the information coming from the detection of a same astrophysical event through different cosmic messengers: cosmic rays, photons or GWs. This was shown with the detection of the first GW-EM multi-messenger observation of a binary neutron star merger (GW170817/GRB170817A) [START_REF]GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral[END_REF] and the first potential coincident detection of a high-energy neutrino and gamma rays from the blazar TXS 0506+506 [START_REF] Collabration | the AG-ILE[END_REF][START_REF]Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert[END_REF].

Cosmic Rays

Cosmic rays consist mainly of high-energy protons and nuclei coming from the cosmos. They are detected directly by experiments on board satellites and balloons and indirectly by observing the extensive air showers they generate in the Earth's atmosphere. The flux of cosmic rays measured on Earth is shown in Fig. 1.1, represented by a broken power law spectrum with energies that span over about 10 orders of magnitude. Two changes of the spectral index are observed in the distribution of the cosmic ray flux at "low" (∼PeV) and "high" (∼ 10 3 PeV) energies, called respectively the knee and the ankle. The knee is though to reflect the maximum proton energy that most Galactic accelerators can reach. A second knee appears due to the fact that this maximum energy is shifted for heavier elements present in the CRs compared to protons. The ankle is believed to indicate the transition between Galactic and extra-galactic origin of the CR sources.

The very high energies these particles can reach suggest that some astrophysical objects provide acceleration sites capable of bringing these particles up to extremely high energies. However, the sources of the CRs cannot be directly identified, because their directions are deflected by their interaction with magnetic fields. One way of identifying CR sources is detecting neutrinos produced by interactions of CR in or around the source.

Neutrinos: a new window to the universe

Fig. 1.7. By detecting the atmospheric neutrino flux through the Earth, the ORCA detector will be sensitive to the neutrino mass ordering.

Recent results by the IceCube Neutrino Observatory

The first evidence for a high-energy diffuse neutrino flux of cosmic origin was reported by the IceCube (IC) Collaboration in 2013 [START_REF]Evidence for high-energy extraterrestrial neutrinos at the icecube detector[END_REF][START_REF]Observation of high-energy astrophysical neutrinos in three years of icecube data[END_REF]. Only events with an interaction vertex inside the detector volume and an energy above ∼10 TeV were considered for this analysis. This gave name to the IceCube sample called High-Energy Starting Events (HESE). The HESE selection allows to veto atmospheric muons (which is one of the main background contributions as will be described section 3.1) and gives access to neutrino events coming from the whole sky. The drastic background reduction from these conditions allowed for the discovery.

In the first analysis, the sample had 28 signal events and the energy threshold was ∼60 TeV. Since then, the lastest HESE sample analysed accounts for 82 neutrino events with energies from 20 TeV to 2 PeV. Most of these events are shower-like events (defined in section 2.1.2) with angular resolutions of 10 to 30 degrees [START_REF]Observation of astrophysical neutrinos in four years of icecube data[END_REF][START_REF]Observation of astrophysical neutrinos in six years of icecube data[END_REF]. The angular resolution is the uncertainty on the estimation of the neutrino direction from the reconstruction, which will be introduced in section 3.4.4.

An astrophysical neutrino flux has also been confirmed by additional IceCube searches using other methodologies, such as the muon neutrino diffuse flux search giving name to the IC muon-track sample [START_REF]A measurement of the diffuse astrophysical muon neutrino flux using eight years of icecube data[END_REF]. Despite the fact that the angular resolution is of the order of 1 • for the muon track events, no significant evidence for a preferred sky location has been observed.

The physical information that can be extracted about this flux from IC data are the energy spectrum and the neutrino flavour ratio. For the neutrino spectrum, different hypotheses are tested : an unbroken power-law with a single spectral component, a broken power-law (single spectral power-law with a cut-off) and a double power-law, with two spectral components. The first scenario turns out to best fit the IC data both for the HESE and the muon-track sample.

The best-fit value obtained from the last HESE search (7.5 yr) is a neutrino energy spectrum following an unbroken power law with spectral index of α=2.89 [START_REF]Characterization of the astrophysical diffuse neutrino flux with icecube high-energy starting events[END_REF]. This analysis applies to all-sky and all-flavour neutrino events. For the muon-track sample, the best fit is an unbroken power-law with a value for the spectral index of α=2.28, according to the latest results (9.5 yr). This analysis is sensitive only to the northern hemisphere and the ν µ flavour [START_REF]Measurement of the diffuse astrophysical muon-neutrino spectrum with ten years of icecube data[END_REF]. Therefore, it is not sensitive to Galactic sources, observed in the southern hemisphere.

A third sample has been considered: the cascade-only events. Events from the full sky are observed with this analysis, that includes both ν e and ν τ neutrino flavours (complementary to muon-tracks) and 4 yr of data at the moment. In this case, the best-fit coming out from the measurements is a spectral index of α=2.48 for an unbroken power-law. The last updates of these results were presented at ICRC2019 [START_REF]Characterization of the astrophysical diffuse neutrino flux with icecube high-energy starting events[END_REF][START_REF]Measurement of the diffuse astrophysical muon-neutrino spectrum with ten years of icecube data[END_REF] and are summarised in Fig. 1.8.

The tension between the measurements from the different samples could be explained if the origin of the two fluxes is different, motivated by the two searches having been carried on different regions of the sky. In particular, the muon-track sample can be explained as an extra-galactic component with an E -2 -E -2.2 spectrum. While the HESE sample may be partly originated from a closer (local) component, with a softer spectrum. In Fig 1 .9 we show the best fit for each of the two analyses, which are in tension with each other. The conclusion is that the origin of this flux still remains a mystery.

Multi-messenger connections and neutrino production

However, the observation of very-high energy gamma-ray emission could a be hint of hadronic acceleration. Moreover, now we have observed galactic sources in gamma rays at higher energies, since the HESS Collaboration recently announced a strong evidence of a PeV cosmic-ray emitter (PeVatron) in the Galactic Center [START_REF] Collaboration | Acceleration of petaelectronvolt protons in the Galactic Centre[END_REF]. Despite of the huge effort, new missions and more data, no clear confirmation of any other sources where hadronic processes are in play has been possible up to date.

Multi-messenger results

The beauty of the multi-messenger astronomy is that each of the messengers brings different and complementary information. Adding all this information together could allow for a complete understanding of the astrophysical phenomena and the objects in play and also give access to relevant measurements such as the time delay between the different messengers for better constraining their relation and also some physical parameters (e.g. the neutrino mass). Thus, the combination of all this information from a single source is more valuable than the sum of the information from different sources from a single messenger.

With the multi-messenger observations in 2017, MM astronomy became a reality. As the first multiwavelength observation and the beginning of the GW astronomy, this was a breakthrough in the field of astroparticle physics. Now, it is clear that MM astronomy is the best way to proceed to learn as much as possible from the most catastrophic phenomena in the Universe and to solve the mystery of the UHE cosmic-ray sources. Closing the loop by detecting both neutrinos and EM or/and GW radiations from a same source, or even better detecting the three messengers from a unique event, is the goal of neutrino telescopes participating in MM campaigns.

It is impressive how once a transient phenomena is detected with a certain messenger, many different observatories put their efforts together to follow-up this event, searching for a counterpart both in real-time and with a refined analysis later on. In the last years, the participation and fast response of the community has significantly increased.

As seen in this section, different messengers can be emitted by the same astrophysical event very close in time. The multi-messenger astronomy tries to exploit this correlated emission to find, among other things, which are the yet unknown high-energy CR and HEN sources. The search in a restricted area and time window allows for a significant background reduction compared to diffuse and time integrated point-source searches, while the signal expectation is not lowered in case of a localised transient event. Therefore, it yields an increase of the discovery potential of an astrophysical source, notably for neutrino telescopes.

The binary neutron star merger: GW170817

The GW170817 gravitational-wave event occurred shortly after the advanced Virgo (aVirgo) detector joined the data taking and only a few days before the end of the run for an upgrade of the detectors [START_REF]GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral[END_REF]. However, only the advanced LIGO (aLIGO) detectors observed it, as will be explained later on in this section. This event was the first direct detection of a binary neutron star (BNS) system through the GW signal from the merger of the two compact objects. This happened almost fifty years after the first direct detection in radio of a BNS system by Hulse and Taylor [START_REF] Damour | 1974: the discovery of the first binary pulsar[END_REF]. Before this detection, previous GW signals were detected from Binary Black Hole (BBH) mergers, with different characteristics that will be detailed below. More than 70 observatories took part in the multi-messenger follow-up. The chronology is reported in Fig. 1.12.

The measured masses for the two merging objects were in agreement with masses of known Neutron Stars (NSs). The nature of these objects was later confirmed by the electromagnetic observations Figure 1.17: 90% confidence level (CL) upper limits on the neutrino spectral fluence obtained with ANTARES, IC and Auger data [START_REF] Antares | Search for High-energy Neutrinos from Binary Neutron Star Merger GW170817 with ANTARES, IceCube, and the Pierre Auger Observatory[END_REF]. On the top, for the search of a prompt extended emission over ±500 s with neutrino predictions from [START_REF] Kimura | High-Energy Neutrino Emission from Short Gamma-Ray Bursts: Prospects for Coincident Detection with Gravitational Waves[END_REF]. On the bottom, for the search of a long neutrino emission over 14 days with neutrino flux expectations from [START_REF] Fang | High-Energy Neutrinos from Millisecond Magnetars formed from the Merger of Binary Neutron Stars[END_REF].

The case of blazar TXS 0506+506

On September 2017, one high-energy neutrino was observed by IceCube in the direction of the blazar TXS 0506+506 in coincidence with a gamma-ray flare detected by Fermi-LAT and MAGIC [START_REF] Collabration | the AG-ILE[END_REF]. The evidence of a multi-messenger connection from this source motivated a search for a point-like neutrino excess from this blazar in the archival IceCube data. Surprisingly, a neutrino flare of 13±5 neutrinos was found in 2014-2015 [START_REF]Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert[END_REF]. The two flares are shown correspondingly in Fig. 1.18 (2017) and Fig. 1.20 (2014-2015). Going back to the electromagnetic data, no coincident flare was observed during this earlier period. Yet today, many people are trying to interpret the experimental data in order to understand the leptonic and hadronic processes at play for the two flares.

Regarding the 2017 flare, one can state the facts that on the one hand if the emission is purely leptonic, then no neutrino is expected in coincidence. On the other hand, if the emission is hadronic, then it is constrained by the X-ray detection. Let's see the different cases in Fig. 1.19. On the left plot, one sees that the leptonic models only can fit the EM spectral distribution observed. But does not explain that neutrinos are produced. On the middle, we see that he typical pγ models are not compatible with the X-ray observations. On the right, we have the case where the conventional synchrotron selfcompton emission dominates and there is a sub-dominant hadronic component that could lead to the observed neutrino flux, with a consistent spectral energy distribution between the data and the model. Distribution (SED) seem to be in contradiction with observations. The theoretical challenge is to explain on the one hand, where all the energy in HE photons and electron goes (since no EM flare is observed), and on the other hand the high neutrino flux, whose luminosity is about 4 times larger than the gamma-ray luminosity.

The first attempts to model this flaring emission are the so-called one-zone models. In this case, one has to accept that either the Eddington luminosity is significantly exceeded or that the observed neutrino flux is not reproduced by the model. In fact, more than two neutrino events emitted are difficult to accommodate in this model. Multi-zone models (external radiation fields or compact core models) can produce substantially larger neutrino fluxes with reasonable energetics as well as a spectral hardening in gamma rays, seeming good candidates to explain the data [START_REF] Padovani | Dissecting the region around IceCube-170922A: the blazar TXS 0506+056 as the first cosmic neutrino source[END_REF]. However, the spectral hardening observed in Fermi data is not significant and still debated. One of the most recent studies on the modeling of this source can be found in [START_REF] Zhang | A Neutral Beam Model for High-Energy Neutrino Emission from the Blazar TXS 0506+056[END_REF][START_REF] Petropoulou | Multi-Epoch Modeling of TXS 0506+056 and Implications for Long-Term High-Energy Neutrino Emission[END_REF][START_REF] Rodrigues | Leptohadronic Blazar Models Applied to the 2014-2015 Flare of TXS 0506+056[END_REF].

The ANTARES Collaboration also carried out a search for high-energy neutrinos in the direction of TXS 0506+506. Three different analyses were performed: a real-time follow-up, a time integrated point-source search and a time dependent search for a neutrino flare. They all yield no excess of neutrinos from this source [START_REF]The Search for Neutrinos from TXS 0506+056 with the ANTARES Telescope[END_REF].

After this short overview with the latest interpretations about the TXS 0506+506 observations, the conclusion is that more multi-messenger associations are needed for solid predictions as well as a multi-wavelength monitoring of the candidate neutrino sources for a better indication of an hadronic contribution.

Candidate neutrino sources

Natural suspects for neutrino sources are astrophysical objects which exhibit a hint for particle acceleration because if hadrons are accelerated on these sites, they could be sources of HEN. The most relevant candidate sources, galactic and extra-galactic, are discussed below.

Extra-Galactic neutrino potential emitters

• Active Galaxy Nuclei (AGN) are very luminous compact regions located at the center of a galaxy which probably host a Super Massive Black Hole (SMBH) actively accreting matter which emits radiations from the radio domain to the gamma-ray band. These objects are known to release an amount of energy placing them as the most luminous persistent sources. This energy is thought to be coming from the gravitational energy released by matter falling onto the SMBH, generating an accretion disk. In some cases, AGNs may also emit relativistic jets while the exact connection between accretion and relativistic ejections are still not precisely understood. Neutrino production is possible in both the accretion disk and in the jets. In the first case, the pion production is provided by thermal photons while in the latter the target can also be synchrotron photons.

It is convenient to divide AGNs according to the strength of the radio signal into radio-quiet and radio-loud AGN. In the radio-loud objects, the emission contribution from jets and lobes is prominent especially for radio emission. In the radio-quiet objects, the continuum radio emission comes from core regions since jet and jet-related emission are weak. We focus in this section on neutrino production in CR accelerators. The accelerators at these sources can be jets for radioloud AGNs, or AGN cores for both radio-loud and radio-quiet AGNs. Different classifications exist for AGNs (Fig. 1.21) depending on the orientation of the jet with respect to the observer, which is also related to the intensity of the radio signal. In particular, if the jet axis is oriented along the line of sight, such objects are called blazars. Blazars are interesting as neutrino emitters because higher neutrino fluxes are expected when the jet is directly pointing towards the observer. The radio and X-ray fluxes detected can be explained by synchrotron and/or Inverse Compton acceleration. For higher energies, both leptonic and hadronic models have been used to fit the photon spectral energy distribution of observed blazars.

The IceCube Collaboration has performed different searches considering jetted AGNs [START_REF] Hooper | Active Galactic Nuclei and the Origin of IceCube's Diffuse Neutrino Flux[END_REF] and AGN cores [START_REF]Search for high-energy neutrinos from agn cores[END_REF] in order to estimate their contribution to the observed diffuse neutrino flux.

The observational evidence of a high-energy neutrino emission from the direction of blazar TXS 0506+506 has led to different searches aiming at proving them as cosmic neutrino sources. In particular, the IceCube Collaboration has performed searches using the Fermi blazar catalogs [START_REF]The contribution of Fermi-2LAC blazars to the diffuse TeV-PeV neutrino flux[END_REF][START_REF]Searches for steady neutrino emission from 3FHL blazars using eight years of IceCube data from the Northern hemisphere[END_REF] as well as dedicated time dependent searches on the archival data as it was done for the TXS 0506+506 2014 flare (see section 1.4.1).

None of these searches yields to a contribution larger than 30% of the total astrophysical neutrino flux measured by IceCube. However, this can still be due to the fact that the catalogs built from EM observations are not representative of the source population. In fact, some recent models show that unresolved blazars could power the diffuse IceCube (PeV) neutrino flux without violating the limits imposed by the lack of correlations with known sources provided some astrophysical conditions are fulfilled. The ANTARES Collaboration has also carried out similar kind of searches [START_REF]Search for muon-neutrino emission from GeV and TeV gammaray flaring blazars using five years of data of the ANTARES telescope[END_REF].

• Fast Radio Bursts (FRBs) are astrophysical phenomena showing an intense radio emission in a very short time period (a few ms). So far, they have been measured in the 400 MHz and 1.4 GHz bands by various radio telescopes [START_REF] Amiri | Observations of fast radio bursts at frequencies down to 400 megahertz[END_REF], except for one observation at 8 GHz [START_REF] Gajjar | Highest Frequency Detection of FRB 121102 at 4-8 GHz Using the Breakthrough Listen Digital Backend at the Green Bank Telescope[END_REF]. No counterpart (optical/x-rays/gamma-rays/VHE gamma-rays) has been identified yet despite many multi-wavelength follow-ups. Their origin is still unknown but measurements indicate that they are extra-galactic/cosmological sources [START_REF] Thornton | A Population of Fast Radio Bursts at Cosmological Distances[END_REF].

There seems to be two different classes of FRBs, the repeating ones and the single cataclysmic events. However, the lack of observations does not allow yet for a clear classification. For a recent review on the possible origin of FRBs, see [START_REF] Petroff | Fast Radio Bursts[END_REF]. Indeed, models which include non-explosive events driven by a neutron star, are an example of good astrophysical candidates to explain both types of repeating and non repeating FRBs. These models include giant pulses from young and rapidly rotating neutron stars, magnetar giant flares and hyperflares from soft gamma-repeaters as potential sources; as well as the possibility that they originate from the interior of young supernovae or by a young neutron star embedded in a wind bubble. On the other hand, violent cataclysmic events could be powered by compact objects where the progenitor does not survive afterwards, where a explosion takes place, such as neutron star mergers, possibly associated to short Gamma-Ray Bursts.

A large fraction of the total energy radiated during these radio bursting events may be emitted at high energy while being still undetected. In fact, if the radio emission is likely produced by coherent emission of leptons, hadronic processes may take place in these sources. In this case, HEN can be produced by photo-hadronic interactions. These hadronic processes may occur in the energetic outflow released during a cataclysmic FRB event or in the vicinity of the FRB progenitor through the interaction of the outflow with the surrounding environment.

A single detection of a gamma-ray GRB-like counterpart in association with FRB 131104 has been achieved, but with a small significance to allow for any conclusion. The lack of an FRB countepart to GRB170817A, also constrains their association with short GRBs. Neither the IceCube Collaboration nor the ANTARES Collaboration have found any neutrino signal in correlation [START_REF]The search for high-energy neutrinos coincident with fast radio bursts with the ANTARES neutrino telescope[END_REF][START_REF]A Search for Neutrino Emission from Fast Radio Bursts with Six Years of IceCube Data[END_REF]. In fact, if FRBs do emit neutrinos and they are also the source of short GRBs, then this FRB sources can be ruled out in a very nearby environment (d<1kpc) by ANTARES limits [START_REF]The search for high-energy neutrinos coincident with fast radio bursts with the ANTARES neutrino telescope[END_REF].

Due to the lack of additional information on the broadband FRB spectra, it is very difficult to discriminate between the various proposed models. This makes of FRBs a very promising target for future space and ground missions, remaining still an intriguing mystery.

• Gamma-Ray Bursts (GRBs) are very luminous prompt emissions of MeV (and higher energy) photons, typically emitted in very collimated jets. They are among the most energetic processes observed in the Universe. They are believed to be produced by electrons that are accelerated in the relativistic jet by shock waves. However, if protons are also accelerated in GRBs, CRs and neutrinos may also be produced.

The so-called "fireball" models stand that the radiation pressure accelerates the fireball to relativistic speeds [START_REF] Piran | Gamma-ray bursts and the fireball model[END_REF][START_REF] Eichler | A compact fireball model of gamma-ray bursts[END_REF]. This would generate internal shocks in which hadrons may be accelerated and subsequently interact producing neutrinos. According to these models, a large density of photons is radiated, leading to a large number of emitted neutrinos. For this reason, GRBs are one of the preferred neutrino candidate sources.

Two different types of GRBs have been identified according to their duration, short ( 2 s) and long, and they are believed to have a different origin. On the one hand, long GRBs are thought to be produced in the late stage of rotating massive stars, with the evidence of the association of GRBs with Core-Collapse Supernova [START_REF] Barnes | A GRB and Broad-lined Type Ic Supernova from a Single Central Engine[END_REF]. On the other hand, short GRBs are believed to be originated in compact binary mergers (of two neutron stars or a neutron star and a black hole). This was confirmed by the recent multi-messenger observation of a binary neutron merger through GWs (GW170817) in coincidence with a short gamma-ray burst (GRB170817A), as detailed in section 1.4.1 [START_REF]An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A[END_REF].

A combination of different components can be identified in the detected lightcurves of short and long GRBs: the prompt emission, followed by an extended emission (EE), then X-ray flares, and finally plateau emission, (the afterglow). Prompt emission from the central engine is considered responsible for X and γ rays.

For each of the components, different energy scales for the neutrino emission are expected, going from MeV neutrinos produced during the compact object formation (after the stellar collapse or the merging of two compact objects), passing through TeV-PeV neutrino radiation following the prompt phase and up to the PeV-EeV energies reached by neutrinos released at the afterglow. This makes GRBs prime candidates for neutrino emissions. A review of the neutrino production mechanisms will be made in chapter 9 and more details can be also found in [START_REF] Zhang | Model-dependent high-energy neutrino flux from Gamma-Ray Bursts[END_REF].

Regarding the long GRB emission, present models rely on the induced gravitational collapse for a possible explanation [START_REF] Becerra | On the induced gravitational collapse scenario of gamma-ray bursts associated with supernovae[END_REF]. In a binary system with a massive star exploding in supernova and a NS companion, the supernova ejecta of the first component would be accreted onto the compact (NS) component. According to this paradigm, electrons and positrons annihilate in the accretion flow producing neutrinos, with energies of some tens of MeV. Contrary to other well known scenarios (such as the Sun or core-collapse supernova), in this case the neutrino-self interaction becomes more relevant than the matter effects. This is due to the extremely high neutrino density near the NS surface, particular to these models. Aside from MeV neutrinos, GeV-TeV neutrinos can be produced within shocks inside the jet and PeV-EeV neutrinos may be released through the interaction of CRs with the interstellar medium.

The lack of a neutrino counterpart observed has set very stringent limits to the neutrino flux predicted by these models. The latest results by the IceCube [START_REF]An absence of neutrinos associated with cosmic-ray acceleration in gamma-ray bursts[END_REF][START_REF]An All-Sky Search for Three Flavors of Neutrinos from Gamma-Ray Bursts with the IceCube Neutrino Observatory[END_REF] and ANTARES [START_REF]Search for muon neutrinos from gamma-ray bursts with the ANTARES neutrino telescope using 2008 to 2011 data[END_REF] Collaborations on neutrino searches from GRBs suggest that these sources do not account for more than 1% of the total diffuse neutrino flux measured by IceCube.

In the last year, the first detections of GRBs at very high energies (TeV) were achieved by the MAGIC, GRB 190114C (GCN#23701), and H.E.S.S, GRB180720B [START_REF]Gamma-Ray Burst observation at Very High Energy with H.E.S.S[END_REF] and GRB190829A (GCN#25566), Cherenkov Telescopes. The high-energy γ-ray emission by these sources makes them interesting candidates for neutrino production and they will be studied in details in Part III.

Among the sources described here, it is to be mentioned that both GRBs and magnetars together with supernova explosions are also expected to be sources of GW emission. The first coincidence of GW emission with a GRB has already been discussed in section 1.4.1. The different sources of GW emission and their interest as potential neutrino emitters will be discussed in chapter 9 of this manuscript.

Neutrino source candidates in our Galaxy

• Supernova remnants (SNRs) are the matter ejected in supernova (SN) explosions surrounding the newly formed compact object (typically a NS) after the stellar collapse. The supernova ejecta collide with the interstellar matter, forming a shock wave where particle acceleration might take place.

Indeed, cosmic rays are believed to be accelerated in supernova remnants also according to the "diffusive shock wave acceleration model". Consequently, they are believed to be a natural candidate neutrino source. In fact, SNRs are considered to explain the production of CRs with energies up to the knee (10 15 eV) and thus they are one of the preferred candidate source of hadronic acceleration [START_REF] Kappes | Potential neutrino signals from galactic gamma-ray sources[END_REF][START_REF] Villante | How precisely neutrino emission from supernova remnants can be constrained by gamma ray observations?[END_REF].

Nowadays, several SNRs have been observed to emit gamma rays with energies up to the TeV. Different types of SNR exist depending on the morphology. In shell-type SNRs, light emission is dominated by the presence of an expanding outer-shell, which is formed as the shock wave from the SN explosion expands throughout the interstellar medium, heating it. In this environment, interactions of CRs with ambient matter are expected to produce neutrinos and gamma rays via the decay of charged and neutral pions, as explained in 1.4.

Pulsar wind nebulae are hosted by SNR and are due to the wind of the rapidly spinning neutron star created after the CCSN, also called pulsar. In this case, the non-thermal emission comes predominantly from the compact object result of the progenitor star which finished its life with the SN explosion. The remnant is formed at the center and fills the SNR with what is referred to as "pulsar wind", consisting of electrons and positrons emitting strong synchrotron radiation. Two alternative scenarios are possible for hadronic acceleration at these sites [START_REF] Amato | Signatures of high energy protons in pulsar winds[END_REF]. Both the shocks in the pulsar and the magnetic field configuration of the pulsar could lead to the acceleration of hadrons. The supernova remnant itself would provide a target environment for the interaction of these particles. Again, leptonic and hadronic models are considered to explain the observed fluxes.

• X-rays binaries are binary systems that consist of a compact object (a neutron star or a stellar mass black hole) which accretes matter from a companion star [START_REF] Christiansen | High-energy neutrino emission from x-ray binaries[END_REF]. An accretion disk is formed around the compact object, which is the engine of the observed radiation. They are called X-ray binaries because most of the energy is indeed released through X-rays, but a gamma-ray component is typically also observed. While the first one may be due to the synchrotron radiation (leptonic), the latter could be related with a hadronic component.

If the system exhibits a relativistic jet, as it happens in some cases, then the system is called microquasar. In this case, the hadrons of the jet can reach much higher energies (up to a hundred of PeVs or more). Microquasars can be powered either by a weakly magnetised neutron star or by a black hole. Some of them are gamma-ray sources, as proved by the observation of very highenergy emission from the microquasar LS 5039 using the HESS telescope. In microquasars, the presence of relativistic hadrons in the jets can lead to neutrino production through photo-hadron or proton-proton interactions. In the latter case, the target protons are provided by the stellar wind of the companion.

However, a hadronic component from these sources is difficult to motivate using the scenario in section 1.4. The arguments are well explained in [START_REF] Cerutti | High-energy gamma-ray emission in compact binaries[END_REF]. On the one hand, proton-proton processes are not favored in these binary systems since the interaction time pp (Eq. 1.5) is very large for these sources with a low matter density. This implies that the protons have a larger probability of escaping the source than of interacting producing accelerated hadrons. On the other hand, photo-hadronic processes (Eq. 1.4) are not favored either due to the energy threshold, which is of some PeV for protons interacting with visible or UV light. Moreover, there is no evidence for protons to be accelerated to such high-energies on these systems given their size and magnetic field (see Fig. 1.2).

The latest results from the ANTARES [START_REF][END_REF] Collaboration report no evidence of neutrino emission found so far. Some predictions for the IceCube neutrino observatory are presented in [START_REF] Christiansen | High-energy neutrino emission from x-ray binaries[END_REF].

• The Sun is the first astrophysical source of neutrinos identified. Indeed, neutrino production is expected at the several layers of the Sun by different mechanisms.

First, the core of the Sun is known to be a source of nuclear reactions turning Hydrogen to Helium and producing a large flux of neutrinos [START_REF] Perkins | Particle astrophysics[END_REF]. The fusion of atoms in the Sun's core leads to neutrinos being produced through different interaction channels: the so-called pp, pep and hep chains; the 7 Be and the 8 B solar neutrinos are the main channels [START_REF] Raymond | Solar Neutrinos. II. Experimental[END_REF]. Their energies extend from hundreds of keV to tens of MeV.

Also in the solar plasma a thermal neutrino flux is expected, being the dominant component in the keV energy range [START_REF] Vitagliano | Solar neutrinos at keV energies: thermal flux[END_REF]. In this case, neutrino pairs are produced by non relativistic electrons coupling to the Sun's electromagnetic field. Different processes contribute to the total thermal neutrino flux: atomic deexitacion, bremsstrahlung, Compton scattering and photon decays. Due to the low energy threshold, this flux has not been observed so far.

Similarly to the interactions happening in the Earth's atmosphere, one can expect neutrino production from cosmic-ray interactions with the solar atmosphere [START_REF] Edsjo | Neutrinos from cosmic ray interactions in the sun[END_REF]. This neutrino flux accounts for the addition of the so-called prompt component (produced by charmed hadrons), the contribution from the different mesons (kaons and pions) and also from the decay of secondary muons into neutrinos. The high-energy mesons in the solar atmosphere have a larger chance to decay before being absorbed than in the Earth's atmosphere. The resulting high-energy solar atmospheric neutrino flux is therefore larger than the terrestrial one. However, these high-energy neutrinos might be lost through interactions with the solar material when traveling towards the Earth. This solar atmospheric neutrino flux has not been detected so far. Even though, predictions have evaluated the expected event rates [START_REF] Edsjo | Neutrinos from cosmic ray interactions in the Sun[END_REF] and large neutrino detectors such as IceCube or KM3NeT might be sensitive to this flux.

Finally, solar flares may also be considered as a transient neutrino source as proposed in [START_REF] Fargion | Detecting solar neutrino flares and flavors[END_REF].

The creation of a solar flare is due to the magnetic reconnection of the Sun's magnetic field. As a consequence, electrons and ions present on the solar atmosphere are accelerated with the solar flare emission. Once the accelerated ions reach the chromosphere, the higher density of this layer forces them to interact. Then, the threshold for pion production can be reached for protons which are energetic enough. This would give rise to neutrino production with energies from MeV up to a few GeV.

• The Galactic Center and the Galactic Plane are regions of interest for high-energy neutrino astronomy because of various reasons [START_REF] Fusco | Diffuse neutrino emissions from the southern sky and mediterranean neutrino telescopes[END_REF]. For what concerns the Galactic Center, a SMBH has been found at the location of SgrA*, which is the only known source producing PeV photons, as mentioned in 1.4, and hence of high-energy protons. Secondly, the high density of dust and of astrophysical objects around the Galactic Center and in the Galactic Plane, that are active regions of star formation, makes these sources good candidate sites for hadronic acceleration. Not only the Galactic Center but also the Fermi Bubbles present strong non-thermal gamma-ray emission and dense hadronic environment where neutrinos could be produced [START_REF] Cheng | Multi-wavelength Emission from the Fermi Bubble I. Stochastic acceleration from Background Plasma[END_REF][START_REF] Cheng | Multi-wavelenght emission from the Fermi Bubble. II. Secondary electrons and the hadronic model of the bubble[END_REF][START_REF] Lunardini | High Energy Neutrinos from the Fermi Bubbles[END_REF]. These sources being extended regions, a diffuse neutrino flux is expected to arise from them rather than a point-like emission. The neutrino signal predicted could be detected by the neutrino telescopes.

Recent combined searches by the ANTARES and IceCube Collaborations report a non-significant excess of 1.9 σ for an extended region of 2 • around the Galactic Center. Constraining upper limits have been derived for the neutrino flux from this source [START_REF]ANTARES and IceCube Combined Search for Neutrino Point-like and Extended Sources in the Southern Sky[END_REF]. Also a combined search with ANTARES and IC for a neutrino emission from the Galactic Center has been performed and yield no significant excess [START_REF]Joint Constraints on Galactic Diffuse Neutrino Emission from the ANTARES and IceCube Neutrino Telescopes[END_REF]. This search allowed to exclude the hypothesis of a Galactic Center contribution explaining the IceCube measured flux (with Galactic and Extra-Galactic origin) described in 1.3.2. Also neutrino searches from the Fermi Bubbles search have shown no significant signal contribution from this source so far [START_REF]Neutrinos from the Fermi Bubbles with ANTARES[END_REF][START_REF] Sherf | IceCube constraints on the Fermi Bubbles[END_REF].

• Supernovas are, as already mentioned, the second identified source of astrophysical neutrinos. Indeed, the prompt neutrino flux at MeV energies from the core-collapse phase of SN1987A was observed. Currently, no neutrino detector is sensitive to CCSN MeV neutrinos beyond the Small and Large Magallanic Clouds. This prompt neutrino emission and production mechanism will be discussed in detail in Part II together with the experimental performance of current and nearfuture detectors and the physical implications of the next observation.

As the previous described sources, CCSN can also be classified in two types according to the presence or absence of certain elements in their optical spectra: Type II in the presence of hydrogen and Type I in absence of hydrogen in their spectrum. The Type I can be divided into three sub-classes: Ia in the presence of Si, Ib in the presence of He and absence of Si and Ic in the absence of Si and He. With respect to the believed physical mechanism giving rise the Supernova explosions, one can distinguish two different kinds of events: Core-Collapse Supernova (CCSN) and Thermonuclear Supernova. The focus is given to the first type, CCSN, since the presence of hydrogen allows for nuclear reaction producing thermal neutrinos that are being released.

After the prompt emission, CCSN are believed to produce neutrinos also at higher energies. A particular situation is that high-energy (GeV-TeV) neutrinos can be emitted from the shock of jets released during the explosion [START_REF] Esmaili | Constraining high-energy neutrinos from choked-jet supernovae with IceCube high-energy starting events[END_REF], that could be promtly detected and allow for a fast follow-up. Also, there is evidence for dense material around the progenitor undergoing the Core-Collapse (circumstellar medium, CSM). In this case, proton-proton interaction in the CSM may lead to an efficient hadronic acceleration, with 10-1000 HEN events expected to be observed in a detector like IceCube from explosions occurring at 10 kpc [START_REF] Murase | New prospects for detecting high-energy neutrinos from nearby supernovae[END_REF]. In this case, the signal may be seen hours to days after the collapse.

If fact, neutrino emission is also expected from these sources at the so-called pre-supernova phase [START_REF] Kato | Presupernova neutrino emissions from ONe cores in the progenitors of core-collapse supernovae: are they distinguishable from those of Fe cores?[END_REF], mainly due to the silicium burning. This neutrino radiation will be at lower energies and it will have a considerably lower luminosity than the observed spectrum at tens of MeV energies from the collapse phase itself. This signal would help both to alert of a CCSN event happening and to probe the final stages of the star evolution. However, with current experiments the detection of such neutrinos is only possible for very nearby sources (∼0.2 kpc).

Chapter 2

Neutrino telescopes

The present chapter introduces the detection principle of Cherenkov neutrino telescopes, with a focus on the main neutrino interactions at high-energies (TeV-PeV range), to which large underwater detectors are sensitive. The ANTARES and KM3NeT detectors, the latter being under construction, are described. The analyses presented in this manuscript rely on data of these experiments, but other relevant detectors for the global comprehension of the thesis context are also described. The basics of the detection technique, the detector layouts and data acquisition system are described.

Detection principle

Neutrinos can only be detected when they interact through the weak nuclear force with a nucleon or with electrons/positrons. Depending on the force carrier, the interaction can occur via neutral current (NC), through the exchange of a Z boson, or charged current (CC), by the exchange of a W boson.

High-energy neutrino interactions will yield relativistic charged particles subsequently inferring Cherenkov light in media such as sea water. The Cherenkov light is then detected with a threedimensional array of photomultiplier tubes (PMTs).

Cherenkov radiation

Emission of Cherenkov light takes place when a charged particle travels through a transparent medium with a velocity that exceeds the speed of light in the medium. This is due to the polarization of the molecules and atoms of the media by the charged particle crossing it at relativistic speed. This radiation is emitted under a characteristic angle with respect to the incoming particle, called the Cherenkov angle, which is given by the following expression:

θ c = arccos( 1 β • n ), (2.1)
where β is the velocity of the particle (v) expressed as a fraction of the speed of light in vacuum (c), i.e β = v c , and n is the index of refraction of the medium. In water, this angle turns out to be θ c =42.5 • for highly relativistic particles (β ≈ 1). As seen in Fig 2.1 (left), where the detection principle is illustrated, a cone of light under this Cherenkov angle is the observational signature of the passage of a relativistic charged particles. The two event topologies observed in water Cherenkov detectors are illustrated in Fig 2 .1 (right) and will be detailed in section 2.1.2.

The expected number of photons emitted per unit of length x, and wavelength λ, can be expressed as

The information and power are transferred to the DU with the use of an electro-optical cable, which provides the power supply, and 18 optical fibers for data transmission. As in ANTARES, though, the DU keeps itself in vertical position by design (due to the buoyancy of the DOMs), an additional buoy is placed on the top of the string to help keeping it upright in case of fast strong current.

The Data AcQuisition System

As ANTARES, KM3NeT also adopts an "all-data-to-shore" DAQ design, so that all signals are sent to the shore station. Signals satisfying a threshold of 0.3 pe are considered. The Time over Threshold (ToT) is the time that PMT signal is measured to be above the threshold of 0.3 p.e.. The data streams arrive on shore and are assembled in a computer farm. They contain all hit information given by the PMTs: the arrival time, the ToT, and the PMT identification where the hit was detected.

A total of 25 GB of data are sent each second to shore per building block. This huge amount of data needs to be filtered and reduced as will be discussed in section 3.3. Apart from physics data that is permanently stored, a sampling of the rates of all PMTs is sent with a lower frequency. This sampling of the baseline rates is needed in order to know the total optical background for its implementation in the Monte Carlo simulations and event reconstruction.

On-shore, hit data are grouped in 100 ms time segments (timeslices) to be processed by parallel software data filters. The data acquisition of a PMT is suppressed when its rate is detected above 20 kHz over a 100 ms basis. This is called the high-rate-veto logic, that is applied so that DAQ does not saturate and the PMTs are not damaged when bioluminescence conditions produce a big increase of the rates.

Two types of data are available after the data filtering: triggered events and timeslice data. Timeslice data consists of all hit data for a selection of coincidences that is based on (i) a maximal time difference between the hit times defining a coincidence (ii) a minimum number of coincidences (iii) a maximal opening angle between the corresponding hit PMTs. Multiple timeslice streams can be produced with selections dedicated to different purposes.

A triggered event is built when at least one trigger algorithm has identified a cluster of causally connected coincidences matching a topology of interest (see section 3.3). The hits matched by the trigger as part of the physics signature are referred to as triggered hits. A triggered event stores also the information on all the hits recorded by the detector in a time window that extends over the time range spanned by the triggered hits (snapshot).

For the purpose of CCSN neutrino searches (that will be discussed in Part II), a dedicated data stream containing all high-level coincidences is continuously acquired for online monitoring and permanent storage. The same data stream is simultaneously analysed in real time for the purpose of alert generation. The raw data from the two sites is then combined at the computer farm to evaluate a combined trigger. A buffer for the lower multiplicity coincidence data is foreseen in order to store the maximum amount of useful raw data in case an alert is either received or self-generated.

The structure of the processing chain is outlined in Fig. 2.7. A common infrastructure is shared between the CCSN processing pipeline and the online event reconstruction for high-energy neutrino events. In this way, all the real-time alerts for the multi-messenger follow-ups are handled following the same chain and at the same infrastructure.

The DAQ system is present on shore and manages the data quality (DQ) and the data filters. It accounts for a control unit and a GPS for the online time calibration. The DAQ works according to the following chain:

1. A monitoring of the mean baseline rates PMT by PMT is done.

Other Cherenkov neutrino detectors 2.4.1 The IceCube Neutrino Observatory

The IceCube neutrino observatory is located in Antarctica, at the South Pole. The South Pole offers ice, rather than water, as transparent medium for Cherenkov radiation. Ice has several advantages and disadvantages compared to seawater. The main advantage of ice is the stable, low noise rate of about 500 Hz, compared to the 200-400 kHz due to 40 K decays and bioluminescence in KM3NeT detectors. However the optical properties depend on the quality of the ice and on the depth, which complicates the analysis of experimental data. On the one hand, the strong scattering causes a larger delay in the photon propagation, leading to a worse angular resolution in ice compared to water. On the other hand, the larger absorption length of ice results in better photon collection. Also, the ice is not homogeneous; there are layers of distinct properties, in contrast to seawater.

The IceCube neutrino telescope consists of a km 3 instrumented ice volume located 1.5 km below the surface. The deployment started in 2003 and was completed in December 2010, with the final detector consisting of 86 vertical strings, each connecting 60 digital optical modules, or DOMs. This makes a detector with a total of 5160 PMTs. The strings have an averaged horizontal spacing of 125 m while the DOMs are located every 17 m along the string.

IceCube is the successor of the AMANDA detector, that will not be detailed here. It was thus built from the knowledge acquired with the first experience from AMANDA. The two detectors are compared on an schematic view in Fig 2 .9, together with the two "sub-detectors" described below.

A Digital Optical Module consists of a 35 cm diameter glass sphere which contains a 10-inch PMT with its own DAQ system and readout electronics. The DOMs are required to withstand pressures up to 600 atm and temperatures down to -55 • C. The DOMs were designed so to have a maximum noise rate of the PMTs of ∼500 Hz and a TTS≤2.5 ns for single photo-electron pulses. A set of LEDs are included in the DOM for calibration and determination of the ice optical properties.

A set of ice tanks are installed in the surface aiming at the detection of the products of the cosmic ray interactions in the upper layers of the atmosphere. They constitute a different sub-detector called IceTop, which is also used as a veto to reject the atmospheric muon background in neutrino searches, described in 1.3.2. The IceTop surface array consists of 81 pairs of ice tanks placed on the same grid as the IceCube strings. Each tank has a diameter of 1.8 m and a depth of 50 cm and contains two IceCube DOMs. The distance between the two tanks in a pair is of 10 m and each pair is placed in a triangular Figure 2.12: On the right, the schematic configuration of Super-Kamiokande, with the outer and inner detectors. On the left, a picture from the interior of the detector. The total detection volume is divided into an outer shell of 2.5 m width and an inner region with a diameter of 33.8 m and a height of 36.2 m. The two regions are separated by a support structure, sustaining the PMTs.

Gd. This provides promising expectations for source pointing (neutrino astronomy) and measuring the neutrino mass ordering (see section 1.3.1).

Hyper-Kamiokande is the coming successor to Super-Kamiokande, yet a proposed project. The construction is expected to start mid 2020 and the scientific data-taking is scheduled to begin in 2025. It will be located about 8 km south of Super-Kamiokande at 648 m underground, equivalent to a shielding of 1750 m of water. The detection tank will be buried 600 m deep to reduce interference from cosmic radiation. In addition to the measurement of solar, atmospheric and supernova neutrinos, Hyper-Kamiokande will use a beam of neutrino/anti-neutrino from the J-PARC accelerator for oscillation measurements.

Hyper-Kamiokande detector will be 20 times larger than Super-Kamiokande, with a tank with 1000 million liters of ultrapure water. This larger effective detection volume (560 kton) will be accompanied by a proportional growth in the number of sensors (photomultipliers). The tank of Hyper-Kamiokande will be a double cylinder, each with outer dimensions of 48 m x 54 m x 247.5 m.

Chapter 3

From the detected photons to the physics results: analysis tools This chapter describes what happens from the moment a photon hits the detector up to the final results obtained with the measured data. In this way, the present chapter provides an overview of the different data treatments and analysis tools used in neutrino astrophysics. The triggering, simulation, and reconstruction techniques are covered together with the characteristics of the physical backgrounds and some statistical concepts of interest for the analyses presented in the following chapters.

Sources of background in the Mediterranean Sea

This section aims at describing and characterizing the different possible sources of light impacting the detector that may render difficult the neutrino signal detection.

There are essentially three relevant sources of background: bioluminescence, radioactive decays in sea water and atmospheric background. The PMT counting rates are dominated by the continuous emission of radioactive decays, and can occasionally increase due to bioluminescence activity. Due to this baseline, the ANTARES and KM3NeT telescopes are continuously detecting photons even if daylight is not visible at the depth they are deployed.

The main radioactive isotope present in the seawater salt contributing to this background is 40 K, which β-decays into a relativistic electron inducing Cherenkov emission. The electrons produced by these radioactive decays have energies up to 1.33 MeV.

Biolominescence is the background source coming from light emission by biological organisms in sea water. It has two different components, a continuous one that determines the baseline, and a discrete one which appears as localised bursts of light in the detector lasting for some seconds. Bioluminescence can exceed the background due to 40 K decays by as much as a factor of 20. This background contribution is correlated with the sea current and shows a seasonal dependence, as more biological organisms are present in spring.

The atmospheric background is originated from the interaction of cosmic rays in the atmosphere generating muons and neutrinos, which in turn can produce muons after interacting, both producing Cherenkov radiation in seawater. Atmospheric muons and neutrinos represent two different background types in neutrino telescopes, which cannot be identified in an event basis, but can be discriminated in an statistical basis.

While the first two optical backgrounds can hardly mimic a cosmic neutrino interaction, the atmospheric backgrounds are the main source of concern for the search for high-energy astrophysical neutrinos. The muon component can be mitigated by looking at upward-going muon track-like events, since only neutrinos can travel through the Earth. As regards atmospherics neutrinos, one can disentangle them from the astrophysical signal using the fact that a different energy spectrum is expected for atmospheric neutrinos and high-energy cosmic neutrinos, as can be seen in Fig. 1.3. Other strategies can be to look for accumulations in space or time, since the atmospheric neutrino background is homogeneous in time and space.

Contrary to high-energy searches, when one is interested in low-energy neutrinos the dominant background components are the two first optical backgrounds described in this section. Nevertheless, the KM3NeT multi-PMT technology is well suited to handle this, as will be shown in Part II.

The multi-photon Cherenkov radiation will result in coincidences at the few-nanosecond scale between the different PMTs in a DOM. The number of PMTs in a DOM detecting a photon within a time window of 10 ns is later on referred to as multiplicity (M). Radioactive decays in sea water and atmospheric muons are the dominant contributions to the multiplicity spectrum in the ranges M ≤ 5 and M ≥ 8, respectively. The contribution of coincidences from uncorrelated photons produced by bioluminescence or radioactive decays becomes negligible above M = 3. This signature can be used to discriminate between the different background sources and the signal and will be exploited to search for low-energy astrophysical neutrinos in Part II.

Detector calibration

In order to identify the signature of neutrino interactions in long-string underwater Cherenkov detectors, one follows the time, position and amplitude sequences of the photons observed through the different PMTs. Therefore, it is of major importance to achieve a precise timing, positioning and p.e. yield of the detector light sensors. In this sense, an accurate calibration procedure is needed for achieving the less biased results. This section briefly describes the different calibration procedures used in ANTARES and how they have been adapted to KM3NeT.

Time calibration

Two main types of time calibration are needed in ANTARES. On the one hand, the absolute timing of the events is required to correlate them with any astrophysical phenomena observed in the Universe. This is obviously of crucial importance for multi-messenger astronomy, but does not require a much better precision than O(ms). On the other hand, a more demanding and accurate relative time calibration between the PMTs with a ≤1 ns precision is needed to achieve a good angular resolution. For the latter, two measurements are performed: the time resolution of each OM and the relative time offset between OMs.

For an absolute time calibration, an echo-based clock system is used to synchronize all the optical modules of the ANTARES detector. The absolute time is synchronised with respect to a GPS signal, which presents an accuracy at the level of ∼100 ns. The time delays from the shore station to each LCM is the main source of uncertainty for the determination of the absolute time.

Detector calibration 57

Several factors affect the measurement of the time between the photon being detected in a PMT and reaching the shore station (T 0 ), which changes with time. The time offsets between the different lines may also vary with time. For these reasons, the relative time calibration between OMs is regularly monitored in situ. Different methodologies are used to achieve a better time resolution: the time residuals from the reconstruction of muon tracks, coincident events coming from the radioactive decays of 40 K nuclei in sea water and the Optical Laser Beacon system. Combining all of them, different calibrations are carried out: time differences between PMTs in an OM (for KM3NeT) or between OMs in the same storey (for ANTARES), time differences between DOMs (or storeys) in a detection line, and time difference between the different lines. The same strategies and methods are applied in KM3NeT, with the advantage of the additional information of the time delays between the 31 PMTs of a DOM, allowing for a more accurate timing.

The impact of the time calibration on time-dependent searches and final reconstruction parameter quality is not negligible. This has been evaluated in [START_REF]Time calibration of the ANTARES neutrino telescope[END_REF], where a new time calibration was incorporated.

Position calibration

Sea currents produce a movement of the detection lines, which are pulled up by buoys. Therefore the position of the OMs slowly changes with time. For this reason, a position calibration in needed to determine the position and orientation of each storey in almost real time as well as the absolute detector position. This is required to meet the targeted precision on the event reconstruction.

To this aim, triangulations of the measured acoustic signals at each storey are performed to determine their position. This is done by an acoustic sensor located at the bottom of the detection lines. In addition, several hydrophones are strategically placed at some detection storeys. The time delay between the emission and reception of the acoustic signals allows for measuring the distance between the storeys and inferring their position. In fact, by monitoring the sound velocity in seawater using oceanographic instruments, distances can be determined to infer the storey's position.

The tiltmeters and compass hosted by the storeys measure their orientation, allowing for an independent measurement of their position. Finally, the absolute detector position is obtained by the GPS of the boat used during the deployment of the lines.

The deviation of the OM position due to sea currents can reach up to several meters at the top of the line in ANTARES. The positioning system of the ANTARES detector is described in [START_REF]The positioning system of the ANTARES neutrino telescope[END_REF]. After the calibration, an accurate positioning with an uncertainty of the order of 10 cm is achieved well within specification. The positioning affects the final reconstruction parameters and analysis results significantly, specially when looking at space coincidences with signals observed by other instruments. The same strategy is used for the KM3NeT positioning calibration.

Charge calibration

Together with the time and the position, the energy reconstruction is the other required ingredient for an accurate reconstruction of the events. A charge calibration is demanded for a best energy estimate. Establishing the relation between the number of photo-electrons and the measured amplitude of the PMT signal is the main goal of the charge calibration.

Measurements before deployment have shown a linear relation between the number of photoelectrons and the digitised amplitude output [START_REF]Performance of the front-end electronics of the ANTARES neutrino telescope[END_REF][START_REF]The ANTARES Detector: Electronics and Readout[END_REF]. The calibration procedure relies on this assumption with an in situ monitoring of the positions of the pedestal (obtained with random triggers) and the photo-electron peak. The impact of the charge calibration (resolution ∼40%) on the final reconstruction is less relevant compared to the previous ones.

Physics triggers

As it would be impractical to store all data registered by the detector, a series of triggering and filtering algorithms are applied to the data once on shore. The goal is to select as much as possible series of hits resulting from physical events (neutrinos or muons) while rejecting the optical background. To do so, different criteria are used in ANTARES and KM3NeT, which are described in this section.

ANTARES

In ANTARES, causally correlated hits between the OMs are searched for. Combining them in different ways, the following triggers can be defined. The original ingredients are the L0 hits, already defined before as the signals passing the 0.3 p.e. threshold.

The level 1 hits (L1 hits) are defined as two or more hits from optical modules of the same storey that occur within a 20 ns time window. Hits with a high amplitude (typically more than 3 p.e.) are also classified as L1 hits. The set of L1 hits being causally connected is considered as resulting from a physical event (as opposed to optical background). Some higher level trigger conditions are then applied for a better selection of the physics events, further discriminating the astrophysical signal. The more relevant ones used for ANTARES data analysis are described below.

The 3N trigger is a robust criterion used to identify events likely to originate from a muon track. They are subsequently used to reconstruct the trajectory of the track. Different directions are scanned to evaluate wether the different hits can have been emitted or not by a same muon track. The final condition is to detect 5 L1 hits in at least one of the 210 predefined directions within 20 ns.

The TQ trigger works in a similar fashion to the 3N condition, but it applies an additional requirement by considering only upward-going events (now just half of the directions are scanned) with at least two L1 triggers and four additional L0 hits, within 20 ns.

The T3 trigger is built using L1 hits in coincidence on neighbor storeys of the same line within a time window of 100 ns (if adjacent storeys) or 200 ns (if next-to-adjacent). The 2T3 trigger is a more stringent version of this condition and requires at least three L1 events in one line triggered within 2.2 µs, or four in the full detector in the same window.

TAToO triggers

Aside from these triggers aimed at data filtering, there exist additional criteria applied to data in order to define a TAToO trigger, which is required for sending alerts to other instruments. As described in [START_REF]The antares telescope neutrino alert system[END_REF], these conditions are:

• Multiplet: Detecting at least two track-like event candidates for a neutrino-induced muon coming from compatible directions in the sky and within a predefined time window.

• High-energy: Detecting a single high-energy muon-neutrino inducing the observed muon track, using pre-defined cuts on the energy estimation.

The TAToO framework will be mentioned later in Part III when describing the follow-up of real-time alerts received from another observatories with ANTARES.

KM3NeT

In KM3NeT, there are three sets of criteria used to define different kinds of hits: -L0: pulse which exceeds the PMT threshold (0.3 p.e.), also referred to as single hits.

-L1: two or more coincident L0s within a predefined time window in different PMTs of a same DOM.

-L2: an L1 where the constituent L0s are separated by less than a predefined maximum space angle on the DOM.

The L1s are currently stored in runs of about 6 h duration with a frequency of 1 time-slice every 20 (downscaling rates by a factor of 20), mainly for calibration purposes and L0s only in short dedicated runs for evaluating the baseline rates. All events triggered by any of the following sets of requirements are stored for physics analysis.

Once the different kinds of hits are defined, three triggering algorithms are implemented in the KM3NeT DAQ to identify different physical signatures. The 3DShower cascade trigger assumes that light is emitted isotropically from the neutrino interaction vertex and looks for causally connected L1s (3 for ORCA and 5 for ARCA) on DOMs separated by the maximum distance D max .

The 3DMuon trigger is designed to look for the track-like events. It looks for at least 4 (5) causally connected L1 hits in ORCA (ARCA) detector within a cylinder of width R max . Both R max and D max have been optimised for each detector configuration.

Finally, the mixed (MX) trigger, MXShower, uses a mixture of L0s and L1s, in order to lower the trigger threshold and include events which do not feature the minimum of 3 (5) causally connected L1s required in ORCA (ARCA) by the 3D cascade trigger. The parameters used by the different triggers can be adapted in order to cope with the varying ambient conditions.

The simulation chain in ANTARES and KM3NeT

The software and simulation packages together with the reconstruction algorithms used within the KM3NeT and ANTARES frameworks are briefly discussed in this section. Some of the tools are common to both detectors, others will be specified for each of them. All the chain is outlined for ORCA and ARCA in Fig. 3.1 and the different steps are explained hereafter.

Event generation

Generation is the first step of the Monte-Carlo simulation chain, which consists in reproducing neutrino interactions in sea water inside a given generation (or interaction) volume, as well as atmospheric muon interactions. The different generation codes used are shortly described in the following:

• gSeaGen and GENHEN are the two different neutrino generators used in KM3NeT, specifically implemented for neutrino telescopes. While gSeaGen is based on GENIE [START_REF] Andreopoulos | The GENIE Neutrino Monte Carlo Generator: Physics and User Manual[END_REF] and is valid up to energies of about 5 TeV, GENHEN is an internal tool developed inside the ANTARES and KM3NeT Collaborations with the purpose of simulating neutrino interactions in seawater at high-energies (valid from 1 GeV to 1 EeV). gSeaGen is thus used for ORCA production and GENHEN for ANTARES and ARCA Monte-Carlo (MC) simulations.

Neutrinos are typically generated isotropically over the full sky and over large energy ranges. These neutrino interactions with nucleons are simulated using the measured parton distribution functions to calculate the deep inelastic scattering cross sections. Even if extrapolated for larger

• lenugen is a new simulation tool developed in the framework of this thesis that implements MeV neutrino interactions in seawater [START_REF] Colomer | Detailed KM3NeT optical module simulation with Geant4 and supernova neutrino detection study[END_REF]. The aim of this generator is to estimate the interaction rate of CCSN neutrinos in the KM3NeT neutrino telescopes and will be detailed in chapter 5. It can be used not only for CCSN signals but also to simulate any astrophysical neutrino flux within the energy range from 1 MeV to 100 MeV, by accounting for the corresponding spectrum via appropriate weights. The higher energies implemented here overlap with the lower energy threshold currently simulated for ORCA.

Particle and light propagation

Propagation is the step where the secondary particle products of neutrino interactions in seawater are generated and propagated until they are stopped (interact/decay), inferring the Cherenkov radiation that is produced. Light is also propagated until it is absorbed or detected by the PMTs. For this purpose, a dedicated detector file with the specific geometry is used. These codes account for water properties and the various effects such as scattering or absorption.

• KM3Sim is a package based on GEANT4 [START_REF] Agostinelliae | Geant4-a simulation toolkit[END_REF]. It is is a fully detailed simulation tracking every single particle interacting and Cherenkov photon produced. It has been developed inside the KM3NeT Collaboration [START_REF] Tsirigotis | Hellenic Open University Reconstruction & Simulation (HOURS) software package: User Guide & short reference of Event Generation, Cherenkov photon production and Optical Module simulation[END_REF]. Its computing time scales with the energy of the neutrino. This is why it is used for ORCA (GeV energies) and CCSN neutrino productions but not for higher energies (ARCA/ANTARES). It accounts for the light coming from the primary and secondary particles. Because of the large atmospheric muon statistics to be simulated, the use of KM3Sim is not appropriate for large MC productions.

• KM3 is a light generation and propagation program which uses lookup tables rather than a full simulation as KM3Sim. All relevant physical processes such as energy losses, hadronic interactions, light emission and multiple scattering are considered in the simulation. The emission of the Cherenkov light is performed on a statistical basis, i.e. using the probability of a photon to produce a hit on a PMT. The computation of such probability is taken from tables which include the probability distributions of the number of hits and the arrival times of the hits for photons originating from different positions and with different orientations with respect to the OM. The tables used by KM3 are based on GEANT3 software. It is thus much faster and it is currently used for ANTARES and ARCA HEN simulations. It is again an internal software inside the ANTARES and KM3NeT Collaborations.

KM3 uses the multi-particle approximation, in which all particles that are not electrons or muons are simulated as equivalent electrons with the appropriate light yield. This collective approximation of the hadronic cascade makes KM3 unsuited for the simulation of low-energy neutrino events in ORCA where the individual hadronic cascade topology plays a role in event reconstruction, while the approach is well suited for ANTARES and ARCA given the larger spacing between the optical modules and the higher energy threshold.

• JSirene is a framework for the light propagation recently developed within the KM3NeT Collaboration. Instead of using tables, is takes analytical PDFs that give give the users the probability for a photon, produced at a certain distance with a given energy and with a certain angle with respect to the light sensor, to arrive to a PMT and to be converted into a photo-electron. The distance and the angle to generate the PDFs are computed from the interaction vertex for tracks and from the maximum of electron emission in the case of a shower.

A comparison between the three light generators has been performed, and the three of them lead to compatible results with the few percent differences being understood.

In fact, aside from the development of the low-energy neutrino generator lenugen, during the thesis a contribution was made to the work on the comparison among the three light codes and the extension of the ORCA MC production up to higher energies (1-5 TeV) in order to have an overlap region with the ARCA detector and to be able to use ORCA on its sensitive energy range for neutrino astrophysics.

Detector response

JTriggerEfficiency (JTE) is the internal software used to simulate the PMT response, including electronics, accounting for the individual PMT efficiencies and the detector calibration. The program is responsible for the application of the triggers defined in section 3.3. By default, only events surviving at least one trigger are kept for the physics data analysis. JTE is the KM3NeT version while in ANTARES it is Trigger Efficiency (TE) that covers the same functionality.

Briefly, after the light propagation has been simulated, the time transit spread (TTS) of the PMTs is simulated. In the KM3NeT software, a gaussian smearing is applied to the hit arrival times to simulate the TTS. In ANTARES, it is simulated directly from its measured values. Coincident hits on the same PMT are also merged into a single pulse with an increased ToT.

Regarding KM3NeT, JTE allows for disabling the triggers in case all hits need to be kept. In addition to the detector response to individual hits, the background due to environmental conditions can also be directly simulated at this step, including the 40 K contribution at each multiplicity and the total baseline rates. Note however that the program does not provide the possibility to simulate time/space correlations from bioluminescence.

Event reconstruction

Reconstruction is a fundamental step in the analysis chain with neutrino telescopes. The patterns of the hit time, the hit amplitude and the hit position over the detection strings are used in order to trace back the trajectory of the particle (lepton) inducing the Cherenkov light. In this way, the interaction vertex, the direction of the outgoing lepton and its energy can be inferred. Different approaches are followed according to the detector configurations and the event topology.

• JGandalf and AAFit are the main muon track reconstruction algorithms used respectively in KM3NeT and ANTARES. The main similarities and differences between the two are highlighted in the following paragraphs.

The reconstruction chain for AAFit is based on a multi-step procedure which consists on a linear pre-fit (χ 2 minimizer), an M-estimator fit (also a minimizer) and a maximum likelihood fit with a simplified PDF [START_REF]Searches for Point-like and Extended Neutrino Sources Close to the Galactic Center Using the ANTARES Neutrino Telescope[END_REF]. Based on causality criteria, a pre-selection of hits is applied to feed the reconstruction algorithm and discard pure-noise hits. After these three steps a final maximum likelihood fit, which gives the direction of the reconstructed track, is performed. The PDFs used to build the likelihood contain only the information of the hit time and the expected arrival time. This likelihood maximization is sensitive to the starting direction from the M-estimator. Because of this, the two last steps (M-estimator best fit and likelihood maximization) are repeated for eight alternative additional starting points, which are chosen from the pre-fit. The number of starting points providing a reconstructed track direction in agreement within one degree from the preferred result is kept for further quality assessment.

The approach used in JGandalf [START_REF]KM3NeT/ARCA Event Reconstruction Algorithms[END_REF] is slightly different. As in the AAFit algorithm, the first step is also a linear pre-fit based similarly on a χ 2 minimization. Causally connected hits are used in this pre-fit to avoid optical backgrounds or scattered light. Different permutations of this hit selection are done from the causally connected hits, based on the minimization values. A best fit value is defined from the pre-fit, selecting the "best direction". The pre-fit procedure is repeated for different directions within one degree from the selected one. In the end, the twelve directions with a best fit value are chosen and the muon trajectory is fitted using a likelihood maximization, which is evaluated for each of these twelve directions. The PDFs used for the likelihood include information about the PMT response as a function of the minimum distance of the muon track to the PMT, the orientation of the PMT, and the time residual of the hit, which are computed semi-analytically from simulations.

• AAshowerfit and TANTRA are the shower reconstruction algorithms used respectively in KM3NeT-ARCA and ANTARES. While for tracks the vertex position can be reconstructed, in the case of shower events it is the position of the maximum of the shower development that is fitted. Also, since tracks can start outside the instrumented volume but showers are seen as contained events in the detector, it is easier to infer the shower energy than the track energy from the estimate of the energy deposited in the detector.

TANTRA is the main cascade reconstruction algorithm used in ANTARES [START_REF]An Algorithm for the Reconstruction of Neutrino-induced Showers in the ANTARES Neutrino Telescope[END_REF]. It is based on a two-step procedure: first the reconstruction of the interaction vertex and second the fit of the direction of the cascade. A specific selection of the hits is applied prior to each of these two steps.

The fit of the cascade direction is performed by means of a likelihood maximization. This likelihood is built by computing the probability of measuring a given charge on a given PMT. It is built using the signal and background PDFs which depend on the charge of the hit, the neutrino energy, the distance between the PMT and the interaction vertex, and two angles: the angle between the neutrino direction and the vector which connects the PMT with the interaction vertex and the angle between the direction of the PMT and the incident photon.

AAshowerfit is the main shower reconstruction framework used in KM3NeT/ARCA [START_REF]KM3NeT/ARCA Event Reconstruction Algorithms[END_REF]. As TANTRA, it is based on an initial vertex position fit followed by a cascade direction fit. For the latter, no information of the previous fit is used. The hit pre-selection is performed in two steps. First, hits occurring in one PMT within a time window of 350 ns are merged into a single hit, whose arrival time is the time of the first hit. Then, among the merged hits only those that arrive in the same DOM in coincidence (within 20 ns) are used for the vertex fit, which is based on an M-estimator. The starting point of the M-Estimator is taken as the center of gravity of all the selected hits, and the starting interaction time is taken as the mean of the hit times minus 500 ns. The PDFs used in the likelihood are built by computing the number of photons which are expected to be detected from a shower-like event as a function of the distance from the interaction vertex to the center of the DOM, the direction of the cascade, the direction of the PMT and the deposited energy of the event.

Moreover, the Dusj reconstruction technique for cascade events has been adapted for the three detectors [START_REF]An algorithm for the reconstruction of high-energy neutrinoinduced particle showers and its application to the ANTARES neutrino telescope[END_REF]. Slightly different versions are implemented for ORCA, ARCA and ANTARES according to the detector geometry but with the same approach, which is also a maximum likelihood fit. The Dusj reconstruction is divided into three main steps: hit selection, maximum likelihood fit and calculation of additional quality parameters. Both in ANTARES and KM3NeT, some Dusj parameters are used in an event classification via a random decision forest (RDF) algorithm. In particular, some of its variables include multivariate techniques in order to distinguish 3.5. Statistical concepts used in particle and astro-physics 67

Statistical concepts used in particle and astro-physics

When working on particle physics or astrophysics, we usually deal with the question: is this data containing the "signal" we are looking for or is it just background (or noise)? With signal referring to the physical measurement or characteristic we want to evidence and background or noise is any other thing producing the same observational features, sometimes very difficult to disentangle from the searched "signal".

Thus, several strategies and techniques are developed with the purpose of having the best signal and background discrimination, typically called the event selection of the analysis (or analysis cuts), that will be described for the different works presented in this thesis.

But some standard criteria and parameters must be defined in order to state in which case one can claim a discovery after the analysis is done. In other words, when the probability to observe in your data the same "signal" pattern from background is small enough to say that the data is not compatible with the background only hypothesis.

This section aims at providing a general idea and simple description of the statistical definitions and methods used in this thesis. The interested reader can find more information in [START_REF] Lista | Statistical methods for data analysis in particle physics[END_REF].

Test statistic, p-value and significance

The p-value and significance are concepts typically used in particle physics and astrophysics.

The test statistic is the parameter defined in order to compare the background and the "signal" events. The test statistics (TS) is usually chosen to provide the best possible separation power between the signal and the background only hypotheses.

What is done in an analysis is to characterize the background and the signal. The optimised selection cuts are then applied to obtain a final data sample with, for instance, the best signal to noise ratio. After that, the value of the test statistic is computed for this data set. Then, in order to evaluate how significant is this data set, the computed test statistic is compared to the distribution of the test statistic for the background hypothesis. This allows to estimate the probability to obtain such or a greater value of the test statistics from background. This probability is what is called the p-value. The standard criterion is that a p-value (p) smaller or equal than 2.7×10 -3 is an evidence and a p-value p ≤3×10 -7 leads to a discovery.

In Fig. 3.7, an illustration of the definition of the significance and the power of a hypothesis test is provided. Two hypotheses are compared: background only (H 0 ) and signal + background (H 1 ), with the observed value of the test-statistic (TS th ). The significance gives the probability of wrongly rejecting the null hypothesis (H 0 ), i.e. of observing a TS value larger than TS th from the H 0 hypothesis. The power is the probability of having a test statistics from the H 1 hypothesis larger or equal than the observed TS th , i.e. the probability of rejecting the null hypothesis H 0 when the alternative hypothesis H 1 is true.

The p-value can also be related to the concept of False-Alarm Rate (FAR), which is the number of times (in a pre-defined time window) this value of the test statistic would be obtained in the case where there are only background events in the data. In some sense, FAR can be also translated into a p-value, and it is usually done. But the real meaning is lost since the information on the time window is lost. Moreover, it is not directly compared to the signal expectation and its rate, so it is tricky to convert it into a detection significance as described in next paragraph.

with the χ 2 probability distribution:

f (p 1 , ..., p N ) = ∏ i p i (3.8) -2 ∑ i p i = χ 2 no f ,p (3.9)
with no f = 2N being the number of degrees of freedom and p the combined p-values given by the χ 2 probability.

One of the problems encountered using this method (coming from the way of weighting the two pvalues) is that if one wants to combine two p-values with one of them being larger than 0.5, the combination leads to a worse significance result than the best p-value that is combined by its own. However, this is not what one looks for when profiting of the combination of additional data. This problem was encountered when combining ORCA and ARCA for time-dependent CCSN analyses (see chapters 6 and 7). Moreover, in the case when the number of signal and background events for the two combined experiments are quite different (e.g. by an order of magnitude), the weighted combination turns to be the best approach. This was found when applying a different selection in ARCA and ORCA for CCSN neutrino searches (chapters 6 and 7) that could lead to this condition.

A possible strategy that can be used in order to solve this issue is the linear combination of the significances, that would be done according to:

σ comb = ∑ i σ i W i ∑ i W 2 i (3.10)
where W i is a weight applied to the significance of each data set i, which should be predefined and can be optimised. This weight is needed to account for the different signal contribution on each experiment/data set. Indeed, when the knowledge of the experimental data is limited to the size and precision of the samples but further details are not known, there is strong motivation to weight the two p-values differently.

The relevant message in the end is that the perfect way for the p-value (or significance) combination has not been yet found. Therefore, the best way to proceed, if possible, is combining directly the experimental data samples rather than the p-values. In fact, this is the strategy followed in the combined ANTARES and IceCube analyses (e.g. [START_REF]ANTARES and IceCube Combined Search for Neutrino Point-like and Extended Sources in the Southern Sky[END_REF]).

Moreover, combining data (or what is the same, the PDFs used in the likelihood analysis that is typically carried out in these cases) would allow for the combination not only of data from different experiments but even of different samples from the same detector. For example, imagine one would like to combine the HESE and muon-track IceCube samples to enhance the significance of a given analysis performed using both separately.

The sensitivity, discovery potential and upper limit

In the previous section, we discussed how to estimate and provide information about the significance of an observation. On the current one, we want to try to answer to the following questions:

• What is the performance of the detector?

• What are the best selection cuts to optimize the analysis?

• In case of a non-significant observation, can we say something about the signal we search for and constrain the models from the non-observation?

First of all, it should be noted that the data analyses in particle and astroparticle physics are done blindly, i.e. without looking at the relevant data where the searched-for signal may be contained (see [START_REF] Roodman | Blind analysis in particle physics[END_REF], where different strategies to blind the data are described). Therefore, the definition and optimization of the analysis are done using MC simulations and without looking at the data where the analysis will be applied. Different criteria can be used to optimize the analysis:

1. For the best discovery potential: get the greatest chance to detect a signal of a given amplitude.

2. For the best sensitivity: get the most stringent constraint and model discrimination power from a non-observation.

Upper limit

We tackle the case of a non-significant observation. This means, for instance, that we have a number of observed events over the background expectation but not enough to say it that is not compatible with a background fluctuation with a high enough probability (at least above 3σ). In this case, an upper limit (usually at at 90% CL) can be derived, i.e. a constraint can be stated on the maximum number of signal events we expect from the searched source from the fact that it was not observed.

Let's take the easiest example, the case of n obs =0 with a poissonian behavior of the data. In that case, the Poisson probability of observing 0 events is smaller equal to 10% when 2.3 events are expected as maximum from signal plus background. So when the background is negligible, the upper limit at 90%CL is µ 90% s 2.3. The upper limit is therefore defined as the maximum number of events that may be originated from signal, given the (known) background expectation and the observation n obs , and cannot be detected. Thus, it sets a limit on the maximum expected signal from a source, that is used to constrain the models. Unless no events are observed, the procedure consists in fitting n s (typically using an unbinned likelihood method, but others exist) considering that the background is well known and characterised, and the total number of observed events, n obs . From the fitted value of n s one gets the corresponding value of µ 90% s . In order to do this fit, a signal model must be used.

Sensitivity

The sensitivity corresponds to the largest number of signal events that the detector would be able to distinguish from background (typically in 50% of the cases). Smaller signals will be indeed compatible with background. In other words, the sensitivity is the smallest signal that can be proved. Thus, this limit value quantifies the sensitivity of the experiment to a given signal. The sensitivity can also be seen as an average upper limit.

Discovery potential

The discovery potential is defined as the number of signal events that need to be emitted from the source (at least) in order for your experiment to be able to claim a discovery at a given significance. In other words, it indicates how strong the signal has to be for the experiment to achieve a significant detection. As the sensitivity, it is computed without looking at the unblinded data and used as criteria to define and optimize the selection cuts in the analysis as mentioned before.

Chapter 4

Core Collapse SuperNova neutrinos: What we know today.

The current chapter briefly presents the core-collapse supernova (CCSN) explosion mechanism and the neutrino production in such energetic phenomena, motivating the search carried out during this thesis. The CCSN neutrino fluxes studied are introduced, with a discussion on the potential of a multimessenger detection of a CCSN event and a short description of the SuperNova Early Warning System (SNEWS).

Historical introduction to CCSN neutrinos

It was already in 1934 that the mechanism of stellar evolution was linked to the formation of a compact object at the end of the life of a massive star. At the same time, Supernovae remnants were proposed as a candidate site for the process of hadronic acceleration. This was the idea of W. Baade and F. Zwicky, published in [START_REF] Baade | On super-novae[END_REF][START_REF] Baade | Cosmic rays from super-novae[END_REF][START_REF] Baade | Remarks on super-novae and cosmic rays[END_REF], who first used the term supernova (SN).

They based their arguments on the insight that the energy released observed from the SN phenomenon originates from the gravitational binding energy of the collapsing star. This basic picture continues to be the solid foundation of our present knowledge of stellar evolution and the birth of neutron stars (NSs).

Therefore, these objects start to be investigated as sources of cosmic rays, which were first identified as of extra-terrestrial origin by V. Hess in 1911. The origin of these really high energetic particles reaching the Earth still remains a mystery (see chapter 1).

The discovery in 1968 of the Crab pulsar inside the Crab nebula, with the testimony of the Crab SN observed in 1054, confirmed the existence of neutron stars as well as their association with SN remnants. This has been firmly established also by many recent observations. A direct confirmation of the scenario of stellar core collapse, with neutrinos as possible agents to drive the SN explosion, occurred with the detection of two dozen neutrinos from SN 1987A [START_REF] Burrows | Neutrinos from SN 1987A[END_REF] in the underground experiments of Kamiokande II [START_REF] Hirata | Observation in the Kamiokande-II Detector of the Neutrino Burst from Supernova SN1987A[END_REF], Irvine-Michigan-Brookhaven [START_REF] Haines | Neutrinos from SN1987a in the IMB Detector[END_REF] and Baksan [START_REF] Alekseev | Detection of the neutrino signal from SN 1987A using the INR Baksan underground scintillation telescope[END_REF]. This event originated in the Large Magellanic Cloud, a dwarf galaxy satellite of the Milky Way. The total luminosity released in neutrinos is measured to be around 3×10 53 erg/s and events were observed over about 10 s [START_REF] Burrows | Neutrinos from SN 1987A[END_REF]. The time profile of the detected events in shown in Fig. 4.1.

Since then, no nearby supernova has occurred. With only 1-3 events expected per century in the Galaxy, astronomers anxiously wait to the next SN in the Milky Way. Current and near-future neutrino detectors will be sensitive only to nearby supernova, and only a few of them will reach a distance horizon outside of the Galaxy, up to 50-500 kpc [START_REF]Eleven Year Search for Supernovae with the IceCube Neutrino Observatory[END_REF][START_REF]Search for Supernova Neutrino Bursts at Super-Kamiokande[END_REF][START_REF]Neutrino astrophysics with Hyper-Kamiokande[END_REF]. Sampling the CCSN progenitors population in our Galaxy, the probability of a CCSN occurring as a function of the distance can be inferred (see Fig. 4.2). As expected due to the higher density of stars in the Galactic Centre, the probability peaks at that region. From this distribution, one can infer that more than 99% of Galactic CCSN will happen within ∼21 kpc from the Solar System.

Initially, the electron neutrinos produced in these electron captures can freely escape the stellar core. But the core continues contracting under gravity, and when the so-called nuclear density is reached, neutrinos get trapped in the collapsing stellar core. The neutrinosphere is the name given to the border defining the limit between the confinement and the free escape of neutrinos, i.e. it is defined as the last scattering surface for neutrinos. Their radius depends on the interaction probability, thus mainly on the neutrino flavour and the number of targets. Different neutrinospheres can be identified for ν e , ν e and ν x = {ν µ /ν µ , ν τ /ν τ }. A smaller radius implies a lower scattering probability and higher mean energy of emission.

When the collapsing core reaches the nuclear density saturation point (ρ 0 ∼2.6×10 14 g cm -2 ), nuclear interactions become repulsive, which produces the bouncing of the core, creating a shock that starts propagating towards the interstellar medium. At this point, neutrinos can not freely escape anymore, as it has been mentioned above. With the shock, the outer layers of light elements are expelled (Fig. 4.4 upper right). The bouncing of the core gives birth to the proto-neutron-star (PNS), which consists on the neutron rich matter that remains close to the core and it is not expelled. The core bounce is followed by the emission of an intense flash of ν e from electron captures, which takes place as the shock crosses the ν e neutrinosphere. This is identified as the first neutrino emission phase, called shock-breakout neutrino burst (Fig. 4.4 upper right), which lasts some milliseconds and produces a large peak in the ν e luminosity. The time evolution of the neutrino luminosity during the burst is shown in Fig. 4.5 (left).

During the propagation of the shock inside the outer core, it loses energy though the photo-dissociation of iron nuclei and electron captures. This prevents the shock from propagating for more than some milliseconds, and the shock is stalled well before the boundary of the iron core (Fig. 4.4 middle left). However, while the shock propagates, it carries matter with neutrinos towards the less dense outer regions, where the core becomes again transparent to neutrinos.

In fact, the shock expansion loses energy until it is stopped, and neutrinos can freely escape again.

The ν e burst is then followed by an accretion phase, during which the outer matter shells are ejected. It last hundreds of milliseconds long. Electron neutrino flavor dominates over the accretion phase, since ν e and ν e streaming away from the neutrinosphere are reabsorbed by free protons and neutrons:

ν e + n → p + e - ν e + p → n + e + .
But emission of all flavor neutrinos is possible by neutrino-antineutrino pair creation. The time profile of the neutrino luminosity predicted during the accretion phase is shown in Fig. 4.5 (middle)

The stalled shock receives energy from the neutrinos escaping from the neutrinosphere. This situation defines the phase of neutrino heating (Fig. 4.4 middle right). During the accretion phase the core is stirred by violent hydrodynamical instabilities. In particular, the Standing Accretion Shock Instability (SASI) has been shown to take place in the latest 3D simulations. Both SASI and convection are believed to play a relevant role in the shock revival by enhancing the neutrino heating. Finally, neutrinos are able to transfer enough energy to the stellar plasma and accelerate the shock, which is revived (Fig. 4.4 lower left).

The SASI mechanism is thought to favor the energetic final explosion, which is not yet fully reproduced by simulations and could explain the asymmetry of the shock as well as the neutron star kick observed. The presence of fast time variations in the neutrino luminosity due to the SASI oscillations can be observed in Fig. 4.5 (middle). An observational confirmation of the presence of such hydrodynamical instabilities during the CCSN accretion phase would significantly help to unveil the explosion During a CCSN, ∼99 % of the gravitational binding energy is released in the form of neutrinos with energies of 1 to 100 MeV over a timescale of a few seconds. For a typical total energy of 3 × 10 53 erg, this equates to an emission in an excess of 10 58 neutrinos. This highly efficient energy loss via neutrinos occurs because neutrinos interact only via weak interaction and can easily escape, whereas photons remain trapped for a longer time. Indeed, the main phases of a core-collapse supernova explosion occur at a stage in which the star is opaque to optical photons. In summary, the neutrino emission occurs in three main phases. At first, the neutronisation burst results in a bright pulse of ν e as the shock breaks out crossing the ν e neutrinosphere. In the following accretion phase, an intense all-flavour emission takes place over a few hundreds of milliseconds, as the core is heated and stirred by the infalling matter. Finally the remaining energy is radiated through an all-flavor emission during the thermal cooldown of the core on a 10-20 s time scale.

In this mechanism, illustrated in Fig. 4.4, the shock expansion is driven by the neutrino-energy deposition to the stellar plasma. The neutrino time profile of the three phases is shown in Figure 4.5. The simulation of the accretion phase is described in [START_REF] Tamborra | Neutrino emission characteristics and detection opportunities based on three-dimensional supernova simulations[END_REF] and the simulation of the burst and cooling phases used here can be found in [START_REF] Hüdepohl | Neutrino signal of electroncapture supernovae from core collapse to cooling[END_REF]. More detailed information about the physics of the explosion and its implementation into numerical simulations can be found in [START_REF] Janka | Neutrino dirven explosions[END_REF][START_REF] Peres | Transport de neutrinos dans les supernovas gravitationnelles[END_REF].

Prompt SN neutrino fluxes and spectra

Simulations of the SN explosions are well advanced nowadays and are compatible with the detected spectra and time distributions of the only CCSN detected through neutrinos so far: SN1987A (for a review see, for example, [START_REF] Valentim | Evidence for Two Neutrino Bursts from SN1987A[END_REF]). The neutrino flux depends on the spectral pinching shape parameter, the total neutrino luminosity and the mean neutrino energy. Different simulations using different models predict a different time dependence and different values of these 3 parameters. These differences come mainly from the different neutrino transport models used, the different simplified treatment of General Relativity considered, and some different assumptions. In this study, a state-of-the-art 3D simulation of the accretion phase of a CCSN provided by the Garching group is considered.

The simulations used for this thesis work were performed with the PROMETHEUS-VERTEX code [START_REF] Rampp | Radiation hydrodynamics with neutrinos* -variable eddington factor method for core-collapse supernova simulations[END_REF], which couples the hydrodynamics solver PROMETHEUS with the neutrino transport code VERTEX. Such a numerical code is used for treating the time and energy dependent neutrino transport in hydrodynamical simulations of CCSN. The code is based on a variable Eddington factor method to deal with the solution of the Boltzmann equation. This code is well suited to solve relativistic and multidimensional problems accurately. This simulation has been extensively used to test IceCube and Super-Kamiokande sensitivity to CCSN neutrinos [START_REF] Tamborra | Neutrino emission characteristics and detection opportunities based on three-dimensional supernova simulations[END_REF][START_REF] Tamborra | Neutrino signature of supernova hydrodynamical instabilities in three dimensions[END_REF].

As it was shown in ref. [START_REF] Tamborra | Neutrino emission characteristics and detection opportunities based on three-dimensional supernova simulations[END_REF], the time dependent SN neutrino spectrum can be represented by a quasi-thermal distribution of the form:

dΦ ν dE ν (E ν , t) = L(t) ν SN 4πd 2 × f (E ν , E ν (t), α(t)) (4.2) f (E ν , Ẽν (t), α(t)) = E α(t) ν Γ(1 + α(t)) 1 + α(t) E ν (t) (1+α(t))
exp -

E ν (1 + α(t)) E ν (t) (4.3)
where < E ν > is the average neutrino energy, L(t) ν SN is the neutrino luminosity and α =

E 2 ν -2( E ν ) 2 ( E ν ) 2 -E 2 ν
is the spectral pinching shape parameter, spanning in the range of 2 α 5.

The spectral pinching parameter indicates the shape of the quasi-thermal distribution. α = 2 corresponds to a Maxwell-Boltzmann distribution, while the spectrum is "pinched" for α > 2. In fact, the energy dependence of the cross section results in a radial smearing of the neutrinosphere and a corresponding alteration (pinching) of the neutrino thermal spectrum.

Furthermore, the flavors have an expected energy hierarchy. Energies decrease with increasing order of the interaction strength: ν e have more interactions than ν e because of the excess of neutrons in the core, so less average energy, and ν e have more interactions than the other neutrino flavors (noted ν x ), which are restricted to neutral current interactions.

As explained in ref. [153], data are provided in files for each neutrino flavor (ν e , ν e and ν x ) containing the current post-bounce time in the first column and the luminosity, the average neutrino energy and the second energy moment of the neutrino for three different observer directions in the following three columns.

The time and energy evolution of these three parameters is given by the simulation. The time dependence of the three parameters is shown in Fig. 4.7 for the 27 M ⊙ progenitor. How these parameters behave in time from the core bounce at the collapse stage is one of the open questions and different prediction come out from the different models.

The evolution of the neutrino flux is shown in Figure 4.8 as a function of the energy. It can be seen that, during the first ∼ 30 ms of the explosion, the ν e flux from the neutrino burst are dominating. The fluxes evolve towards equipartition among the three flavors at the end of the accretion phase (>400 ms after T 0 ). The neutrino fluence (time-integrated spectrum) at a reference distance of 10 kpc is shown in Figure 4.9 for the three considered progenitor models.

In the following, KM3NeT sensitivity will be tested using the neutrino flux simulated for:

1. Four progenitor star simulations of masses: 40 M ⊙ [START_REF] Walk | Neutrino emission characteristics of black hole formation in three-dimensional simulations of stellar collapse[END_REF], 27 M ⊙ [START_REF] Tamborra | Neutrino emission characteristics and detection opportunities based on three-dimensional supernova simulations[END_REF], 20 M ⊙ [START_REF] Tamborra | Neutrino emission characteristics and detection opportunities based on three-dimensional supernova simulations[END_REF] and 11 M ⊙ [START_REF] Tamborra | Neutrino emission characteristics and detection opportunities based on three-dimensional supernova simulations[END_REF]. The first is an example of failed CCSN, in which case a BH is formed at the end of the explosion, with a sharp cut-off on the neutrino luminosity and no electromagnetic counterpart is expected.

The second and latter will be compared as extreme cases for the CCSN sensitivity in chapter 6.

The second and third are compared in section 7.

Neutrino flavor conversion models in CCSN

The traditional picture of neutrino flavor conversion occurring in CCSN is that adiabatic flavor conversion (MSW effect, see section1.3.1 or [START_REF] Wolfenstein | Neutrino oscillations in matter[END_REF]) takes place inside the star. An analogy with solar neutrinos is used here. The occurrence of the MSW effect for the high energy solar neutrinos shows that these particles change flavor in vacuum in a very different way than in matter. This also applies to MeV CCSN neutrinos. A nice overview of neutrino flavor conversion in CCSN is given in [START_REF] Volpe | Neutrino Astrophysics[END_REF].

In the inner high density regions of the star, the neutrino flavor and matter eigenstates coincide. While propagating towards the edge of the star, they can suffer resonance effects that lead to neutrino flavor conversion. It is believed that the MSW resonance condition is fulfilled for CCSN neutrinos as for solar neutrinos, leading to flavor conversion [START_REF] Mikheyev | Resonance Amplification of Oscillations in Matter and Spectroscopy of Solar Neutrinos[END_REF].

The MSW effect in supernovae is well established. Actually, since the star is very dense, the MSW resonance condition can be fulfilled three times for typical supernova density profiles [START_REF] Dighe | Identifying the neutrino mass spectrum from the neutrino burst from a supernova[END_REF]. The sign of the neutrino mass-squared differences determines if neutrinos or anti-neutrinos undergo a resonant conversion. The MSW effect in CCSN is illustrated in Fig. 4.10, for the two neutrino mass ordering hypothesis. In case of Normal Ordering (NO), ν e flux will be affected by the MSW effect. If the true ordering is the Inverted Ordering (IO), then the ν e flux is suppressed through the resonance. In fact, the recent measurement of the third mixing angle θ 13 being fairly large suggests that the entire threeflavor conversion process would be adiabatic. In this picture, all ν e will undergo the MSW resonance and leave the star as ν x in case of inverted mass ordering. In the normal ordering hypothesis, a 70% ν e survival probability is expected. The adiabatic evolution implies that the mass eigenstates mixing according to neutrino oscillations in matter (see 1.3.1) is suppressed at the resonance, i.e. the strong matter effect in the extremely dense CCSN media "de-mixes" neutrinos. In this case, electron neutrinos can efficiently convert into muon and tau neutrinos, which can be considered as a same flavor state from what their evolution concerns in this context. In the following, the non-electron neutrinos will be noted ν x . The problem can be therefore simplified to two mass eigenstates.

Towards a multi-messenger detection of the next Core-Collapse Supernova: the SNEWS network 83

Even though the adiabatic flavor conversion is a good approximation, recent calculations have shown the emergence of new phenomena that could make the neutrino evolution become completely non-adiabatic when the shock passes through the MSW region. The effect of neutrino-neutrino interactions, the presence of shock waves and turbulences, as well as steep changes of the stellar density profile, are examples of physical processes that affect the flavor conversion in CCSN, leading to a complicated non-adiabatic case. This is an additional uncertainty in the predicted flux.

The ν e flux arriving at the detector will be some superposition of the original ν e and ν x flux spectra. The two extreme possibilities will provide the maximum variation in the number of expected neutrinos. The first is the hypothetical scenario where no flavor conversion (NFS) takes place, which corresponds to the original ν e spectrum as emitted at the source. The second is the opposite case, given by the scenario where all ν e will oscillate into ν e (Full Flavor Swap, FFS). Fluxes in this case correspond to the expected detected SN neutrino flux at Earth if the true hypothesis for the neutrino mass ordering is the inverted ordering. For the purpose of the analysis developed in this chapter, no flavor conversion will be considered.

Towards a multi-messenger detection of the next Core-Collapse Supernova: the SNEWS network

If an astrophysical process is driven by non-spherical mass-energy dynamics including quadrupole or higher order contributions, Gravitational Waves (GWs) are emitted together with neutrinos and photons. Such asymmetric magnetohydrodynamic processes are expected to take place in CCSNe, in particular, during the stalled-shock phase previous to the explosion. In fact, these GW emission may be crucial to fully understand the CCSN mechanism.

The latest advances in 3D CCSN simulations have led to a number of gravitational wave signal predictions from these sources [160,161,162,163]. However, there is a large uncertainty on the models leading to different predictions of the GW signal. Despite the lack of knowledge of the exact GW signal, some common features happening in CCSNe have been identified to enhance the GW emission. In some models, a GW signal peak is predicted at the core bounce time for rapidly rotating CCSNe. Simulations also show that the SASI instability might give rise to low frequency gravitational wave emission. Additionally, high-frequency gravitational-wave emission related to the oscillations of the surface of the proto-neutron star (PNS), called g-modes, is also present in simulations.

The current sensitivity of GW detectors is not high enough to detect extragalactic CCSN by themselves due to the small amplitude of the expected signal [START_REF] Roma | Astrophysics with core-collapse supernova gravitational wave signals in the next generation of gravitational wave detectors[END_REF]. Therefore, identifying the core-bounce time or the SASI oscillations with a resolved neutrino light-curve can be helpful to identify a GW counterpart to a CCSN. The detection of GWs from a CCSN could allow to constrain the explosion mechanism, as well as the presence of hydrodynamical instabilities predicting specific features (SASI and g-modes) in the observed signal.

These simulations provide the prediction of the expected GW signal shape in the time-frequency domain. An example is shown in Fig. 4.11, which illustrates the interest of timing the CCSN signal via a prompt neutrino detection in order to achieve a GW detection. Knowing the frequency range in which the signal shows up, as well as having possible hints on the time window where to look at, is specially relevant for GW detectors to reduce their noise. The evolution of the frequency in time also helps to discriminate between the patterns corresponding to different signal sources, and discriminate the GW signal from noise.

Chapter 5

CCSN neutrino simulation in KM3NeT

This chapter is devoted to describe the context of CCSN neutrino detection with the KM3NeT neutrino telescopes and explain the detailed simulation of the detector response to CCSN neutrino fluxes that has been developed during this thesis. Moreover, the SNOwGLoBES public software for a fast simulation of the CCSN detection rates is presented.

General context

Although KM3NeT detectors are mainly designed for high-energy neutrino detection, the 10 MeVscale neutrino signal from a CCSN can be identified as a simultaneous increase of the counting rate in the PMTs of the detector.

The main interaction modes of these MeV neutrinos (see [START_REF] Scholberg | Supernova Neutrino Detection[END_REF]) in water are:

• The interaction with free protons (Inverse Beta Decay, IBD): ν e + p → e + + n • The interaction with free electrons (Elastic Scattering, ES): e -+ ν → e -+ ν • The interaction with oxygen nuclei: ν e + 16 O → e -+ 16 F , ν e + 16 O → e + + 16 N The outgoing electron/positron produced through these interactions radiates Cherenkov light that can be detected by the PMTs. The length of the Cherenkov track released is some centimetres. In particular, IBD interactions lead to charged particle tracks of about 0.5 cm × E ν

MeV length [START_REF]Icecube sensitivity for low-energy neutrinos from nearby supernovae[END_REF].

Event reconstruction is not possible due to the short track length of low energy positrons/electrons produced in MeV neutrino interaction compared to the large distance between the DOMs. However, a supernova neutrino burst should produce a collective increase of PMT rates in the whole detector.

Using the simulation described in this chapter, the goal of chapter 6 will be to evaluate the discrimination power between this MeV neutrino signal and main background sources, which have been described in section 3.1. The optical background due to 40 K decays in sea water and bioluminescence can be significantly reduced by using nanosecond coincidences between the nearby placed PMTs (as explained in section 3.1). This technique has been tested with the ANTARES telescope [171], consisting of storeys with three 10-inch PMTs (see section 2.2), and has been optimised for the KM3NeT telescope where the directional DOMs containing 31 3-inch PMTs provide better background rejection power. Atmospheric muons represent also a source of background for this measurement.

The Cherenkov photons from CCSN neutrinos can be detected by the KM3NeT DOMs as hits on single PMTs or coincidences between multiple PMTs on the same DOM. A coincidence is defined as a sequence of hits on the same DOM within a predefined time window. The number of PMTs in a DOM detecting a hit within 10 ns is called multiplicity (M). As a generalisation, coincidences and single hits are from now on referred as events with multiplicity M = 1 for single hits and M ≥ 2 for coincidences.

MeV neutrino interactions in sea water

In this section, we go into the details of the Monte Carlo simulation framework for low-energy neutrino generation developed during this thesis work (called lenugen, see section 3.4). The aim is to estimate the number of CCSN neutrino events that will interact in our detector as a function of the neutrino energy and time and to build the interaction rates. For this, two ingredients are needed: the fluxes as a function of energy and time (as predicted by the 3D CCSN Garching models, given in section 4.3), and the interaction cross section of each interaction channel.

Computing the interaction rates

As stated in section 5.1, MeV CCSN neutrinos can undergo three different interactions: Inverse Beta Decay (IBD), Elastic Scattering (ES) and neutrino interactions with oxygen nuclei. They account for about 97%, 3% and less than 1% of the interactions, respectively. Therefore, KM3NeT will be sensitive mainly to the ν e signal detected indirectly via IBD interactions.

Indeed, the elastic scattering interaction cross section is well lower than the one of IBD. Moreover, the outgoing electrons producing the Cherenkov light have a lower energy (about 1 MeV) compared to the IBD positrons, making it difficult to get a detected photon from this interaction. As regards the interaction with oxygen nuclei, its energy threshold is higher due to the higher mass of oxygen compared to protons and electron. Therefore, the probability of this interaction occurring at the typical CCSN energies over the accretion phase (1-30 MeV) is significantly lower than the one of IBD, as inferred from Fig. 5.1.

Because the KM3NeT detector is mainly sensitive to IBD interactions, whose emission takes place predominantly during the accretion phase, and three-dimensional simulations only include this time window (see section 4.3), which lasts about half a second, the focus will be placed for the subsequent study on this time window. The burst contribution only accounts for ∼1 per mille of the total detected signal in KM3NeT, while the cooling can bring up to about 20% of the detected events. Therefore, increasing the time window would only degrade the sensitivity to these MeV neutrinos.

Only charged particles will produce light observed in water Cherenkov detectors. Due to the low energy and short length of the tracks released by CCSN neutrino interactions, no secondary particles will lead to additional leptons inducing detectable light. Therefore, only the primary lepton is simulated in the framework discussed.

In the current simulations, cross sections are computed from the latest models available for this energy range for the IBD and ES interactions [START_REF] Strumiaa | Precise quasielastic neutrino/nucleon cross-section[END_REF][START_REF] Radel | Neutrino electron scattering[END_REF]. For the neutrino interactions with oxygen, we use cross sections from the tables used by SNOwGLoBES [START_REF] Beck | SNOwGLoBES: SuperNova Observatories with GLoBES[END_REF]. For the simulation of the outgoing particles, we use the angular differential cross sections, shown in Figure 5.2, to account for the directionality dependence of their energy. In practice, the angular dependent lepton spectrum is used for getting the information of each interaction (energy, direction and interaction mode). The positron energy in the IBD processes is calculated as indicated in [START_REF] Strumiaa | Precise quasielastic neutrino/nucleon cross-section[END_REF]:

E e = (E ν -∆m)(1 + E ν m p ) + E ν m p cosθ (E ν -∆m) 2 -m 2 e κ κ , (5.1)
where, m e is the mass of the electron, m p the mass of the proton, E ν the energy of the incoming neutrino, θ the scattering angle, i.e. the angle between the incoming ν and the outgoing lepton, ∆m =

m 2 n -m 2 p -m 2 e 2m p and κ = (1 + E ν m p ) 2 -( E ν m p cosθ) 2 .
The ES electron energy is given be the following expression, derivated in [START_REF] Radel | Neutrino electron scattering[END_REF]:

E e = m e (1 + E ν m e ) 2 + E 2 ν cosθ 2 m e (1 + E ν m e ) 2 -( E ν m e cosθ) 2
.

(5.2)

Figure 5.3 shows the cross section as a function of the neutrino energy integrated over all scattering angles, for the IBD (left) and ES (right) interactions, respectively. The total cross section is obtained by integrating the differential cross section in energy and over the possible scattering angles. Finally, the interaction rates, shown in Figure 5.4, are computed for the accretion phase using the above-mentioned flux and the integrated cross sections with the following relation:

R int (MeV -1 s -1 ) = σ(cm 2 ) × flux(cm -2 MeV -1 s -1 ) × N target (5.3)
where N target is the number of protons, electrons or oxygen nuclei (depending on the considered interaction channel) in a reference water detection volume, which is arbitrary taken as equal to 100 kton.

For the neutrino interactions with oxygen, the angular dependence is taken into account using the kinematics of the interaction. The 2D distributions obtained for ν e + 16 O and ν e + 16 O interaction rates are shown in Figure 5.5 for a 100 kton water detector. The output of the simulation contains the information about the incoming neutrino and the outgoing particles for each generated interaction. Following this step, the Geant4 event-by-event simulation KM3sim (see section 3.4 or ref. [START_REF] Tsirigotis | Hellenic Open University Reconstruction & Simulation (HOURS) software package: User Guide & short reference of Event Generation, Cherenkov photon production and Optical Module simulation[END_REF]) is used to propagate these particles inside the detector, and simulate the Cherenkov light production and detection. The DOM model in KM3Sim defines each PMT as a flat disc, and includes the full PMT description through a detailed parametrisation of the angular PMT acceptance and the PMT quantum efficiency (QE). The photon detection efficiency is calculated by detailed simulations for each incident angle and wavelength.

The output light files are processed through different steps with the KM3NeT software, called Jpp [START_REF] Jong | [END_REF] for the complete simulation of the detector response. First, J AANeTPreProcessor removes all the interactions for which there is no hit PMT and converts the KM3Sim files into root format. Then, JEventTimesliceWriter (JETW) simulates the PMT response, generating the "real hits" (i.e., observed p.e.) from the MC photons, and providing the time-over-threshold (ToT) information. Here, photons impinging in coincidence on the same PMT are merged. The output MC data format is converted at this stage into the same as the sea data format used by the DAQ. The data are structured in Timeslices, which are time segments of 100 ms duration (see section 2.3.2). In fact, JETW is equivalent to JTriggerE f f iciency, described in section 3.4.3, but without applying the triggers, and with the possibility of keeping the MC time ordering information of the simulated events. Finally, J MonitorMultiplicity is used to build time coincidences between the different PMTs in a DOM.

In this framework, all simulated neutrinos are forced to interact, since significant MC statistics is needed, and the input interaction rates are provided for a reference detection volume. Therefore, a scaling factor must be applied to the output MC hits in order to reproduce the total number of events that will be observed in the KM3NeT detector from a CCSN event emitting a given neutrino flux, noted N det and given by Eq. 5.4:

N det = N MC • N SN N gen • (ρ water • V gen ) 10 8 kg • N DOM , (5.4)
where N MC is the number of events in the output of the Monte Carlo simulation (observed hits), N gen the total number of generated neutrinos, N SN the total number of CCSN neutrinos interacting in a reference water mass of 100 kton (volume of 10 5 m 3 ) from a source distance of 10 kpc, ρ water • V gen the mass of the chosen generation volume and N DOM the number of DOMs of the detector. The first factor accounts for the simulated statistics compared to the number of neutrinos expected to interact from a CCSN at a given simulated distance. The second factor is for the correction of the simulation reference volume (100 kton) to the KM3NeT effective detection volume.

The values obtained are N SN = 3964 for the 11 M ⊙ , N SN = 12 930 for the 27 M ⊙ , and N SN = 32 562 for the 40 M ⊙ . For the neutrino generation, the contribution of the salinity to the seawater density is neglected and ρ water is assumed as equal to the pure water density, ρ water = 10 3 kg • m -3 . The effect of the salinity is taken into account at the light propagation stage and simulated by KM3Sim.

For the estimate of the sensitivity in chapter 6, a fixed time window of 500 ms will be used for all progenitors. Therefore, the numbers provided in the previous paragraph have to be rescaled to evaluate signal expectation in this window. For the 11 M ⊙ progenitor, this is done by artificially extending the tail of the signal, assuming a constant interaction rate between 340 and 500 ms. For the 27 and 40M ⊙ progenitors, the number of signal events within 500 ms is computed from the integral of the total interaction rate in the first 500 ms of the simulation. The numbers become then: N SN = 5657 for the 11 M ⊙ , N SN = 12 216 for the 27 M ⊙ , and N SN = 30 852 for the 40 M ⊙ .

Optimisation of the generation volume V gen

The generation volume has been optimised in order to maximise the expected CCSN neutrino rates inside it. The optimization is performed using the double coincidence selection: events that give at least 2 hits within 10 ns in two different PMTs of the same DOM. This choice is made because if V gen is optimised for double coincides, no signal efficiency will be lost either for higher multiplicities, and single simulation can be used to explore all possible selections. CCSN neutrino rates have been computed for different radii of the sphere from the complete Monte Carlo simulation. The results are shown in Figure 5.6. A saturation is reached at r = 20 m for events producing at least two hits, hereafter referred to as double coincidences. The choice of a 20 m radius is conservative when events with higher number of hits are considered, as the optimal radius decreases with the coincident number of hits generated by one single neutrino event. Coincidences between different events are not probable to happen due to the distance between the CCSN interactions being larger than µs.

Note that the optimal generation volume obtained is larger than the distance between optical modules in KM3NeT/ORCA. This means that some photons will be detected and shadowed by another DOM, closer to the interaction vertex, which effect is not taken into account in the simulation. In fact, In practice, the background for a time bin in a detector of N DUs is simulated integrating over N/n time bins of the measured background with n = 1, 2 DUs. By default, the N/n time bins are chosen as a continuous sequence of the original data, but additional randomisation can be added to reduce the amount of correlations in the output. An example of the measured lightcurve applying a coincidence selection with 5 ns window is shown in Fig. 5.7, for ORCA (right) and ARCA (left).

CCSN neutrino lightcurve using L1 data

The simulation of the different stellar progenitors are used to compute the CCSN neutrino lightcurve, with masses: 40 M ⊙ , 27 M ⊙ and a 20 M ⊙ . From the output of the lenugen simulation, the number of detected events for each time bin i, N det [i] is estimated in analogy with equation 5.4:

N det [i] = N MC [i] N gen • N SN 10 8 kg • (ρ water • V gen • N DOM ) (5.5)
where N MC [i] is the number of events in the simulation output for the time bin i (events per bin) and ρ water the water density. N MC [i] follows the time distribution of the generated neutrino spectrum.

Parametrisation of the detector response and SNOwGLoBES

SNOwGLoBES stands for Supernova Neutrino Observatory with GLoBES, and it is a public software available under the GitHub repository: https : //github.com/SNOwGLoBES/snowglobes. It allows to compute the detection rates for different experiment configurations using a smearing matrix to simulate the detector response for a given CCSN neutrino flux model [START_REF] Beck | SNOwGLoBES: SuperNova Observatories with GLoBES[END_REF].

The work done to implement the KM3NeT detector into SNOwGLoBES is presented here. This work has been performed to provide an easy and fast way of estimating the expected number of CCSN neutrinos detected by the different neutrino detectors involved in the SNEWS collaboration. The MC framework presented before is a proprietary code belonging to KM3NeT and is not dedicated to be used outside the Collaboration.

Parametrisation of the detector response and SNOwGLoBES

97

The total effective mass is computed as an average over energy, and changes with the progenitor/model spectrum. The effective mass as a function of the multiplicity is provided for three different progenitors of 11 M ⊙ , 27 M ⊙ , and 40 M ⊙ , with different average energy. As shown in Table 5.2, the KM3NeT efficiency also depends on the multiplicity selection applied. The effective mass of a KM3NeT 115-lines instrumented block is 40-70 kton for all coincidences and 1-3 kton for coincidences with six or more hit PMTs. Chapter 6

Detecting CCSN neutrinos with KM3NeT

This chapter is dedicated to the detection method and performance of the KM3NeT detectors to MeV CCSN neutrinos. The signal and background characterization, the noise rejection strategies and the systematic uncertainties on the analysis will be provided. Both the real-time (online) capabilities and the performances from a refined dedicated search (offline) for the detection of the CCSN neutrino signal in KM3NeT will be described.

Signal and background

Recapitulating from sections 5.1 and 3.1, the MeV neutrino signal from a CCSN will be identified as an overall increase of the detection rate. The multiplicity distribution of signal events can be compared with those of the background sources, which are bioluminescence, radioactive decays in sea water (and in the DOM glass) and atmospheric muons. This is used to identify the different contributions and reject what does not look like CCSN neutrinos.

On this analysis, the signal is estimated from 3D CCSN simulations (described in section 4.3) while the background is measured from data. The CCSN simulations provided by the Garching group have a limited duration, covering only the accretion phase. Table 6.1 reports the expected number of detected events from a CCSN neutrino flux as a function of the multiplicity for three considered stellar progenitors, with masses of 40 M ⊙ , 27 M ⊙ and 11 M ⊙ , at a reference distance of 10 kpc. As already mentioned, the background of single hits (L0s in section 3.3) is dominated by radioactive decays, accounting for typical rates of 200 -250 kHz per DOM. The rates are also subject to significant diffused or local increases due to bioluminescence activity. These features make very difficult to exploit this channel for the CCSN detection. Coincidences are in general given by different types of Cherenkov light emissions. Radioactive decays (mostly 40 K) dominate at low multiplicities, with a rate that roughly follows the empirical expression that has been derived in the Collaboration from the first 102 Chapter 6. Detecting CCSN neutrinos with KM3NeT Table 6.2 for each multiplicity. The ORCA background rate for M ≥ 6 is only slightly higher than the residual radioactivity contribution (0.05 Hz), confirming an excellent performance. A signal event from a CCSN neutrino interaction will be vetoed if occurring within ±τ veto from the time of any background coincidence with multiplicity ≥ 4. The coincidence rate per DOM with M ≥ 4 being equal to 5 Hz, the corresponding dead time fraction is 2 • τ veto • R M≥4 • N DOMs totalling 2% for a full ORCA-like building block and 6% for a full ARCA-like building block. Simulations show that veto fraction due to two coincident signal events is less than 1 per mille of the detected CCSN interactions.

The rejection efficiency in ARCA is limited by the relation between maximum multiplicity and distance of closest approach of the muon to the DOM, which is illustrated in Fig. 6.3. About 40% of muons producing a maximum multiplicity of 6 have the closest approach to the DOM in the 5-8 m range, while about half of the muons producing a maximum multiplicity of 4 have the closest approach between 7 and 15 m. Therefore, a spacing between adjacent DOMs below 23 m is required in order to reject at least 40% of the muons. This condition is not satisfied by the ARCA geometry.

Muon rejection: triggered events veto

In order to improve the performance of the muon filter and reduce the dead time, an alternative approach has been implemented exploiting the KM3NeT physics triggers, generally used to identify track-like and shower-like events at higher energies (detailed in section 3.3), as a veto mechanism.

Background rejection 103

KM3NeT triggers are designed to look for clusters of hits correlated in space and time across multiple DOMs, in order to identify track-like or shower-like events. The main information content of a triggered event is a collection of triggered hits, namely the set of causally-connected hits recognised by the algorithm as part of a physics event, usually atmospheric muons.

For each triggered event, a veto window is defined by a set of DOMs and a time interval that covers all the triggered hits. In parallel, coincidences are filtered and clustered as described in steps 1 and 2 of subsection 6.2.1. For each cluster, the (first) coincidence having the highest multiplicity is considered. The coincidence is discarded if it occurs on a DOM and at a time covered by the veto window. The surviving coincidences are counted as potential signal events in the final distribution.

To test the approach, data of ARCA2 and ORCA4 have been analysed. Each run is processed using timeslice and triggered event data. All available triggers (described in section 3.3) are considered. The typical parameters for each trigger are the following:

• 3DMuon: minimum 3 L1 hits on 3 different DOMs within a cylinder of 43 m diameter for ORCA; min 4 L1 hits on 4 DOMs, within a cylinder of 120 m for ARCA.

• 3DShower: 3 L1 hits on 3 different DOMs with D max of 52 m for ORCA and 250 m for ARCA.

• MXShower: one L1 + at least 7 L0 hits on 3 different DOMs with D max 47 m for ORCA and within 110 m for ARCA.

In this analysis, for each triggered event produced by the data filter, a veto is applied on the set of DOMs detecting at least one triggered hit in the time interval defined by the range of the triggered hit times. Typical values for this interval are ∼ 1 -3 µs. The remaining coincidences are analysed on a DOM-by-DOM basis. If one or more coincidences occur in a DOM within 1 µs, only the coincidence with the highest multiplicity is kept. This filtering strategy results in an effective reduction of the background rates and in the suppression of spurious coincidences. This is verified on data from the ARCA2 and ORCA4 detectors. The rejection efficiency evaluated on the operating detectors is given in Table 6.3. Comparing with Table 6.2, the trigger veto is shown to be more efficient for the atmospheric muon rejection than the coincidence veto. The efficiency of the background rejection is also evaluated for a full KM3NeT ARCA and ORCA building block by means of a Monte Carlo simulation. The simulation chain is based on the atmospheric muon event generator ▼❯P❆•❊ [START_REF] Becherini | A Parameterisation of single and multiple muons in the deep water or ice[END_REF] and the Cherenkov light simulator ❏❙✐r❡♥❡ which is part of the custom KM3NeT software suite ❏♣♣ [START_REF] Jong | [END_REF]. The generation of the simulated hit data follows the procedure outlined in [START_REF] The | Dependence of atmospheric muon flux on seawater depth measured with the first KM3NeT detection units[END_REF]. The fraction of coincidences rejected by the trigger as a function of the multiplicity is shown in Figure 6.4 (left) for the ARCA and ORCA building block simulations. The denser geometry of the ORCA detector allows to identify and suppress more than 95% of the background starting at multiplicity eight or above. For comparison, ARCA reaches 65% rejection efficiency at multiplicity eight. Figure 6.4 (right) shows the comparison of the background and expected signal rates after the filter, in contrast to Fig. 6.2 which is shown before the rejection.

Flux model

The second type of systematic uncertainties is related to the total observed rate of each neutrino flavor, including changes in the neutrino-flavor dependent luminosity and energy. These uncertainties are given by the variations observed within the different hydrodynamical simulation codes, coming from the neutrino transport mechanism or the relativistic approach used, among others. The oscillation effects in the star and in the Earth as well as opacity effects due to neutrino-self interaction will also produce a change in the total amount of ν e emitted and detected. However, for what concerns this study, only detector-related uncertainties will be taken into account.

Due to the large uncertainties in the final neutrino flux, the NFS hypothesis is assumed for the oscillation scenario as a reference to evaluate the detector performance in this analysis, for the different progenitors considered (see section 4.3). In fact, the impact of this assumption compared to the opposite extreme case (FFS) depends on the energy neutrino spectrum predicted for each progenitor. As an example, in case of FFS, the variations are respectively a 15% loss for the 27 M ⊙ progenitor and a 26% gain for the 11 M ⊙ model. This will correspond to use the most optimistic expectation for the 27 M ⊙ while the most pessimistic scenario for the 11 M ⊙ , which are the two extreme cases for which the sensitivity will be shown.

Sensitivity of KM3NeT detectors to a CCSN neutrino signal

In summary, the analysis steps to evaluate the sensitivity as explained is this section are following:

• The coincidence rates as a function of the multiplicity are measured from ARCA2 and ORCA4 data for the background estimate, and evaluated from simulations for the signal expectation.

• Two approaches are used to filter and reduce the atmospheric muon background.

• The efficiency of the filter for the full detector at each multiplicity is evaluated from the simulation of a full building block, for the ORCA and ARCA geometries.

• The background rate after the filter is given by the coincidence rates measured in the sea multiplied by the rejection efficiency expected for the full detector.

• The multiplicity selection providing the best sensitivity is identified.

• The robustness of the muon filter with respect to the optimised multiplicity selection is tested on ARCA2 and ORCA4 data.

• The detection sensitivity is estimated from the expected number of signal and background events in a 500 ms search window, within the optimal multiplicity range of the selection. This is done for the complete ARCA and ORCA detectors (230 and 115 DUs respectively).

Sensitivity definition

The sensitivity of an experiment to a given signal hypothesis can be characterised by its expected median significance. Here, it is of interest to evaluate the KM3NeT sensitivity to a CCSN neutrino signal by reporting the expected median significance. Hereafter, sensitivity and median significance will be referred to independently with this same definition.

The expectation values of signal and background, µ s and µ b , are used here for the evaluation of the median significance. In general, in a Poisson counting experiment with known background, the expected significance is derived from the Poisson p-value, evaluting the probability of observing n ≥ µ b + µ s when expecting µ b . A good approximation of the full numerical calculation for the sensitivity is given by the formula in Eq. 6.2, whose derivation can be found in [START_REF] Cowan | Asymptotic formulae for likelihood-based tests of new physics[END_REF]:

z = 2 • (µ s + µ b ) • ln 1 + µ s µ b -µ s (6.2)
where z is the sensitivity, calculated directly from the number of expected background (µ b ) and signal events (µ s ). In this analysis, µ s and µ b are evaluated for a 500 ms time window from the onset time of the event, assumed to be known from an independent observation. The median significance z derived from Eq 6.2 is defined as the equivalent Gaussian significance with the one-sided convention, and is given in "number of sigmas".

Notice that the approximation of the significance in Eq. 3.7 is usually considered as valid for a sufficiently large number of data events, signal (n s ) + background (n b ), but it is strictly correct only if n s << n b , as shown in [START_REF] Cowan | Asymptotic formulae for likelihood-based tests of new physics[END_REF]. In the statistical regime for CCSN neutrino searches, Eq. 6.2 should be used to evaluate the significance in an accurate way.

The significance does not linearly depend on the signal-to-noise ratio, but on their absolute scale. Therefore, a signal selection that increases the signal-to-noise but reduces the total amount of events is not guaranteed to provide a better result.

Combined sensitivity

In order to compute the combined sensitivity for both KM3NeT detectors, ARCA and ORCA, different approaches can be followed to combine the p-values or median significances. A nice overview of the different combination methods can be found in [START_REF] Cousins | Annotated bibliography of some papers on combining significances or p-values[END_REF].

One of the most common approaches is combining p-values using the Fisher's method. The significance (given by Eq. 6.2) can be converted into a p-value according to the following relation:

p i = Er f c z √ 2 (6.3)
Then, the p-values are combined in a χ 2 test statistic as follows:

χ 2 2k = -2 k ∑ i=1 ln(p i ) (6.4)
The χ 2 probability with number of degrees of freedom equal to twice the number of combined p-values (2k) gives the resulting p-value, and therefore the median combined significance.

It can happen that the optimal selection is different for each detector, as well as different orders of magnitude in the number of background events can be expected for the detectors that are going to be combined, resulting in different sensitivities. In this case, the Fisher method is not optimal and will penalize the most performing detector sensitivity when combining it with a worse one.

The weighted combination of significances, also called Stouffer's combination, is a better option in this case. This approach is used by the NovA Collaboration 1 and the combined significance can be written as follows:

z comb = z ARCA • z re f ARCA + z ORCA • z re f ORCA (z re f ARCA ) 2 + (z re f ORCA ) 2 (6.5)
where z re f ORCA and z re f ARCA are the reference sensitivities for ORCA and ARCA at 10 kpc.

Multiplicity selection

The comparison between expected rates in subsection 6.1 suggests the range above multiplicity 5 as the most favourable in terms of signal-to-noise ratio. After the muon filter is applied, the optimisation of the multiplicity selection is performed by maximizing the sensitivity in the two detectors for the signal expected considering each progenitor model.

Considering the background rates after the muon rejection approaches described in subsection 6.2.2, the sensitivity as a function of the number of expected background and signal events is estimated for the two progenitors and the two detectors, for a reference distance of 10 kpc. The results are summarised in Fig. 6.8. Here, the background data is extracted from ORCA4 and ARCA2 and scaled up to the full detector size. Because of the large variability of the ORCA detection efficiency with the number of active PMTs discussed in section 6.3, only timeslices with more than 99% of active PMTs are considered for the ORCA background estimate.

To account for the difference between the real detector (used to measure the background) and the nominal detector (used to simulate the signal), the background level is scaled to the nominal efficiency for each detector. This determines the average QE of each detector that is used to estimate the background expectation in a nominal detector. For ORCA4, the average efficiency of the DOMs is 0.96 for the selected data period, with variations below 1% over time. For ARCA2, an average efficiency of 1.025 is measured for the selected runs. The scaling applied to the background follows the relationship established in Fig. 6.7 for the signal.

The conclusion extracted from Fig. 6.8 is that not in all cases there is an optimal multiplicity selection. Therefore, the best multiplicity selection is chosen so that to maximise the 5σ discovery distance for the lower progenitor mass. The multiplicity range [START_REF]Observation of gravitational waves from a binary black hole merger[END_REF][START_REF] Patrignani | Review of particle physics[END_REF] is found to be the optimal for both ARCA and ORCA, specially considering that for M=12 the signal expectation for the 11 M ⊙ progenitor is close to zero.

Online supernova trigger in KM3NeT

An approach for the real-time search of a CCSN neutrino burst applicable already in the construction stage of KM3NeT has been developed and is operational since summer 2019. The data from the first deployed ARCA and ORCA DU have been extensively analysed by sampling the background on a τ = 100 ms time scale in order to characterise the background distribution.

The signal search is based on the definition of a trigger level (x) as the number of events in the chosen multiplicity selection (after the muon filter) over a time window of duration nτ. The search is performed updating the (sliding) time window at a frequency τ -1 . In practice for n = 5, every 100 ms the number of background event is evaluated over the previous 500 ms of data to produce the trigger level x. With the notation used in subsection 6.6.4, µ b = N ρ nτ, where N is the number of DOMs in the detector and ρ is the (average) background rate per DOM in the designated multiplicity range.

In the case of a single detector, as a Poisson counting experiment, the false alarm rate (FAR) for an observation above or equal to a trigger level x d is:

FAR(x d ) = 1 τ • +∞ ∑ x=x d P (x, µ b ) (6.6)
where P indicates the Poisson probability function. In analogy with the trial factor usually considered in different domains, the sampling frequency τ -1 can be seen as a trial rate for the online supernova search.

Under these conditions, x d can be set to the expectation value of signal plus background:

x d = N • (ρ • nτ) + x nτ 10 kpc • 10 kpc d 2 (6.7)
where x nτ 10 kpc is the expected number of selected signal events on a time window of duration nτ for a reference distance of 10 kpc (µ s = n 10 kpc s using the convention of subsection 6.6.4).

The time window is fixed a priori to nτ = 500 ms for the real-time search. The signal and background expectation values are calculated accordingly. Combining the two equations, the maximal distance producing a signal observation above the allowed FAR can be determined. In fact, the false alarm rate can therefore be expressed as an observation frequency for a trigger level greater or equal to the expectation from a CCSN neutrino burst as a function of the distance.

To understand the shape of this relation, in Fig. 6.12 the number of signal events as a function of the distance is shown on the left. On the right, the FAR (computed from Eq. 6.6) for a background observation n b greater or equal to an arbitrary x is shown as a function of x for ARCA and ORCA, considering the expectation value of the background in each detector, µ b .

For the KM3NeT combined search, the procedure is the following. First, one infers the combined significance distribution as a function of the number of signal and background events from Eq. 6.5, as a function of the distance. Then, one converts the combined significance z into a probability distribution P (z) following Eq. 6.3. Finally, the false alert rate can be expressed as the product of the trial rate and the p-value, integrated above the expected combined significance, z comb , for the signal plus background hypothesis at a distance d:

FAR(X d ) = 1 τ • +∞ z comb P (z) dz, ( 6.8)

Inter-DOM coincidences from a CCSN signal.

In this section, the possibility of using inter-DOM coincidences for CCSN detection is tested. The motivation is that it could potentially give a better background rejection and also give sensitivity to the neutrino energy spectrum. For this purpose, the simulation has been performed for 3 neighbor DOMs, assuming a 27 M ⊙ progenitor flux. In this case, the generated volume is taken to be a cylinder of 20m radius and 38 m height, with the ORCA inter-DOM separation of 9 metres.

Two types of inter-DOM coincidences are considered, noted (2+1) and (1+1) coincidences. A (2+1) inter-DOM coincidence is defined as an event giving at least 2 hit PMTs in a DOM and a hit in a neighbor DOM within a 50 ns time window. The time window is taken by a simple computation of the travel time between the two DOMs. The (1+1) inter-DOM coincidence does not require a second hit in one of the 2 DOMs.

From a CCSN of 27 M ⊙ at 10 kpc, the following formulaegive the expected number of inter-DOM coincidences that would be seen by the full ORCA detector, composed of 115x11 cylinders as the one simulation: where N MC are the number of detected hits with the defined coincidence condition, (1+1) or (2+1), N SN the total number of CCSN interacting in a reference volume of 10 5 m 3 of water, and N gen the number of simulated neutrinos. This expressions are equivalent to Eq 5.4 in chapter 5.

N 1+1 = N MC ×N SN ×V gen
From 40 K background, the expected L0 rate in each DOM is: R 1 = R 2 = 200 kHz (per DOM). For (1+1) inter-DOM coincidence from 40 K background withing δt = 50 ns, one gets:

R(1 + 1) bckg = 2 × δt × R 1 R 2 = 2 × 50 × 10 -9 × 4 × 1e10 = 4000 Hz.
During the simulated window for the considered 27 M ⊙ progenitor, ∆T =0.543 s, it is obtained: N(1 + 1) bckg = 2172 inter-DOM events in a three DOM cylinder from background. Thus, in the full ORCA detector, we expect over the search time window:

N(1 + 1) bckg = 2172 × 115 × 11 = 2.25 × 10 6 inter-DOM background events.
The simulation estimate for a CCSN at 7.5 kpc is: N(1 + 1) signal = 3822 inter-DOM events for the full ORCA detector. Provided that when looking at inter-DOM coincidences the statistics remain in the Gaussian regime, the significance can be computed as:

signi f icance(σ) = N signal √ N bckg = 3822 √ 2.25×10 6 = 2.5σ.
The same calculation is done for the (2+1) inter-DOM coincidences. The M≥2 40 K measured rate that is: R 3 = 1 kHz (per DOM), so we have:

R(2 + 1) bckg = 2 × δt × R 1 R 3 = 2 × 50 × 10 -9 × 2 8 = 20 Hz between 2 DOMs.
In the full ORCA detector, the background expectation becomes:

N(2 + 1) bckg = R(2 + 1) bckg × ∆T × N 3DOMs = 20 × 0.543 × 115 × 11 = 11.240 background events.
This is compared with the signal expectation from the simulation results: N(2 + 1) signal = 819 inter-DOM events in the full ORCA detector from a SN at 7.5 kpc. The significance reached is of: Chapter 7

Constraining the CCSN mechanism with KM3NeT

The current chapter addresses the KM3NeT potential to extract information about the CCSN physics and constrain the CCSN neutrino emission models. The chapter is organised as follows. First, the astrophysical constraints from the first real-time follow-up of unmodelled GW bursts are described. Second, the constraints on the CCSN energy spectrum and the determination of the mean neutrino energy are discussed. Finally, the constraints on the presence of fast-time variations on the neutrino lightcurve due to hydrodynamical instabilities are presented.

First multi-messenger results with KM3NeT data and the CCSN trigger

This section presents the first KM3NeT follow-up of unmodelled GW alerts, and aims at providing the p-value and setting the upper limits on potential CCSN neutrino emission in correlation. In particular, a lower limit on the CCSN distance and an upper limit (UL) on the total energy emitted through neutrinos, at 90% confidence level (CL) are obtained from a non detection of an MeV neutrino burst in coincidence with the unmodelled bursts GW signal alerts. A real-time search for an MeV neutrino emission is done applying the CCSN analysis on data from the ORCA4 lines. The search is performed within 400 ms after the GW trigger time.

Procedure of the follow-up

The evolution with time of the detector efficiency due to the time dependence of the background rates varying with the sea current and data taking conditions must be taken into account to evaluate the expected background from the measured data.

The trigger level is defined as the event count in the CCSN selection integrated over the previous 400 ms (see Chapter 6). The search is done over 400 ms from the time of the GW alert1 . From data, the observed trigger level and its background expectation are estimated, providing the corresponding pvalue. If no significant excess is observed, a 90% confidence level upper limit on the number of signal events is derived using the Feldman and Cousins method [START_REF] Feldman | A Unified approach to the classical statistical analysis of small signals[END_REF][START_REF] Karbach | Feldman-Cousins Confidence Levels -Toy MC Method[END_REF].

The signal expectation is evaluated from simulations after applying the CCSN trigger (muon veto and multiplicity selection described in sections 6.2.2 and 6.6.3) in the search window. It is corrected accounting for the number of missing DOMs and the CCSN trigger detection efficiency at the time of the alert, which depends on the effective number of active channels and varies with time in correlation with the data-taking conditions.

Finally, if the is no significant observation,the upper limit on the number of signal events is compared with the signal expectation from different models, to derive physical constraints:

• A lower limit on the distance to the CCSN using the two Garching progenitor models considered for the sensitivity estimate, with masses of 27 M ⊙ and 11.2 M ⊙ .

• An upper limit on the total neutrinos emitted from the CCSN assuming a quasi-thermal distribution as in Eqs. 4.2,4.3 with the following parameters:

-A total neutrino energy of E 0 ν = 3 × 10 53 erg. -A fixed pinching shape parameter with value α = 3.

-A fixed average neutrino neutrino of < E ν > = 15 MeV. f 0 = 25% of the neutrino signal emitted in τ 0 = 100 ms from the onset of the event.

f = 70% of the neutrino signal emitted over τ = 400 ms from the start of the signal.

Gravitational wave trigger S191110af: results

On November 10th 2019, the LIGO-Virgo detectors triggered an unmodelled GW signal burst (see Chapter 10 for the description of the gravitational wave detectors and search methods), released in the circular GCN #262222 . These kind of signals are of interest as potential CCSN sources. However, this alert was retracted as the probability of this event being of terrestrial (background) origin was rather high (see GCN #26250). Figure 7.1 shows the time evolution of the event count and detector efficiency ǫ around the time of the event. The event count corresponds to the number of coincidences between 6 and 10 hit PMTs after muon rejection on a timeslice of 100 ms basis.

Lower limit on the Core Collapse Supernova distance

The trigger level is shown as a function of the timeslice in the top plot of Fig. 7.2 around the time of the alert. Remind from Chapter 6 that the trigger in the number of observed events within the multiplicity selection, not passing the muon filter. At the time of the analysis, he multiplicity cut was set in [START_REF]Observation of high-energy astrophysical neutrinos in three years of icecube data[END_REF][START_REF]Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert[END_REF]. The detector efficiency is shown on the bottom plot as a function of time within the same window. For ORCA4, the trigger level is zero on a 400 ms window centered around the GW S191110af alert time (T0). For ARCA1, the trigger level is 2 at 400 ms after the T0. For ORCA4 efficiency is assumed conservatively at 0.55 (for an observed value between 0.57 and 0.6). ARCA1 efficiency is of ∼100%.

The outcome of the KM3NeT simulations of the response to the Garching flux models is used to evaluate the signal expectation over the search window. For a CCSN at 10 kpc and four instrumented DUs, the number of expected signal events obtained, S 0 , are:

• for the 27 M ⊙ progenitor: S 0 = 4 with ǫ = 100% and S 0 = 2.2 with ǫ = 55%;

• for the 11 M ⊙ progenitor: S 0 = 1 with ǫ = 100% and S 0 = 0.55 with ǫ = 55%.

In case of the combination of ORCA4 and ARCA1 detectors, accounting for the missing DOMS and detector efficiency, the values obtained are:

Using the gammapy statistics toolkit3 , the 90% CL upper limit on the expectation value for the signal is estimated using the Feldman and Cousins method as S 90% ORCA = 1.72 for an observed trigger level of X data = 0 events, and a background expectation value of µ b = 0.8 in the ORCA4 detector. In ARCA1, the observed trigger level is in this case X data = 2, with a background expectation of µ b = 0.6. The combined upper limit is obtained using the total number of observed and expected events, resulting in S 90% = 5.11.

The upper limit on the number of signal events (S 90% ) is converted into a lower limit on the CCSN distance by using the relation:

D 90% = (10kpc) × S 0 S 90% (7.1)
This gives the following lower limits on the distance using ORCA4 only:

• for 27 M ⊙ : D 90% = 11.3 kpc;

• for 11 M ⊙ : D 90% = 5.7 kpc.

This gives the following lower limits on the distance using ORCA4+ARCA1:

• for 27 M ⊙ : D 90% = 7.8 kpc;

• for 11 M ⊙ : D 90% = 3.9 kpc.

Note that in that case, the combination worsens the results because a higher background is observed in ARCA compared to ORCA, resulting in a higher upper limit (S 90% ). Moreover, combining with one additional ARCA line, only increases the signal of 20% compared to four ORCA lines. The same will be seen in the results on the next subsection.

Upper limit on the total energy emitted in neutrinos

The background is directly estimated from data as detailed in the previous subsections. The average background measured over 400 ms when the detector is working at maximum efficiency and the efficiency at the time of the GW alert are used for a blind background estimate. The values are the following:

• Background expectation: ORCA4, µ b = 0.8 and ARCA1, µ b = 0.6

• Observed trigger level: ORCA4, X data = 0 and ARCA1, X data = 2

• Detector efficiency: ǫ = 55% in ORCA4 and ǫ = 100% in ARCA1

The number of expected signal events within 100 ms window, for which the simulations is performed assuming 25% of the emission taking place in this window, is S 0 = 1.22. The number of events in the 400 ms window can be thus derived as: S ǫ=1 = S 0 × f f 0 = 1.22 × 0.7 0.25 ≈ 3.42 events for ǫ = 1, and it becomes S = 3.42 × 0.55 = 1.88 for ǫ = 0.55. Finally, the observed UL on the total energy becomes, for ORCA4:

E 90% ν = S 90% S × E 0 ν = 1.72 1.88 × 3 • 10 53 = 2.75 • 10 53 [erg] (7.2)
Considering the combination of ORCA4 and ARCA1, and accounting for the 4 missing DOMs in ORCA and the efficiency, the number of signal events is in this case: S = (3.42/4) × 0.96 + 3.42 × 0.945 × 0.55 = 2.6, assuming 70% of the energy being emitted in 400 ms in the same way as before. Finally, the observed UL on the total energy becomes, for ORCA4+ARCA1:

E 90% ν = S 90% S × E 0 ν = 5

Gravitational wave trigger S200114f: results

About two months after the first unmodelled trigger was sent, a second alert of this type was received, see GCN #26734 4 . Contrary to S191110af, this second alert was not retracted, and the event was relatively well localised within the Galactic Plane, and with a position compatible with Betelgueuse coordinates. This made of this candidate of interest for the astrophysics community. At that time, ARCA was not taking data due to ongoing operations at the shore station, and the analysis was carried out with the four ORCA lines active.

The same approach as the one discussed for S1901114af was used for the follow up of this event. The number of coincidences in the multiplicity selection 6-10 and the trigger level over 400 ms as measured in ORCA are shown in Fig. 7.3 (top) as a function of time. During the search window, the detection efficiency was 98.5% (Fig. 7.3 bottom), with a large fraction of active PMTs. In this case, two events were observed during the search window, i.e. coincidence level 2 at (T 0 -39) +400 ms, while 1.4 were expected from background. This yields a p-value of 40%, which is not a significant observation, and the corresponding 90% upper limit is S 90% = 4.448 signal events, obtained with Feldman and Cousins.

From these results, constraints on the source distance and the total energy emitted in neutrinos were set, as indicted in the previous subsections. Since no electromagnetic counterpart was observed, the failed CCSN model of 40 M ⊙ used in the sensitivity studies (see Chapter 5) was also incorporated to the analysis this time. The lower limits on the CCSN distance are summarised in Table 7.1. The Galactic coverage provided in the Table 7.1 is evaluated from model in Fig. 4.2, giving the probability of a CCSN ocurring below a certain distance. The upper limit on the total energy emitted in neutrinos, assuming a fixed distance of 10 kpc and a mean neutrino energy of 15 MeV, is evaluated as of E 90% ν = 2.9 × 10 53 erg, at the level of the typical energies expected for CCSN events. the developed framework in a future step.

Sensitivity to fast time variations in the neutrino lightcurve.

Anisotropic hydrodynamical instabilities taking place during the CCSN accretion phase have been predicted by state-of-the-art 3D simulations, and could play an important role in the explosion mechanism. In particular, the Standing Accretion Shock Instability (SASI) is believed to enhance the neutrino heating, favoring the energetic explosion, and could explain the neutron star kick effect that has been observed. The SASI instability produces fast time variations in the neutrino lightcurve with a characteristic oscillation frequency over a specific observer direction. The aim of this section is thus to study the sensitivity of KM3NeT to the SASI features in the neutrino lightcurve.

Event selection

Supernova lightcurve studies (and in general low-energy analyses) rely on the analysis of the aggregate detector hit rate on a time scale of 1 to 3 ms for a duration of a few hundreds milliseconds.

The use of single rates (L0) is disfavored by strong spatially and temporally correlated effects induced by bioluminescence, preventing any approximation of the background as a stationary poissonian or gaussian noise process. The following analysis is therefore limited to all coincidence events. The 10 ns coincidence window used in the multiplicity definition and coincidence-based analyses is optimised for events with many time-correlated photons reaching the DOM, that can exhibit higher time dispersion among the hits. This optimisation is done by maximizing the efficiency, i.e. reducing as much background as possible losing the smaller fraction of signal. Moreover, the selection is done only with coincidence windows which are large enough not to be dominated by short afterpluses (>3 ns) and the electronic response, but short enough to reject the maximum of random coincidences without significantly impacting the expected signal (<10 ns).

For double coincidence data, reducing the time window to 5 ns allows to reduce by a factor two the background of random coincidences, which are the origin of time correlations in the background. Considering the standard deviation of the hit time difference equal to the PMT transit time spread of 2.1 ns, this selection preserves ≥ 95% of the signal. In Fig. 7.9, the signal loss from considering all coincidences from a same neutrino interaction in different PMTs of a DOM compared to applying 5 ns coincidences is shown to be smaller than 5%.

The detected neutrino lightcurve has been simulated for a 27 M ⊙ and a 20 M ⊙ stellar progenitors, and a failed CCSN model of 40 M ⊙ (see Section 5.3). The width of the time bin has been optimised to maximize the sensitivity for the model independent method (defined above in subsection 7.3.3) while keeping resolution to short time structures (<10 ms features), by comparing the results for different time bins between 1 ms and 6 ms. The optimal bin size is found to be 2 ms. The method will be discussed for ARCA, which represents a higher instrumented volume and thus will allow for a better result in terms of time resolution due to higher events statistics per time bin.

The signal rates are Poisson random outcomes of the expectation values given by the models in each time bin. Muon and optical backgrounds have been included using the background simulation based on data that has been introduced in section 5.3.1. Background and signal values in each bin are summed to compute the total number of events per time bin, R i : From now on, the method will be illustrated using the ARCA detector and the 20 M ⊙ stellar progenitor. Fig. 7.11 shows the Power Spectral Density (PSD) after applying the Fourier Transform (FT) to the ARCA lightcurve for three simulated realisations of a CCSN progenitor of 20 M ⊙ (right) explosion at 5 kpc. It is possible to identify the SASI frequency, f SASI = 80 Hz.

R i = Poisson(µ s,i + n b,i ) (7.8)
To estimate the sensitivity to the SASI oscillations peak in the power spectrum, MC pseudo-experiments (PEs) are used. Two different methods will be presented in the following subsections, a model-independent approach and a model-dependent approach. For illustration, the methods will be applied to the full ARCA detectors and the different considered progenitors. Then, a summary of the combined results will be provided for all the progenitors with presence of SASI emission.

Summary of the results

Note that the sensitivity is reported here as the expected significance. Once the sensitivity is evaluated for the ORCA and ARCA detectors as illustrated in subsections 7.3.3 and 7.3.4, one can combine the results with the weighted approach explained in 6.6.2. Due to the intrinsic physical delay between the ORCA and ARCA detectors, the synchronised combination of the data is under investigation.

Results are given in Table 7.2, for the KM3NeT distance sensitivity horizon to SASI oscillations. The horizon is taken as the distance up to which a expected significance of about 3σ is achieved with the model independent search for the two CCSN progenitors. For the failed CCSN, a more conservative horizon is taken, reaching almost 4σ and above 5σ in the model independent and model dependent search, respectively. The Galactic CCSN coverage is computed as the fraction of Galactic progenitors expected below the horizon distance, inferred from Fig. 4.2, and reported in Table 7.2.

The systematic effects related to the uncertainties on the PMT QE (10%), the absorption length (3%) and the bioluminescence conditions producing changes in the number of active PMTs (<0.1σ in ARCA, 0.2-0.4σ in ORCA) have been evaluated and translated into an error in the SASI sensitivity, provided in the Table. Chapter 8

Timing and pointing the CCSN neutrino signal

The current chapter explores the possibility of reconstructing the CCSN direction by triangulation combining experimental data of the different neutrino detectors is discussed as well as using the directional information of the KM3NeT multi-PM optical modules. In addition, the capability of inferring the arrival time of CCSN neutrinos is presented.

Combining experimental lightcurves for timing the CCSN neutrino signal

One of the key points in neutrino astronomy is the angular resolution, i.e. being able to point to the neutrino source. The recent multi-wavelength observations of explosive phenomena in the Universe, and in particular the multi-messenger detection of the binary neutron star merger GW170817 [START_REF] Antares | Search for High-energy Neutrinos from Binary Neutron Star Merger GW170817 with ANTARES, IceCube, and the Pierre Auger Observatory[END_REF], have shown the crucial importance of combining the different information brought by the neutrino, gravitational wave and electromagnetic signal to unveil the mechanisms riding these astrophysical events. For that reason, fast and precise direction reconstruction of the neutrino emission, as well as of the arrival time of the signal, are important for an efficient multi-messenger follow-up. This section reports on the possible strategy to be used for estimating the time delay between the arrival of the neutrino signal observed by the different experiments, and its uncertainty. By exploiting these two measurements, one can use a triangulation method to infer the source localisation on the sky. The possibility of using the triangulation technique has been addressed in several works [START_REF] Burrows | [END_REF][START_REF] Beacom | Can a supernova be located by its neutrinos?[END_REF][START_REF] Mühlbeier | Revisiting the triangulation method for pointing to supernova and failed supernova with neutrinos[END_REF][START_REF] Brdar | Neutrino astronomy with supernova neutrinos[END_REF][START_REF] Linzer | Triangulation pointing to core-collapse supernovae with nextgeneration neutrino detectors[END_REF][START_REF] Hansen | Timing the neutrino signal of a galactic supernova[END_REF]. In fact, using triangulation between CCSN neutrino experiments was first proposed in 1992 [START_REF] Burrows | [END_REF]. That work proposed to infer the uncertainty on the arrival time delay between a pair of detectors from the number of the detected neutrinos in the bulk of the emission and its duration. A Kolmogorov test for direct lightcurve comparison between detectors was later mentioned in [START_REF] Beacom | Can a supernova be located by its neutrinos?[END_REF], where a Rao-Kramer evaluation of the time uncertainty is carried out, with the conclusion that low event statistics detectors available at that time were not useful for triangulation. In [START_REF] Mühlbeier | Revisiting the triangulation method for pointing to supernova and failed supernova with neutrinos[END_REF], the triangulation method is revisited and a rough estimate of the arrival time uncertainty for each detector is computed assuming a generic neutrino lightcurve with an exponential rise. In [START_REF] Brdar | Neutrino astronomy with supernova neutrinos[END_REF], a more detailed lightcurve template is used. The use of the time delay estimate between the first detected events in each experiment was proposed in [START_REF] Linzer | Triangulation pointing to core-collapse supernovae with nextgeneration neutrino detectors[END_REF]. For the latter method, an almost background-free experiment is required in order to reach a good timing accuracy. This implies that the use of large volume Cherenkov neutrino telescopes, as IceCube and KM3NeT, is less effective. Timing with the first events with an exponential fit was also proposed in [START_REF] Hansen | Timing the neutrino signal of a galactic supernova[END_REF].

The new idea investigated during my thesis is making use of the fit to the full spectrum, as proposed in previous works, but in a model independent way that relies on matching experimental detection rate curves. For this, current and near future detectors with large supernova detection rate statistics and sensitive to the same interaction channel, ν e interacting with free protons through Inverse Beta Decay (IBD), are taken in consideration to test the method performance. Using detectors sensitive to different neutrino flavor and interaction channels may introduce a bias in the results. Such approach requires data sharing between the detectors, or having an independent and automatized common analysis platform, which can be realized within the SNEWS global network [START_REF] Scholberg | The SuperNova Early Warning System[END_REF].

For this work, the following experiments are considered: the underground detectors, Super-Kamiokande [START_REF]The Super-Kamiokande detector[END_REF] and Hyper-Kamiokande [START_REF]Hyper-Kamiokande Design Report[END_REF], and the high-energy neutrino telescopes, IceCube [START_REF]The IceCube Neutrino Observatory: instrumentation and online systems[END_REF] and KM3NeT [START_REF]Letter of intent for KM3NeT 2.0[END_REF]. The main interaction channel in water Cherenkov detectors is inverse beta decay (IBD) of electron anti-neutrinos (ν e ) on proton targets. The positrons angular distribution is slightly forward-peaked and high energy events can be selected in order to exploit this directionality [START_REF] Strumiaa | Precise quasielastic neutrino/nucleon cross-section[END_REF]. A good pointing for CCSN is hardly achievable in the water Cherenkov detectors with such technique. The JUNO scintillator detector is sensitive to both IBD and elastic scattering (ES) [START_REF]Neutrino physics with JUNO[END_REF]. It is to be mentioned that JUNO can additionally use the IBD events to identify positrons and neutrons and reconstruct their positions. The direction along the line connecting the positions of both products can be used to infer the neutrino direction [START_REF] Vogel | The angular distribution of the reaction: ν e + p → e + + n[END_REF]. Detectors sensitive to ES interactions can provide information on the CCSN localisation. Nowadays, Super-Kamiokande is the only running detector with enough sensitivity to the ES channel to be able to point by itself to the source [START_REF] Tomàs | Supernova pointing with low-and high-energy neutrino detectors[END_REF].

The results presented in this section have been published in Ref. [START_REF] Coleiro | Combining neutrino experimental light-curves for pointing to the next Galactic Core-Collapse Supernova[END_REF], as well as the codes have been made public in [START_REF] Coleiro | Combining neutrino experimental light-curves for pointing to the next Galactic Core-Collapse Supernova[END_REF].

Simulation

The CCSN neutrino detection rates are estimated through simulations for the different experiments. The proposed simulation, described in this section, relies on a simplified detector response characterisation and a simple parametric function for the evolution of the neutrino luminosity as a function of time. In particular, the detectors are described with two parameters: their effective mass and background.

Additionally, some approximations are made to simplify and speed up the simulations, that allow to easily reproduce the detected neutrino lightcurves. The main assumptions are the following: a fixed detector efficiency, considered time and energy independent, and a steady neutrino energy evolution. These approximations are physically motivated in the context of this work, and required for testing and optimising the method without access to the real detector's information and knowledge of the CCSN neutrino model.

Supernova neutrino fluxes

The all-flavour neutrino total luminosity is set to L 0 ν = 3 × 10 53 erg, as in [START_REF]Neutrino physics with JUNO[END_REF]. It is equally divided among all neutrino flavours and between neutrinos and anti-neutrinos. This is consistent with the more accurate estimate of the ν e fraction of about 0.14 that includes oscillations in the supernova mantle [START_REF] Strumiaa | Precise quasielastic neutrino/nucleon cross-section[END_REF].

The time evolution of the neutrino luminosity is taken from [START_REF] Nardia | [END_REF] and it is described for νe as:

L ν (t) = L 0 ν 6 1 N e -(t a /t) na [1 + (t/t c ) n p ] n c /n p , (8.1)
where N is used to normalise the function as follows:

N = ∞ 0 e -(t a /t) na [1 + (t/t c ) n p ] n c /n p dt . (8.2)
For these studies the chosen parameters are: t a = 0.035 ms, t c = 0.2 ms, n a = 2, n p = 20 and n c = 1.5. The lightcurve simulated using these parameters approximately follows the predicted accretion phase νe luminosity in [START_REF] Tamborra | High-resolution supernova neutrino spectra represented by a simple fit[END_REF]. The chosen value of n c = 1.5 guarantees the convergence of the luminosity integral. The luminosity curve with the assumed parameters is shown in Figure 8.1. The energy distribution can be described by a quasi-thermal distribution [START_REF] Tamborra | High-resolution supernova neutrino spectra represented by a simple fit[END_REF]:

f E (E ν ) = 1 Γ(1 + α) 1 + α E ν 1+α E α ν exp - (α + 1)E ν E ν , ( 8.3)
which depends on the average neutrino energy, E ν , and the spectral pinching shape parameter, α.

Both parameters are generally varying with time. The typical range of the pinching shape parameter is 2 α 5 [START_REF] Tamborra | High-resolution supernova neutrino spectra represented by a simple fit[END_REF].

Only the variation in time of the detection rates is relevant for this study. Therefore, the simulation follows the luminosity time evolution with a steady energy neutrino spectrum with E ν = 14 MeV and α=3. The neutrino luminosity can be converted into a flux dividing it by the average neutrino energy. Assuming an isotropic neutrino emission from a source at a distance d, the differential neutrino flux is:

dΦ dE ν (E ν , t) = 1 4πd 2 L ν (t) E ν f E (E ν ) . (8.4)

CCSN neutrino detection rates

As it is the main channel for the considered water detectors, only the inverse beta decay interaction channel is simulated. The instantaneous event rate in the detector is estimated as the product of the differential neutrino flux, dΦ dE ν , the IBD cross section, σ IBD [START_REF] Strumiaa | Precise quasielastic neutrino/nucleon cross-section[END_REF], the number of targets per unit volume, 2

ρN A µ H 2 O
, the detection efficiency, ǫ det , and the detector volume V det :

R sig (t) = ∞ 0 dΦ dE ν (E ν , t)σ IBD (E ν ) × 2 ρN A µ H 2 O ǫ det (E ν )V det dE ν . (8.5)
The factor 2 comes from the two hydrogen atoms in a water molecule, µ = 18 g/mol is the molar mass of water, ρ is the density of water and N A is the Avogadro number.

The detector properties are converted into the detector effective mass, M eff , in the following way:

M eff (E ν ) = ρǫ det (E ν )V det . ( 8.6)
The detection efficiency depends on the neutrino energy, or more precisely, on the energy of the detectable interaction products. A constant efficiency is assumed above an energy threshold, E min ν . Since this value is around the Cherenkov threshold, and below the energy range where supernova neutrinos are expected, E min ν = 0 is set for simplicity. This assumption removes the energy dependence of the M eff . The detection rate is calculated as:

R sig (t) = M eff L ν (t) E ν 1 4πd 2 × ∞ E min ν f E (E ν )σ IBD (E ν )2 N A µ H 2 O dE ν = M eff L ν (t)I , (8.7)
where the simplified conversion parameter, I, is the same for all the detectors. For a CCSN at 10 kpc, this factor becomes:

I ≈ 4.3 erg -1 kton -1 .
The rates for future scintillator or other non-water detectors can be calculated using Equation 8.7, where M eff is estimated in water equivalent units and N target is the total number of targets in the detector:

M w.e. eff = ǫ det N target 2N A µ H 2 O -1 . (8.8)

Simplified detector model

The detector model is described by two parameters: the supernova detection effective mass, M eff , and the background rate, R bg . The signal rates are estimated for each detector from Equation 8.7. Both the signal and the background rates are translated into an expected number of events per time bin. In order to simulate experimental fluctuations in the detected neutrino lightcurve, the number of events in each time bin is sampled assuming a Poisson distribution.

For the Super-Kamiokande and Hyper-Kamiokande detectors, the effective masses are taken from [START_REF] Migenda | Detecting Fast Time Variations in the Supernova Neutrino Flux with Hyper-Kamiokande[END_REF][START_REF]Search for Supernova Neutrino Bursts at Super-Kamiokande[END_REF]206]. For JUNO, the expected number of proton targets is N target = 1.5 × 10 33 [START_REF]Neutrino physics with JUNO[END_REF], similar to Super-Kamiokande. The same effective mass in water equivalent units, M eff = 22.5 kton, is used for both detectors. In this study, the background rates are negligible for Super-Kamiokande, Hyper-Kamiokande [205] and JUNO [START_REF]Neutrino physics with JUNO[END_REF].

The assumed IceCube detector effective volume is 3.5 Mton [START_REF]Icecube sensitivity for low-energy neutrinos from nearby supernovae[END_REF]. The detector consists of 5160 optical modules, each containing one 10-inch photomultiplier. The background rate per optical module is about 300 Hz, taking an average value between standard and high efficiency optical modules.

The optical module of KM3NeT consists of 31 3-inch photomultipliers. Using nanosecond scale coincidences between the photomultipliers on the same optical module, the variable background from the bioluminescence can be suppressed [START_REF] Colomer | for the KM3NeT Collaboration PoS[END_REF]. The remaining background contribution is mostly coming from 40 K decays in sea water and it amounts to a total rate of R K40 OM ∼500 Hz per optical module [START_REF] The | Dependence of atmospheric muon flux on seawater depth measured with the first KM3NeT detection units[END_REF]. The effective mass of the KM3NeT detectors is estimated as M eff ≈ 180 kton for KM3NeT/ARCA and 90 kton for KM3NeT/ORCA from [203,

Method

Two methods to estimate the time difference of the neutrino arrival times between two detectors have been investigated: the chi-square (section 8.1.3) and the cross-correlation (section 8.1.3). The triangulation method for the source localisation is reviewed in sections 8.1.3 and 8.1.3.

Chi-square method

A method based on χ 2 minimisation has been developed and tested to infer the delay between two lightcurves. This technique is one of the traditional ways to verify the compatibility of two distributions and for parameter estimation. In this case, the estimated parameter is the time delay between the two detected neutrino lightcurves.

Several technical details on the χ 2 method are addressed in the current section: the construction of the chi-square function, the lightcurve normalisation, which takes into account the different background rates and detector efficiencies, the time window and the step size used to calculate the χ 2 .

Chi-square function

The χ 2 method was recently proposed in [START_REF] Brdar | Neutrino astronomy with supernova neutrinos[END_REF] for a similar purpose: defining the supernova emission time delay with respect to some model and estimating the uncertainty. The underlying distribution for the experimental lightcurve is a Poisson for each time bin, which assumes that the number of events in each time bin follows a Poisson distribution with a mean value equal to the average expected number of events computed from a CCSN neutrino emission model. This Poisson χ 2 expression cannot be used to compare two experimental lightcurves since it requires a known expectation value. Therefore, the approach is changed in this work from assuming a Poisson distribution for the content of each bin to a Gaussian. Given that the number of detected events follows a Poisson distribution, the bin size should be optimized in our method to make the Gaussian approximation valid.

Assuming a normal distribution of the number of events in each time bin, the χ 2 expression for the comparison of two experimental time-binned data sets is defined as follows:

χ 2 (τ) = t max ∑ t i =t min ((n t i -τ -m t i ) -E(n t i -τ -m t i )) 2 V(n t i -τ -m t i ) , (8.9)
where τ is the time shift between the detected neutrino lightcurves, n t i -τ is the number of observed events by the first detector in the time bin t iτ, m t i is the number of observed events by the second detector in the time bin t i , E(n t i -τm t i ) and V(n t i -τm t i ) are the expectation value and the variance of the difference in the number of events, respectively. For two normal distributions, the variance of the difference between the number of events corresponds to the sum of their squared standard deviations:

V(n t i -τ -m t i ) = V(n t i -τ ) + V(m t i ) = (σ n t i -τ ) 2 + (σ m t i ) 2 . (8.10)
The value of τ = T match 0 obtained at the χ 2 minimum provides the best estimate of the true time delay between the two detectors, T 0 .

Normalisation of the detected lightcurve

The expectation values still appear in the χ 2 expression in 8.10. Ideally, for the model independent approach that we are trying to build, one wants to get rid of this term. In fact, the lightcurves are normalised in a way so that signal and background expectations are almost the same for both detectors, then the expectation value E(n t i -τm t i ) can be considered null for any t i when τ corresponds to the true shift. Such normalisation can be achieved in two steps. First, the mean detector background is subtracted from the lightcurve so that all combined detectors have a common baseline centered at 0. Second, a normalisation to the detector effective mass is applied in order to account for the different detector efficiencies to the CCSN neutrino signal. Alternatively, this effect can be taken into account by normalising each lightcurve after background subtraction to have unit integral, i.e. scaling to the total amount of signal to which is detector is sensitive. The background expectation value can be taken from a time window in the detected neutrino lightcurve where CCSN signal is not present (off-signal zone) or it can be provided by each experiment based on a longer detector monitoring. In this study, an off-signal zone of 1 s duration is chosen for the background estimate.

Note that such lightcurve normalisation assumes a constant and fixed expectation value of the background rates and detector efficiencies. Even if this is in perfect agreement with the simplified simulations proposed earlier, this is generally not true in the real case. For instance, the neutrino energy spectrum may vary in time and an energy and time dependent detector efficiency may impact the results. Moreover, this approach assumes that the same neutrino flux is arriving to each site. But the observed lightcurve may change between experiments if they show different efficiency evolution or present different contributions from additional interaction channels. Therefore, the described normalisation can be improved to account for these effects by using a more detailed description of the detector response. But this requires an agreement for data sharing between detectors. However, introducing the time and energy dependent detector efficiency will only improve the simulation description if it is taken into account together with a realistic neutrino emission spectrum varying in time. The neutrino emission spectrum from detailed simulations differs across different models. This may bring a bias to a such sophisticated correction.

Chi-square calculation window

The signal arrival time is not known a priori in this model independent analysis. Therefore, a reference time is evaluated to define the window for the χ 2 calculation. The time window of [-300, 300] ms centred at the maximum of the detected lightcurve from one of the detectors is chosen for this analysis. The interval covers the transition between the background and the CCSN neutrino signal as well as the accretion phase, for which most of the neutrino emission is expected [START_REF] Tamborra | High-resolution supernova neutrino spectra represented by a simple fit[END_REF]. Using a time window too long may lead to a degradation of the performance since the optimisation will be more sensitive to background fluctuations. The χ 2 calculation window is fixed with respect to the less performing detector to preserve its background statistics during τ scan. The choice of the fixed detector and the detector for the reference time definition is done to minimize the estimated time delay uncertainty. The procedure for the uncertainty estimation is given in section 8.1.3.

The detected lightcurves are provided as histograms with a fixed bin size. A bin width of 0.1 ms is chosen, and the same value is used for the time shift step τ, in order to reach the O(ms) required resolution. The numbers of events, n t i -τ and m t i , are calculated by summing the events of contiguous bins. The resulting effective bin size is optimised for each detector pair to reach the minimum of arrival time delay uncertainty, δt. Steps of t i+1t i can be optimised in order to increase the calculation speed.

Normalised cross-correlation

The cross-correlation can be used for matching two sets of time series [START_REF] Larsson | Statistical analysis of multiwavelength light curves[END_REF] or for matching a time series with a template model [START_REF] Feigelson | Modern Statistical Methods for Astronomy[END_REF]. The discrete cross-correlation is defined as:

C(τ) = (n ⋆ m) = 1 N t max ∑ t i =t min n t i m t i -τ , (8.11)
where n t i and m t i -τ are the number of observed events by the first and the second detector in time bins t i and t iτ, respectively. N is the number of bins in the search window [t min , t max ], and τ is the time delay between the two lightcurves. The function will present a maximum at τ = T match 0 , allowing to estimate the time delay between the two detectors, T 0 .

In order to account for the different effective masses and background rates of each detector, the zero-normalised cross-correlation is used. Each curve is normalised by subtracting its mean value and scaled by its standard deviation [START_REF] Larsson | Statistical analysis of multiwavelength light curves[END_REF], which can be computed in the search window:

ñ = ∑ t max t i =t min n t i N , m = ∑ t max t i =t min m t i N , (8.12
)

σ n = ∑ t max t i =t min (n t i -ñ) 2 N -1 , (8.13
)

σ m = ∑ t max t i =t min (m t i -m) 2 N -1 . (8.14)
One of the advantages of this method is that fast Fourier transformations can be used to speed up the calculations and the improvement of the response time can be significant for a large number of bins compared to the chi-square method.

Estimating the performance of the lightcurve matching

Simulations of the different detected neutrino lightcurves are performed following the model described in section 8.1.1. An artificial delay of the neutrino signal observed between two sites, T 0 , is applied to the first lightcurve. This T 0 is drawn from a random uniform distribution between -30 and 30 ms. These values are chosen from the typical time delays expected for pairs of neutrino detectors, ∆t ij ≈ 30 ms, given that the Earth diameter corresponds to a time delay of ∼40 ms.

The result is also not expected to change when exchanging the two detectors. The best estimate T match 0 is inferred with the proposed methods described in this section. Finally, T match 0 , is compared to the true T 0 value.

The distribution of T match 0 -T 0 is built from a large number of realisations of the simulated lightcurves. To confirm the absence of systematic effects, the distribution of T match 0 -T 0 should be compatible with a normal distribution with mean zero and standard deviation independent of T 0 . The width of the distribution provides an estimate of the uncertainty on the T 0 measurement, δt.

Tuning the parameters using a bootstrapping

The proposed methods present some parameters that can be slightly tuned for different CCSN models, distances to the source and detectors. In most cases, it was verified that the degradation of the time precision is not significant and a common set of parameters can be identified for future combined analysis.

In order to reach the best performance once the supernova is detected, the following bootstrapping procedure can be set up. The detected neutrino lightcurve from the best performing detector is used as the model. With this model, the detected neutrino lightcurves for all the detectors can be simulated and the procedure to estimate the performance described in section 8.1.3 can be repeated in order to tune the parameters.

The triangulation method

The time difference between the CCSN neutrino signal arrival at two detectors located at r i and r j can be expressed as:

t ij = ( r i -r j ) • n/c, (8.15)
where n is the unit vector that indicates the emission direction. This vector is calculated in the geographic horizontal coordinate system from the CCSN right ascension, α, declination, δ, and the Greenwich mean sidereal time expressed as angle, γ:

n = (-cos(α -γ) cos δ, -sin(α -γ) cos δ, -sin δ). ( 8.16)
On March 21 2000 at noon the J2000.0 equatorial coordinate system matches with the geographic one since γ = 0 • . For this time Equation 8.16 is simplified to the same expression used in [START_REF] Brdar | Neutrino astronomy with supernova neutrinos[END_REF]. The position of the detector k can be inferred from its latitude (φ k ) and longitude (λ k ) angles, and the Earth radius (R Earth ):

r k = R Earth (cos λ k cos φ k , sin λ k cos φ k , sin φ k ) (8.17)
The centers of the HEALPix pixels [START_REF] Gorski | HEALPix -A Framework for high resolution discretization, and fast analysis of data distributed on the sphere[END_REF] with 256 pixels per side (about 0.05 deg 2 per pixel) are used in this work to define the scan grid. The probability that the scanned angles (α, δ) coincide with the equatorial coordinates of the CCSN is given by the following χ 2 function:

χ 2 ij (α, δ) = t ij (α, δ) -T match 0,ij δt ij 2 , (8.18)
assuming that there is no systematic shift in the T match 0,ij determination. The minimum of the function gives the best estimate for the angles (α, δ) of the searched CCSN location in the sky. From Equation 8.18, one can note that the performance depends on the uncertainty of the measured time delay δt ij of each detector pair.

Different detector pairs can be combined into a total χ 2 by summing each contribution:

χ 2 (α, δ) = i<j ∑ i,j χ 2 ij (α, δ) . ( 8.19)
The χ 2 (α, δ) function is converted into a probability as follows:

p(α, δ) = p(χ 2 q ≤ χ 2 (α, δ) -χ 2 min ). (8.20)
Eq. 8.20 is the cumulative distribution function of the chi-square with q degrees of freedom, χ 2 q , evaluated at the value of chi-square difference between the tested point, χ 2 (α, δ), and the minimum chisquare value, χ 2 min , obtained scanning all possible directions. The number of degrees of freedom is given in that case by the number of fitted parameters (α and δ), provided that they are independent, so q=2. The 90% confidence level (C.L.) error region on the source direction is determined by the collection of all the points in the sky for which this probability is p(α, δ) < 0.9 [START_REF] Avni | Energy spectra of X-ray clusters of galaxies[END_REF].

Procedure for the triangulation performance estimation

Two procedures are compared to evaluate the size of the confidence area and determine the uncertainty on the source localisation through the Wilk's theorem: using the true values (Asimov dataset), and the fitted parameters distribution.

For the first one, the confidence areas are built by assigning to each fitted value the true expected delay from a particular CCSN location on the sky at a given event time, T match 0,ij = t ij (α 0 , δ 0 ), where t ij is taken from Eq. 8.15. The procedure described in section 8.1.3 provides the confidence area skymaps which are centred around the true CCSN location with such assumption.

In the second, the fitted value (T match 0,ij ) is sampled through a normal distribution with the mean being the true value (t ij (α 0 , δ 0 )) and the standard deviation the experimental uncertainty δt ij . The error box is computed at 68 and 90% C.L for each simulated set of the delays, T match 0,ij . The average values and standard deviations of the error box areas are estimated, repeating the sampling of T match 0,ij sets. The coverage is verified by computing the fraction of the realisations in which the fitted CCSN position lies inside the estimated confidence area. Additionally, the 68 and 90% C.L. central areas are calculated from the density of the fitted positions among the pseudo-experiments.

Results

In this section, the estimated resolution of the arrival time delay for different detector pairs is shown. Different combinations of three and four detectors are then used to estimate the resulting CCSN localisation uncertainty area.

Time uncertainty results

The results of the chi-square method are given for two different lightcurve normalisations in Tables 8.2 and 8.3. For the first normalisation, the true background value is assumed for the baseline subtraction and the scaling is done according the true effective mass. This corresponds to the ideal case in which the detector efficiency and the background estimations are known a priori. For the second one, the background expectation value is computed as the average rate in a 1 s off-signal region. The integral of the lightcurve in the analysis time window of [-300, 300] ms around the lightcurve maximum is normalised to one. By comparing Table 8.2 and Table 8.3 results, the realistic experimental curve normalisation gives similar performances compared to the ideal case. This justifies the proposed window for background estimation and the window used for lightcurve normalisation. It is verified that the mean of the T match 0 -T 0 distribution is compatible with zero within the statistical uncertainties. The δt obtained from the simulations with a fixed and random delay times are compatible. This confirms that for the assumed model and detector response the chi-square method provides an unbiased estimation

Results of the triangulation: localisation skymaps

Using the uncertainties estimated for each detector combination, the triangulation algorithm is applied to reconstruct the CCSN location on the sky. To estimate the performance of different detector combinations, a CCSN on vernal equinox at noon is assumed for simplicity. The source direction of the Galactic Centre with equatorial coordinates (α 0 , δ 0 ) = (-94.4 • , -28.9 • ) as a benchmark for illustration of the results.

The size of each confidence area is obtained through numerous pseudo-experiments of T match 0,ij sets.

The error box sizes at 68 and 90% C.L. obtained using the true and the fitted values for T match 0,ij are provided in Table 8.5 for different detector combinations, compared to average areas. These results are obtained using the uncertainties from the chi-square method given in Table 8. The real coverage is verified and the values are provided with statistical uncertainties. Table 8.5 indicates that the real coverage of the estimated error boxes with numerous realisations is higher or at the same level as the set confidence level. Therefore, the frequentist statistical coverage is satisfied. In some cases, the obtained average confidence areas using the fitted delays are slightly larger compared to the confidence areas obtained assuming the true delays. However, they are compatible with each other, and also with average error box size, within the statistical errors. Table 8.5: Uncertainty areas of the CCSN localisation (error box) in deg 2 at 90% and 68% confidence level for each considered detector combination, computed in three different ways: a) assuming the true delays; b) with a set of randomised time delay realisations; c) from the surface covering 90% and 68% of the fitted position distribution. The real coverage is also provided in the last row, and it is calculated as a fraction of the realisations for which the true CCSN position lies inside the estimated confidence area for each realisation. The CCSN is considered to occur at the vernal equinox time in the direction towards the Galactic Centre, at a distance of 10 kpc. The results in Table 8.5 indicate that the favourable position of a detector with respect to the source location, and in relation to the other detectors used in the combination, may compensate for a worse time resolution. For example, when replacing KM3NeT/ARCA with JUNO in the combination of three detectors, the area is reduced even though KM3NeT/ARCA presents a large uncertainty in the time delay measurement. Note, however, that for the considered CCSN location and time, the three detector combinations involving KM3NeT/ARCA provide confidence areas with two disjoint regions. although more than four detectors were combined using IBD and ES channels and the uncertainty estimate relies on the matching with a lightcurve template known a priori. In contrast, the result of our work represents a model independent data analysis proposal. In [START_REF] Hansen | Timing the neutrino signal of a galactic supernova[END_REF], the timing with the first IBD events has the best performance comparing to the exponential rise fit. In the latest results with the first events observation method [START_REF] Linzer | Triangulation pointing to core-collapse supernovae with nextgeneration neutrino detectors[END_REF], the time delay uncertainty for Super-Kamiokande and JUNO combination is 5.7 ms. This is larger than 2.8 ms estimated in our work, however, a more pessimistic model was used in the former work. This method requires an evaluation and correction for several biases due to background rates and the steepness of the luminosity curve rise. Biases and the performance degradation in the method proposed here may appear due to the detector efficiency varying with the neutrino energy and in time, or with respect to the event rates. A proper estimation of such effects is possible considering simulations with a detailed emission model and precise detector parameters. This new method relies on the agreement among the different collaborations for making their full lightcurve available to SNEWS while the method in [START_REF] Linzer | Triangulation pointing to core-collapse supernovae with nextgeneration neutrino detectors[END_REF] only requires sending the time information of the first events.

IceCube

The results of this work can also be compared with the expected performance of Super-Kamiokande using the directionality information from the elastic scattering channel. The 68% C.L. area for the combination of four detectors in this work is smaller than the area expected with the actual Super-Kamiokande configuration (∼69 deg 2 [START_REF] Tomàs | Supernova pointing with low-and high-energy neutrino detectors[END_REF]). With gadolinium doping, this area might be reduced down to ∼13 deg 2 [START_REF] Tomàs | Supernova pointing with low-and high-energy neutrino detectors[END_REF]. The expected CCSN 68% C.L. area for the JUNO IBD events reconstruction analysis will be better than 254 deg 2 [START_REF]Neutrino physics with JUNO[END_REF]. The triangulation method presented in this chapter can be proposed as a low latency analysis. The confidence areas from Super-Kamiokande, JUNO and this triangulation analysis are independent and can be combined in order to obtain a joint refined measurement.

8.2. Preliminary study of the sensitivity to the direction of the source using the multi-PMT DOM design of KM3NeT 153

Preliminary study of the sensitivity to the direction of the source using the multi-PMT DOM design of KM3NeT

During the neutrino burst phase of a CCSN, ν e interact with electrons by ES. The outgoing electrons produced are predominantly scattered forward, in the same direction of the incoming neutrino, which also keeps the direction of the source where it was emitted. The first 70 ms of the 1D CCSN simulation of an 8.8M ⊙ progenitor star including the burst are used for this study [START_REF] Hanka | Neutrino signal of electron-capture supernovae from core collapse to cooling[END_REF]. This simulation was chosen because the 3D simulations used in chapters 6 and 7 only focused on the accretion phase, and the ν e emission, providing directional information, is dominant during the burst phase. The total signal predicted by this simulation including only 70 ms with the burst is ∼ 50 times lower than the one from the 3D accretion phase simulation (500 ms duration) of a 27 M ⊙ progenitor used before. This difference is explained by the sum of different things: the shortest window, the lower cross section of the ES compared to IBD together with the small amount of ν e produced in this 70 ms window, and the lower progenitor mass (see chapter 5 for more details).

To have an estimation of the sensitivity to the direction of the source, the hit pattern of the 31 directional PMTs of KM3NeT DOMs can be used. The aim is to look for different PMTs receiving more/less photons when changing the direction of the incoming neutrinos. Here, 6 different incoming neutrino directions were simulated: The angles θ ν and φ ν define the incoming neutrino direction, p, which is given by:

• Dir 1: θ ν = -π 2 , φ ν = -π 2 • Dir 2: θ ν = -π 2 , φ ν = + π 2 • Dir 3: θ ν = -π 3 , φ ν = -π 3 • Dir 4: θ ν = -2π 3 , φ ν = -π 3 • Dir 5: θ ν = -π 4 , φ ν = π 4 • Dir 6: θ ν = -3π 2 , φ ν = π
p = (sinθ ν cosφ ν , sinθ ν sinφ ν , cosθ ν ) (8.21)
The direction of the source (i.e. in the DOM coordinate frame) is opposite to the incoming neutrino direction,p. We define the PMT pointing angles (θ,φ) so that the θ angle is rising from 0 at the north pole of the DOM (positive z) to 180 degrees at the south pole (negative z), and the φ angle (zero along the positive x-axis) is positively increasing when rotating from the x-axis to the y-axis. To go from the incoming neutrino frame to the DOM frame, a rotation of π is applied (θ ν = θπ and φ ν = φπ). The position (x,y,z) and direction (dx,dy,dz) vectors of the PMTs can be therefore defined, using the DOM radius (r = 2 cm), as:

x = rsinθcosφ; dx = sinθcosφ; y = rsinθsinφ; dy = sinθsinφ; z = rcosθ; dz = cosθ;
The first 2 directions correspond to the equator between the northern and southern hemispheres of the DOMs and opposite sides. Directions 4 and 6 correspond to neutrinos arriving in the northern hemisphere of the DOM, and directions 3 and 5 to neutrinos arriving in the southern hemisphere. The six directions are illustrated with circles in Figure 8.7, where the geometry of the DOM is shown. Also, single hits are used here since with higher multiplicity selections, the hit pattern is dominated by the fact that some PMTs have more neighbor PMTs than others and the density of PMTs is higher on the south hemisphere of the DOM. Indeed, it is more probable that low-energy neutrinos produce multiple photons that are detected in different PMTs if there are more neighbor PMTs. With less PMTs further away from each other, the number of coincidences is reduced, whatever is the neutrino direction. This effect has been observed and will be higher than any directionality effect that could be observed, suppressing it.

The 1D and 2D patterns can be seen in figures 8.8, 8.9 for the 6 different simulated directions. The 2D pattern shows the 31 PMT positions as a function of the angles theta and phi. The z axis is the number of hits in each PMT expected to be detected during 70 ms for a SN at 10 kpc. This simulation does not include background.

The closest PMTs to each incoming neutrino direction have been identified and are circled in the 2D patterns of each figure. One can infer from those 2D plots that closest PMTs to each neutrino direction, expected to be the ones with more detected photons, are indeed the ones that receive more hits in the simulation, giving a directionality pattern. The problem is the huge L0 background rate of around 7kHz per PMT, giving 490 events per PMT in 70 ms. This means background is 10 4 times larger than signal.

To get an estimate of the angular resolution, the simulation is repeated many times, including the signal plus background expectation. Each time, the 3-4 more lighted PMTs are taken. From their coordinates, the baricenter is computed to get the most probable direction of the source. The angular distance between the most probable direction and the true direction is computed for each pseudoexperiment. This is put into an histogram, showing the distribution of the angular distance. The mean and width of the distribution finally gives you the angular resolution. Results are shown in Figure 8.10 and the error obtained is one third of the sky (120 degrees). In conclusion, the perspective of pointing to the CCSN source using the directional information of the KM3NeT multi-PMTs gives a large angular uncertainty and is not encouraging. Even though the results are not promising, if a good background characterisation and subtraction of the baseline rates is achieved and the CCSN is close and/or energetic enough, some improvement could be possible. Moreover, the background fluctuations have been assumed to be Poissonian, with an average PMT rate of 7 kHz. However, we now known from the first data that this is optimistic, and a detailed study with a more realistic background model is needed.

Chapter 9

Gamma-ray bursts as multi-messenger sources

In this chapter, the physical processes at play in gamma-ray bursts are addressed from a multi-messenger perspective. The connection between GRBs and GW sources is emphasised, highlighting the interest of the different neutrino searches that are presented in chapters 10 and 11 and have been carried out during the thesis. The different energy scales of interest are reviewed, underlining the differences with respect to MeV neutrino searches described in Part II.

Introduction to gamma-ray bursts

Gamma-ray bursts, introduced in section 1.5, are among the most energetic explosions in the Universe. A non-thermal electromagnetic radiation characterizes the different emission phases of GRBs. In this section, an overview on GRBs is given.

As a reminder from section 1.5, two different types of GRBs are observed, thought to correspond to different typical duration of the gamma-ray emission: short and long GRBs (see Fig. 9.1). Short and long GRBs are respectively related to the coalescence of two compact objects in a binary system and to the explosion of a single massive star. The parameter that is typically used to characterise the GRB is the time in which 90% of the gamma-ray burst luminosity is emitted, called T 90 . The different durations, together with the fact that less and less energetic short GRBs are observed suggests that the sources are not the same and neither the mechanism driving the EM emission may be. This is illustrated in Fig. 9.1, where the number of observed event for each GRB type is shown, and Fig. 9.2, where the luminosity-redshift relation of observed GRBs is presented.

When a supernova progenitor is able to retain a significant amount of angular momentum, an accretion disk might be formed, and the stellar collapse may be accompanied by two relativistic jets launched along the rotation axis of the collapsing star [START_REF] Lovelace | Relativistic jets from accretion disks[END_REF]. In fact, a large angular momentum is required for the system to reach the huge amount of energy that is needed to lauch a relativistic jet, which can be powered by accretion or rotational energy [START_REF] Livio | Supernovae and Gamma-Ray bursts: The greatest explosions since the Big Bang[END_REF]. This specific subset of supernovae are thought to be connected with the emission of a long gamma-ray burst [START_REF] Barnes | A GRB and Broad-lined Type Ic Supernova from a Single Central Engine[END_REF][START_REF] Matzner | Supernova hosts for gamma-ray burst jets: dynamical constraints[END_REF], which represent the most energetic bursts of EM radiation observed.

Examples of the supernova subset represented by long-GRBs are the so called collapsars, with a high-mass progenitor that is able to sustain the energy released by the long GRB taking place with the CCSN explosion. In this case, the remnant can be a NS or a BH. The supranova scenario suggests that a black hole can be formed in a second step from the collapse of the neutron-star remnant left by the

Neutrinos and GWs from compact binary mergers

In 1916, Einstein predicted the existence of gravitational waves 100 years before their first detection in 2015. The theory of General Relativity describes gravity as a geometric property of spacetime, governed by Einstein's equations (Eq. 9.1):

G µν = - 8πG c 4 T µν . (9.1)
This system of equations tells us that the matter-energy distribution, described by the stress-energy tensor T µν , determines the space-time geometry, given by the Einstein tensor G µν . The indexes µ,ν go through the 3 spatial and the temporal dimensions of spacetime. G and c being universal constants for the gravitational coupling and the speed of light in vacuum.

Gravitational waves, as electromagnetic waves, are predicted to travel at the speed of light. The first GW measurements are compatible with this hypothesis. Their amplitude is attenuated proportionally to the distance to the source. Therefore, gravitational-wave detectors will have to be sensitive to space distorsions of the order of 10 -21 m. How to beat this challenge is described in section 10.1.

As an analogy with the electromagnetic force, that accelerates dipoles producing electromagnetic waves, the gravitational force will radiate gravitational waves when the mass-energy quadrupole moment of a system accelerates. An example of wave emitter would be therefore a binary system formed of two close compact objects orbiting around each other, as will be covered in this chapter. Indeed, the coalescence of a compact binary system perturbs the space-time leading to GW radiation due to a high-order (quadrupolar) mass-dynamic asymmetry in the system during coalescence. Three compact binary systems can be identified by gravitational wave detectors: binary black holes (BBHs), neutron star -black hole systems (NSBHs) and binary neutron stars (BNSs).

Numerical simulations allow to reproduce the evolution of these compact binary systems very accurately, showing three different phases: the inspiral, the merger and the ringdown. Fig. 9.6 shows these phases for the BBH case. The duration, amplitude and frequency of the signals and the corresponding waveforms will vary depending on the type of compact binary system as well as with the masses of the colliding objects and the distance to the source.

Neutrinos and GWs from binary black hole mergers

The merging of two binary black holes is believed to take place without any accretion of matter or relativistic ejecta, which means that no particle acceleration is in principle possible at these sources. Therefore, no EM or neutrino counterpart is expected to be observed.

Even though the current picture of the binary system evolution foresees no EM or neutrino emission from these objects, some scenarios predict the possible presence of an accretion disk or a relativistic jet being emitted [232,[START_REF] Perna | Short gamma-ray bursts from the merger of two black holes[END_REF]. In this case, particle acceleration would take place leading to a multimessenger production. The presence of a dense surrounding environment or a strong magnetic field from the merger remnant would be enough to motivate the search for a potential EM and/or neutrino counterpart. One of the possible scenarios is that the two low mass black-holes merging evolve in an AGN accretion disk, in which case the dense environment is procured by the amount of material known to be surrounding the central engine [START_REF] Bartos | Rapid and Bright Stellar-mass Binary Black Hole Mergers in Active Galactic Nuclei[END_REF].

Multi-messenger emission from GRBs 169

Neutrinos and GWs from NSBH systems

As for BNS mergers, the coalescence of a neutron star and a black hole in a compact binary system (NSBH) is believed to radiate GWs, photons and neutrinos. The characteristics of the electromagnetic light-curve may be different because of the different initial masses compared to BNS but the processes in play might be very similar, as predicted in [START_REF] Barbieri | Light-curve models of black hole -neutron star mergers: steps towards a multi-messenger parameter estimation[END_REF]. However, the different models must be confirmed by an observations and the detection of these sources is one of the main targets of the current generation of GW interferometers.

Observational results

Current instruments have allowed for an increased of the observational statistics, with 1-3 GRB detections per day. However, many unknowns remain concerning the theory and mechanism driving the GRB electromagnetic emission. In particular, for many GRBs, the measurement of the source distance is not possible.

A high-energy neutrino detection from a BNS would help in a multi-messenger observation. On the one hand, having the time and position of the transient event from a neutrino detection might help to detect the EM signal, that could be missed without this information due to the small field of view of these instruments. On the other hand, sub-threshold analyses between gamma-ray (or GWs) and neutrino telescopes might allow to identify faint EM (or GW) signals, for which a significant detection would not be possible in neutrinos or gamma-rays (GWs) by their own [START_REF]A Search for Cosmic Neutrino and Gamma-Ray Emitting Transients in 7.3 Years of ANTARES and Fermi LAT Data[END_REF][START_REF]Search for Multimessenger Sources of Gravitational Waves and High-energy Neutrinos with Advanced LIGO during Its First Observing Run, ANTARES, and IceCube[END_REF]. For this reason, neutrino telescopes actively follow both the GW and GRB detections searching for a correlated signal.

Despite of the many improvements, only one multi-messenger detection of a binary neutron system with the GW signal and short GRB associated emission has been observed (see section 1.4.1). This event yielded no neutrino detection, which allowed IceCube to constrain an on-axis jetted emission. This was later confirmed by radio observations. The largest operating neutrino telescopes, sensitive to high (TeV-PeV) energies, constantly perform a follow-up of the different gamma-ray burst detections, with no significant neutrino counterpart identified up to now. The dedicated analyses by the ANTARES [START_REF]Search for muon neutrinos from gamma-ray bursts with the ANTARES neutrino telescope using 2008 to 2011 data[END_REF] and IceCube [START_REF]An absence of neutrinos associated with cosmic-ray acceleration in gamma-ray bursts[END_REF][START_REF]An All-Sky Search for Three Flavors of Neutrinos from Gamma-Ray Bursts with the IceCube Neutrino Observatory[END_REF] collaborations cover the follow-up of O(1000) GRB events, and focus on the search for a prompt neutrino emission, i.e. they don't consider any precursor or late neutrino emission [START_REF] Waxman | Cosmological gamma-ray bursts and the highest energy cosmic rays[END_REF][START_REF] Vietri | The acceleration of ultra-high-energy cosmic rays in gamma-ray bursts[END_REF][START_REF] Paczynski | Neutrino bursts from gamma-ray bursts[END_REF][START_REF] Waxman | High energy neutrinos from cosmological gamma-ray burst fireballs[END_REF]. These analyses allow to set stringent limits to the neutrino flux predicted by these models for GRBs being a population of neutrino sources. Using the available GRB catalogs, results show that these sources do not account for more than 1% of the total diffuse neutrino flux measured by IceCube (considering the source is observed in the electromagnetic spectrum).

Chapter 10

Neutrino follow-up of gravitational-wave sources In this chapter, the current status of gravitational-wave (GW) astronomy is discussed, with a description of the gravitational-wave detectors and the different techniques used to analyze the gravitationalwave data. Finally, the follow-up of the GW triggers and the analysis method to search for coincident neutrinos in ANTARES data with the GW signal, is presented, showing the astrophysical constraints obtained from the analysis results.

Gravitational-wave interferometers

Current gravitational-wave detectors use interferometry as a detection principle. Interferometry exploits the fact that the relative spacetime deformation that is aimed to be measured can be observed as a difference in length between the two arms of a Michelson interferometer. The main working scheme is the following. A laser beam is split into two arms, placed perpendicularly one to the other, by a beam splitter. The two beams are reflected back by two mirrors, placed at the end of each arm. The light travels back through the arms and the two beams recombine at the beam splitter, leading to an interference pattern.

When a gravitational wave crosses the detector, the spacetime perturbation results into the shortening of one length with respect to the other, that is elongated, and a length difference occurs. As a consequence, there is a change of phase of the light that takes place at the recombination point, making the destructive interference become constructive. A simplified picture is given in Fig. 10.1.

Up to now, four GW interferometers have been deployed. Two of ∼4 km arm length in the USA, LIGO Hanford and LIGO Livingston, which have participated in three scientific runs. They were the first to detect a GW, which deserved the Nobel Prize award in 2017. A third detector located in Italy (Pisa), Virgo, with arms of ∼3 km length, which joined LIGO detectors for data taking in August 2015 (end of run O2). A fourth detector undergoing the final stage of the commissioning phase in Japan, called KAGRA, with ∼3 km long arms, will join LIGO and Virgo in future runs.

These complex experiments are equipped with additional instruments that allow for stabilizing the detector and monitoring the different noise contributions. In particular, they host microphones and sismometers among others to identify sources that could mimic the GW signal and veto them. Fabry-Perot resonant cavities are also present, allowing to increase the effective arm length, and therefore the signal amplitude. 2) when a GW crosses the detector and the interference is measured to be constructive (bottom).

Gravitational-wave searches

The search for GW events in the LIGO-Virgo detectors is done with three independent pipelines in parallel. Two of them (PyCBC [239] and GstLAL [240]) are based on Matched Filtering techniques, and are modeled searches which use templates for the signal waveform model. The range of potential merger masses they cover goes from 2 to 500(400) M⊙, respectively. The main difference between them is that in the PyCBC pipeline the significance is computed from the Inverse False Alarm Rate (IFAR), which is the inverse of the number of events per unit time with a given signal to noise ratio expected from background only. GstLAL computes the significance using a log-likelihood method. The third one is Coherent Wave Burst (cWB) [START_REF] Klimenko | Coherent method for detection of gravitational wave bursts[END_REF], which is an unmodelled search for transient signals based on a time frequency analysis that covers signals with duration up to 2s and frequencies up to 1 kHz.

Using time-frequency analysis and Matched Filtering techniques to filter noise, together with a good understanding of the detector, allow to reach the experimental sensitivity to observe such small signal amplitudes.

For the two modelled searches, signal waveform models (or templates) obtained from general relativity simulations are used in order to estimate the parameters of the system: component masses, chirp mass 1 , source location, distance, etc. In the case of an unmodelled burst, there is not existing template that can be used to infer such parameters. Even the distance can not be estimated without a multimessenger counterpart. A coherent signature at each detector is the feature used to identify this kind of signal. The triangulation method can be applied to reconstruct the direction of the source in all the three cases.

State-of-the-art of gravitational-wave astronomy

Since 2015, the Ligo-Virgo Scientific Collaboration has completed three science runs: O1 from September 2015 until January 2016, O2 starting in November 2016 and ending up 31st August 2017, and O3 which covered the period from April 2019 until March 2020, with a month of commissioning break in the middle that divided the run into two parts, O3a and O3b.

O1 led to the first detection of a gravitational-wave signal, which originated from the merger of two black holes in a binary system, with a total of three events detected [START_REF]Observation of gravitational waves from a binary black hole merger[END_REF][START_REF]GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence[END_REF]. During O2, the LIGO detectors started taking data, and some months later the Virgo detector joined the data taking for the first time. O2 led to the discovery of the multi-messenger signal from the coalescence of a binary neutron star system [START_REF]GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral[END_REF] (see section 1.4.1). Additionally, seven BBHs were detected during this observation run. Only three of the seven events ( [START_REF]GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2[END_REF]244,[START_REF]GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence[END_REF]) were published before the release of a final catalog [START_REF]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], where four new events were announced. Finally, O3 has been a tremendous success as well as a step forward for gravitational-wave astronomy. The results coming out of this data analysis will be with no doubt a breakthrough is astroparticle physics and cosmology. The classification in terms of astrophysical origin of the 56 triggered events of O3 is given in Table 10.1. Table 10.1: Event classification of the GW triggers during O3. Three event classes are compact binary mergers (BBH, BNS, NSBH). Terrestrial is the classification used for events with a small probability of being of astrophysical origin in the real-time analysis. Unmodelled is the label given to events that are triggered by cWB but not by the modelled pipelines. Mass Gap corresponds to events which present a reconstructed mass for one of the merging objects which is larger than the limit predicted for neutron stars and smaller than the limit predicted for stellar BHs.

Type

Terrestrial BBH BNS NSBH Mass Gap Unmodelled Events 3 37 6 4 5 1

GW events under study

In this section, some details about the six events that have been analysed as a part of this thesis work are provided. Four out of these six events were not announced as confirmed events before because, for each of them, one of the online or offline criteria failed, or all of them were satisfied but with a low signal-to-noise ratio. The two events that were already published were followed-up in real time by ANTARES, and the offline optimisation is discussed here. These two events are GW170608 [244] and GW170814 [START_REF]GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence[END_REF]. Some relevant information about the six GW events analysed:

• GW170608 is the lightest BBH observed so far. This event happened during a special period in which the LIGO-Hanford detector was going through an alignment process for angular coupling minimisation while the LIGO-Livingston detector was operating in a nominal configuration.

• GW170729 is interesting because it was found with the highest significance by the unmodelled search (cWB [START_REF] Klimenko | Coherent method for detection of gravitational wave bursts[END_REF]), and one of the merging black holes presents a reconstructed mass which is beyond the predicted limits from stellar evolution. This makes this GW source a potential candidate for being of different astrophysical origin. It was only identified in the offline search and thus, no alert was distributed to partner observatories. It is also the GW event leading to the most massive black hole remnant, the most distant source detected and the only one for which a null post-merger spin can be ruled out.

• GW170809 was found online and thus triggered an alert that was sent to electromagnetic observatories.

• GW170814 was identified as a coincident event between Livingston and Hanford detectors by GstLAL [240] when re-analyzing O2 data to incorporate an updated calibration for the Virgo detector, and additional noise subtraction applied to LIGO data. It is also well localised on the sky thanks to the non-observation by the Virgo interferometer.

• GW170818 happened just one day after the detection of the "golden" binary neutron star merger (GW170817). It was not triggered by the real-time search and thus, no alert was sent for an EM follow-up. It was only found by GstLAL in the offline analysis. It is the binary black hole merger with the best reconstructed location of the catalog.

• GW170823 was triggered by the three GW pipelines online and offline. shows the skymap (in equatorial coordinates) containing the O2 events for which an alert was released to the electromagnetic EM community. The skymap in Fig. 10.2 (bottom) represents the events from O1 in 2015 and the two events of O2 for which no alert was sent.

In Table 10.2 we summarize the information about the GW trigger of the events and the neutrino follow-up with ANTARES, with the published GCN numbers given. ANTARES was active at the time of all GW events that triggered an alert. In Table 10.3 the corresponding chirp mass and distance estimated for each event are shown. These parameters might be relevant in a neutrino search, as probability functions for the source being detected in neutrinos as well as for choosing the most relevant sources to be followed. The updated skymaps produced with the LALInference reconstruction algorithm are used for the evaluation of the 90% CL GW contour [START_REF] Veitch | Parameter estimation for compact binaries with ground-based gravitationalwave observations using the LALInference software library[END_REF]. GW skymap for all the events detected during O1 and O2. Top: GW events observed during O2 for which a real-time alert was released. Bottom: GW detections from O1 and the two O2 events that were not triggered online. Figure from [START_REF]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].

Neutrino follow-up

The ANTARES Collaboration responded to most of the GW triggers and performed a search for neutrino emission from these sources. In a first step, a real-time follow-up is done right after the reception of the alert. For this, a fixed event selection based on the quality of the reconstruction (Λ parameter) is applied. Later, a dedicated offline analysis is carried out for each event with refined cuts, as will be described in section 10.4.

The main difference between the two searches is that online searches only rely on upward-going muon neutrinos while offline searches have been extended to the full sky [START_REF]All-sky search for high-energy neutrinos from gravitational wave event GW170104 with the ANTARES neutrino telescope[END_REF] and to neutrinos of all flavours [START_REF] Antares | Search for High-energy Neutrinos from Binary Neutron Star Merger GW170817 with ANTARES, IceCube, and the Pierre Auger Observatory[END_REF]. Moreover, the offline analysis incorporates dedicated time and position calibrations that are not available in real-time. Results from the real-time and refined offline neutrino searches have been published for five GW signals from O1 and O2 [START_REF]High-energy Neutrino follow-up search of Gravitational Wave Event GW150914 with ANTARES and IceCube[END_REF][START_REF]Search for High-energy Neutrinos from Gravitational Wave Event GW151226 and Candidate LVT151012 with ANTARES and IceCube[END_REF][START_REF]All-sky search for high-energy neutrinos from gravitational wave event GW170104 with the ANTARES neutrino telescope[END_REF][START_REF] Antares | Search for High-energy Neutrinos from Binary Neutron Star Merger GW170817 with ANTARES, IceCube, and the Pierre Auger Observatory[END_REF]. This leaves six GW events for which an offline search had not been performed using ANTARES data, and will be the focus of the work presented in the next sections.

Dataset and Monte Carlo simulations

Data taking conditions during August 2017, where most of the events occurred, were quite stable and the sea current and trigger rate quite low. The information about the data quality conditions during each of the six GW runs is reported on Table 10.4. The parameter Qbiolum quantifies the data quality with respect to the bioluminescence conditions: the higher the value of Qbiolum, the lower bioluminescence and the better the conditions.

A specific high-statistics neutrino Monte Carlo simulation was generated for the 6 runs including the GW alert times with the latest run-by-run production. The time of the alerts in UTC and MJD are given in Table 10.5 together with the corresponding run number and its duration.

Localisation of the GW events and ANTARES visibility

In this subsection, we provide the ANTARES coverage at the time of the alert, together with the localisation of the error box of each of the six GW events. The region of the GW error below (upgoing events) and above (downgoing events) is considered separately due to the different background conditions (see section 3.1). The Table 10.6 provides the size of the 90% GW CL area seen as downgoing and upgoing at the time of the GW trigger. Left plots in Figures 10.

Analysis method

In this section, we focus on the strategy followed to search for a neutrino counterpart to transient sources in ANTARES. The criteria followed for the analysis optimization consists in choosing the cuts in such a way that the observation of one event in time and space coincidence with the GW trigger and 10.4. Analysis method passing the selection leads to a detection significance of 3σ.

The short time window and small region of interest for the search in case of a GW detection of a transient source allows to use time and space coincidences for a significant background reduction compared to diffuse or point-source searches, which makes possible an all-flavor search above the ANTARES horizon.

The optimization at 3σ is chosen because on the one hand, it allows for a model independent optimization for the most sensitive channel (upgoing tracks). On the other hand, fixing the background for a 3 σ detection and maximising the signal expectation provides a good compromise between the discovery potential achieved and the obtained upper limits. In fact, this method was first proposed in [START_REF]Search for High-energy Neutrinos from Gravitational Wave Event GW151226 and Candidate LVT151012 with ANTARES and IceCube[END_REF] and has been used not only for GW-HEN analysis but also for the search of neutrino counterparts to Fast Radio Bursts [START_REF] Petroff | Fast Radio Bursts[END_REF].

It turns out that requiring that the probability of observing at least 1 event to be p 3σ = 2.7 × 10 -3 is equivalent to select the analysis cuts so that the background expectation is µ = 2.7 × 10 -3 within the search time window and sky region, as derived in Eq. 10.1. This approximation where the probability is equal to the background expectation is only valid for small µ.

P(n ≥ 1|µ) = 1 -P(n = 0|µ) = p 3σ = 2.7 × 10 -3 1 -e -µ = 2.7 × 10 -3 → µ = -ln(1 -2.7 × 10 -3 ) = 2.7 × 10 -3 (10.1)
For the analysis, four separate samples are considered taking into account the event topologies and the sky regions, dominated by a different background: upgoing tracks, upgoing showers, downgoing tracks and downgoing showers. The selection strategy and quality parameters used to set the optimal cuts is described in the following subsection for each of the samples.

To look for neutrinos in coincidence with a transient event, the data run containing the potential astrophysical signal, covering the full sky, is used to compute the number of events within the search time window and inside the region of interest in the sky where the analysis is performed, separately for the upgoing/downgoing sky coverage.

The search time window used in the analysis is ∆t = ±500 s, which is taken from the statistics on GRB precursors and covers the prompt GRB emission [START_REF] Baret | Bounding the time delay between high-energy neutrinos and gravitational-wave transients from gamma-ray bursts[END_REF]. The spatial search region (RoI for Region of Interest), is defined by the area within the 90% CL contour provided by the GW reconstruction. The number of expected background events within ∆t, N ∆t , is computed according to Eq. 10.2.

N ∆t = number of data events during GW event run run duration × ∆t (10.2)

The rates are assumed not to vary significantly over the run duration. All the rates are then rescaled to get the actual number of events inside the 90% CL sky area (hereafter also referred to as error box) of the GW event, which depends on the declination of the GW event.

The background expectation inside the GW error box cannot be computed using the run of the event only because of the lack of statistics. Therefore, a larger amount of data (several months) is used to evaluate the background inside the 90% GW CL area by using the angular distance from the event position reconstruction to the source position, as stated in Eq. 10.3. Finally, one gets the total number of expected background events in the RoI and within ∆t, N RoI ∆t .

N RoI ∆t = number of data events inside 90% CL area total number of data events (up/down) × N ∆t (10.3)

Optimization of the track event selection

For the selection of track events, a different optimization is performed for upgoing and downgoing events, as explained below. For both, a cut on the angular reconstruction uncertainty β <1 • is applied.

The optimization is mainly based on the reconstruction quality parameter, Λ (see [START_REF]Searches for Point-like and Extended Neutrino Sources Close to the Galactic Center Using the ANTARES Neutrino Telescope[END_REF]), which is computed as the ratio between the likelihood of the reconstruction and the number of degrees of freedom.

The anticumulative distribution of N RoI ∆t for Λ > -6.5 is fitted to an exponential of the form a * exp(-b * x), with a and b the fitted parameters ans x the number of events N RoI ∆t . This fit is assumed to accurately describe the muon rate as a function of Λ. In order to estimate the number of events for high Λ values (where the statistics become too low), the atmospheric neutrino contribution is computed from the MC simulation and added to the exponential fit.

The optimised Λ cut is defined as the Λ value from which the number of background events N RoI ∆t becomes smaller than p 3σ = 2.7×10 -3 . In this way, the optimization is done so that the Poisson probability of detecting at least one event is equal to p 3σ , as explained above. Moreover, this optimisation approach is model independent since no information about the signal is used.

For downgoing events, a cut in the energy estimate of the events is also applied to further reduce the overwhelming atmospheric muon background. This is efficient since cosmic neutrinos and atmospheric muons have a different energy spectrum. The number of hits used in the event reconstruction (N hits ) is used as a proxy of the energy estimate, since they are directly correlated. The optimization for downgoing events is performed as follows:

1. The number of events remaining in the time window ∆t and inside the 90% confidence level area is computed for different cuts in the energy-correlated variable, N hits . For each value of N hits , a cut on Λ is found to have less than 2.7×10 -3 events coming from background after selection. For upgoing events, the optimisation is performed following this only step.

2. The set of cuts (Λ, N hits ) is optimised by comparing the number of survival signal events computed for the different combinations, assuming a signal flux dN dE = φ 0 E -2 , with φ 0 = 10 -8 GeV cm -2 s -1 sr -1 . The set of cuts that maximizes the survival signal is applied as the final selection. In this sense, the downgoing track selection is slightly model dependent since it is optimised for a given spectrum, while for upgoing tracks it is model independent.

Event selection

Optimization of the shower event selection

Once the track selection is applied, the events that do not pass the cuts are taken as shower candidates, so the two event samples are disjoint. While track-like events can start far away from the detector, shower events are required to be contained in the detector. The containment definition is given in [START_REF]Searches for Point-like and Extended Neutrino Sources Close to the Galactic Center Using the ANTARES Neutrino Telescope[END_REF]. Moreover, a pre-selection cut is applied on the output of the M-estimator value from the reconstruction fit (see section 3.4.4), based in [START_REF] Antares | Search for High-energy Neutrinos from Binary Neutron Star Merger GW170817 with ANTARES, IceCube, and the Pierre Auger Observatory[END_REF]. All these conditions are summarised in Table 10.7. [START_REF]An algorithm for the reconstruction of high-energy neutrinoinduced particle showers and its application to the ANTARES neutrino telescope[END_REF], noted L dusj , is used to distinguish track-like events from shower-like events. The RDF is trained using the information on the reconstruction parameters to identify the two topologies. In addition, an extended likelihood ratio, L µ , is also used to discriminate between cosmic showers and atmospheric muons based on the photomultiplier hits information [START_REF] Timothee | Search for high-energy neutrinos from the gacatic plane with the antares neutrino telescope[END_REF], which also gives hint on the event topology.

The shower analysis for the follow-up of GW-O2 candidates uses the same optimisation procedure for upgoing and downgoing events. For each cut in the RDF output, the optimised L µ cut is obtained, using the same p 3σ criterion as for tracks. The set of cuts on L dusj and L µ that maximizes the surviving signal assuming an E -2 neutrino spectrum while fulfilling the p 3σ condition is chosen as the final selection.

The larger angular uncertainty of shower events, which becomes comparable to the size of the 90% CL area of the GW events, needs to be taken into account. In this work, the final acceptance was corrected using the fraction of events that would be truly located and reconstructed inside the error box, using the MC information and called "good" events. In this way, the final acceptance only considers events whose angular error is smaller than the 90% GW confidence area. This uncertainty on the reconstructed direction translates, on average, into a 7% uncertainty on the final shower acceptance.

If there is no clear maximum in the number of signal events, which happens in some cases where a plateau is reached, the optimised L dusj cut value is chosen in order to maximize the event statistics and reduce the uncertainty on the value p 3σ cut in the L µ parameter applied.

Event selection

This section will cover the results of the optimization of the cuts on the quality parameters described before for each of the events, in chronological order, following the method and selection criteria explained in section 10.4. The optimisation method is illustrated with the example of GW170814 for upgoing events and GW170818 for downgoing events.

Analysis results

After unblinding the dataset, no neutrino was found that passed the cuts during the search window and inside the GW error box. The non-detection of neutrino events in time and space coincidence with the six analysed GW sources allows to set constraints on the neutrino emission from binary black-hole mergers.

The detector sensitivity to the searched-for signal depends on the source position and on the neutrino energy. Therefore, constraints are set as a function of the position in the sky and within the 5-95% energy range of the search. The sensitivity is given by the detector acceptance, which is defined as the expected number of signal events passing the selection cuts per given unit flux. Similarly, this sensitivity can also be characterised by the effective area; see section 3.4.5 for their relation. The ANTARES acceptance and effective area are evaluated by means of a dedicated MC simulation performed on a run-by-run basis. This accounts for the detector configuration and variable data-taking conditions for each ANTARES observing run at the time of the GW events under study, which impact the detector sensitivity.

As there is not a precise location of the GW signals, the neutrino emission is considered to come from a point-like source, with the source located at different pixels inside the error box region. The pixel size in which the detector sensitivity is computed is chosen to be large enough to avoid MC statistical fluctuations (18 • in sinus of the declination and 36 • in right ascension). With these considerations, upper limits (UL) as a function of the position on the sky are presented in the form of skymaps (see Figures 10.9 and 10.10). The resulting constraints on the neutrino spectral fluence and on the total isotropic energy emitted through high-energy neutrinos (TeV-PeV range) are summarised in Tables 10.12 and 10.14.

Constraints on the neutrino spectral fluence

Upper limits at 90% CL on the neutrino spectral fluence from a point-like source located in a given position on the sky are calculated using the null result and the detector acceptance.

In the case of no signal event, a 90% CL fluence upper limit can be defined. Using Poisson statistics, this upper limit corresponds to the time-integrated flux that would produce on average N 90% =2.3 detected neutrino events in the pixel containing the source. The 90% UL on the number of events, N 90% , is defined as:

N 90% = dN dE ν (E ν )A eff (E ν , δ)dE ν , (10.4)
where A eff (E ν , δ) is the ANTARES effective area at the alert time, which takes into account the absorption of neutrinos by the Earth and the detector visibility. This effective area depends on the event selection cuts as well as on the neutrino energy and the position of the source. For a neutrino powerlaw spectrum ( dN dE ν ∝ E -γ ), the spectral fluence at the detector can be defined as:

E 2 ν dN dE ν = φ 0 E ν 1GeV -γ+2 (GeV • cm -2 ).
(10.5)

The upper limits obtained, assuming a neutrino spectrum with spectral index γ=2 (generic model typically expected for Fermi acceleration [START_REF] Bell | The acceleration of cosmic rays in shock fronts[END_REF]), are shown in Fig. 10.9 for the six GW events. Table 10.12 provides the average 90% CL upper limits on the neutrino spectral fluence (φ 90% 0 ) inside the error box.

Table 10.12: Average 90% upper limit on the neutrino spectral fluence inside the 90% GW CL contour. The main systematic uncertainties on the estimated fluence upper limits come from two sources. The first one is the uncertainty on the detector acceptance, which is related to the photon detection efficiency of the PMTs. It comprises an angular effect that leads to a 15% uncertainty on the flux of upgoing events [START_REF]Searches for Point-like and Extended Neutrino Sources Close to the Galactic Center Using the ANTARES Neutrino Telescope[END_REF] and a 30% uncertainty for downgoing events [START_REF] Aguilar | Zenith distribution and flux of atmospheric muons measured with the 5-line antares detector[END_REF], and an overall effect due to the quantum efficiency of the PMTs and optical water properties, which results in an uncertainty of about 20% on the total acceptance [START_REF]Measurement of the atmospheric muon flux with a 4 GeV threshold in the ANTARES neutrino telescope[END_REF]. The second source is related to the capability of the MC simulation to reproduce data conditions on a run-by-run basis. This effect was evaluated together for upgoing and downgoing events and amounts to ∼20% [START_REF]All-sky search for high-energy neutrinos from gravitational wave event GW170104 with the ANTARES neutrino telescope[END_REF]. For the shower event topology, an additional systematic effect of ∼7% is introduced to account for the uncertainty on the shower position inside the GW error box. All the mentioned effects account for a total systematic uncertainty on the fluence upper limit of about ∼33% for upgoing and ∼42% for downgoing events. Table 10.13 provides a summary of the current neutrino limits from previous GW-neutrino followup analyses. The first three rows in the Table are two O1 events for which the analysis was performed independently by IceCube and ANTARES telescopes [START_REF]High-energy Neutrino follow-up search of Gravitational Wave Event GW150914 with ANTARES and IceCube[END_REF][START_REF]Search for High-energy Neutrinos from Gravitational Wave Event GW151226 and Candidate LVT151012 with ANTARES and IceCube[END_REF]. For these two events, the value reported in the table refers to the most sensitive detector. The third event (GW170104) is the only published event from O2 before this work. It is an ANTARES only analysis and considers events from the full sky [START_REF]All-sky search for high-energy neutrinos from gravitational wave event GW170104 with the ANTARES neutrino telescope[END_REF]. For the second and third events, the values are extrapolated from the skymaps. This comparison shows that IceCube limits are about one order of magnitude better than the ANTARES results presented here, both in the upgoing and downgoing respective searches. This is due to the larger size (and thus larger effective area) of the IceCube detector. The results of this work show an improvement of 15-30% for upgoing events, which becomes a factor of 2 and up to an order of magnitude improvement in the downgoing search limits obtained. This improvement comes from the addition of the shower channel and a better characterisation of the downgoing background as a function of the declination. In conclusion, in the region below the horizon for IceCube, our results are not competitive, while in the region above the horizon for IceCube, the ANTARES limits are comparable, and a combination may be of interest. ∼0.9 GW170104 ANTARES upgoing [START_REF]All-sky search for high-energy neutrinos from gravitational wave event GW170104 with the ANTARES neutrino telescope[END_REF] ∼2 GW170104 ANTARES downgoing [START_REF]All-sky search for high-energy neutrinos from gravitational wave event GW170104 with the ANTARES neutrino telescope[END_REF] ∼20

GW event

Constraints on the total energy

From the null detection and using the 90% CL upper limit on the neutrino spectral fluence obtained in the previous section, a constraint on the total equivalent isotropic energy (E ν,iso ) emitted by the source in high-energy neutrinos, within the sensitive energy range of the search (TeV-PeV range), can be set.

The mean of the reconstructed luminosity distance (D L ) distribution inside the error box provided by LIGO-Virgo [START_REF]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] is used for the redshift estimate.

The total energy emitted in high-energy neutrinos is computed according to Eq. 10.6 by integrating the neutrino spectrum over the energy range expected to contain 5-95% of detected events (see Table 10.14) together with the measured luminosity distance and the associated redshift,

E ν,iso = 4πD L (z) 2 1 + z E 95% E 5% E -2 ν φ 90% 0 E ν dE ν . ( 10.6)
The average 90% CL upper limits inside the error box are summarised in Table 10.14 together with the 5-95% energy range for each GW event. In Fig. 10.11, these results are shown as a function of the redshift for six GW events, separately for the upgoing (orange) and downgoing (blue) regions of the error box. These results are computed using the average limits and D L measurements inside the 90% GW confidence regions, together with their uncertainty. In Fig. 10.10, results are provided in the form of skymaps with the 90% UL as a function of the position of the sky for the pixels inside the error box. The distance estimate at each pixel provided by the LIGO-Virgo probability map is used, as in [START_REF] Leo | Going the Distance: Mapping Host Galaxies of LIGO and Virgo Sources in Three Dimensions Using Local Cosmography and Targeted Follow-up[END_REF][START_REF] Leo | Supplement: Going the Distance: Mapping Host Galaxies of LIGO and Virgo Sources in Three Dimensions Using Local Cosmography and Targeted Follow-up[END_REF].

As inferred from Eq. 10.6, these limits scale with D 2 L and proportionally to the fluence limits (φ 90% 0 ), which have been here obtained for a E -2 neutrino spectrum. While upgoing background rates are mainly isotropic in local coordinates, the downgoing rates strongly depend on the zenith angle. See for instance events GW170809 and GW170818. The GW170809 downgoing region is very close to the ANTARES horizon, where the background level is very close to the one expected when looking at events traveling through the Earth. On the other hand, GW170818 sky location was almost at the zenith of the detector at the trigger time, where the atmospheric rate becomes about two orders of magnitude higher. The different background conditions lead to the different limits as observed in Fig. 10.11.

Chapter 11. Follow-up of very high-energy gamma-ray bursts with ANTARES

Track selection

Aside from the two differences related to the type of source described above, the track event selection is the same as for GW events, detailed in section. 10.4.1. The only exception was GRB 190114C, for which (as for GRB 170817A), no N hits cut was needed due to the lower background in the short time window and small RoI considered.

Shower optimization

The first time that showers were included in a transient (GW-HEN) analysis [START_REF] Antares | Search for High-energy Neutrinos from Binary Neutron Star Merger GW170817 with ANTARES, IceCube, and the Pierre Auger Observatory[END_REF], the selection was not optimised but based on what had been previously done in point-source neutrino searches [START_REF]First all-flavor neutrino pointlike source search with the ANTARES neutrino telescope[END_REF]. In this thesis, an effort was devoted to define and optimise a shower selection for multi-messenger searches. In a first step, a dedicated optimisation was performed for GW-HEN searches (see section 10.4). For the event GRB 190114C, the same selection was applied.

As the first very-high energy, O(TeV), gamma-ray detections in the late afterglow were announced, the specific characteristics of these events (with a longer emission time and good space localisation), led to further investigation for a better performing optimisation of the shower topology cuts. Therefore, the slightly new selection used in this analysis is presented here.

As already mentioned, in the case of neutrino searches from GRBs, the spatial region of the search is optimised, and not fixed as for GW-HEN analysis. When using a large time window (∼ 12 h for the two long GRBs analysis in this work) and large RoI (10-20 deg radius around the source position), the optimisation is not anymore feasible directly on data because the lower statistics in one run cannot characterise the tail of the background distribution. For this reason, a dedicated run-by-run atmospheric muon Monte Carlo simulation is used to evaluate the background. The data-MC comparisons needed in this case and the higher background rate, led to additional selection cuts in order to reach the p 3σ level.

On Fig. 11.3, we show the cumulative distribution of L µ with a cut on L dusj >0.3 (typical in point source searches), for upgoing (top) and downgoing events (bottom). Both the GRB run (left) and the previous data run (right) distributions are shown. We see that indeed the statistics of one data run do not allow to set a cut using the 3σ optimization. Therefore, the muon MC simulation must be used here to estimate the background.

First of all, one would like to discard as many mis-reconstructed muons as possible. For this, one can make use also of the track reconstruction algorithm (AAFit) for the zenith selection in the shower sample. By requiring that the event is not only reconstructed upgoing/downgoing by TANTRA, but also that it is not reconstructed in the opposite region by the AAFit reconstruction, the background is significantly reduced. Therefore, the upgoing/downgoing selection is applied simultaneously in both the track (AAFit) and shower (TANTRA) zenith reconstruction.

A further step is to use the energy estimate of the shower reconstruction to get rid of atmospheric muons (Fig. 11.4). In fact, when looking at the distribution of the reconstructed energy for muons, we see that there are many events which have no energy estimate and are given a default value of 0.1. The effect is observed both in data and the MC. Also, typical ANTARES analysis are not sensitive to energies below 100 GeV. Indeed, Fig. 11.4 shows that the signal expectation below 100 GeV is negligible, while a fraction (10-20%) of atmospheric background is discarded. Therefore, a cut is set, selecting the events with E sh > 100 GeV. In the same fashion, a cut on N hits,sh is applied in order to further discard atmospheric muons, chosen in the same was as for downgoing tracks (see Fig. 11.5).

Data and Monte Carlo samples 197

After the pre-selection, two additional parameters are used to scrutinize the shower sample. One is an extended likelihood ratio, L µ , which is used to distinguish atmospheric muons from cosmic showers using the PMT hit information. The other is different for upgoing and downgoing events. For upgoing events, the output of the Dusj reconstruction Random Decision Forest (RDF) classifier, noted L dusj , trained to distinguish between an atmospheric muon (track-like) event and a shower-like event is used. Instead, for downgoing events, the shower energy estimate (N hits,sh ) is used, in a similar fashion as for downgoing tracks. In fact, the RDF was trained with upgoing events. In summary, with these considerations and the new pre-selection, the final shower optimisation is performed on the combination of cuts:

• L µ and L dusj for upgoing events, optimised together with RoI.

• L µ and N hits,sh for downgoing events, optimised together with the RoI.

Data and Monte Carlo samples

The analysis makes use of the data and dedicated Monte Carlo simulations for the runs where each GRB were detected. They both incorporate dedicated calibrations and reconstruction, as well as a runby-run reproduction of the data taking conditions. Table 11.2 provides the information about each source and data runs of the analysis.

Neutrino follow-up and event selection 11.4.1 GRB 180720B

For this event, the search is done over 12 h: from the trigger time until the end of the observation by H.E.S.S. Taking into account the ANTARES visibility, this corresponds to a search of 7.6 h for upgoing events covering the prompt phase, and a downgoing search of 4.4 h duration which covers the high energy observations. In fact, this event was not triggered by H.E.S.S. in the online search and the VHE emission was only identified in an offline analysis. For this reason, there was no real-time follow-up by ANTARES of this GRB.

Since the source is moving with respect to the local detector frame during the 12 h search, a full-sky MC is used to estimate the signal expectation. The angular resolution of track and shower candidate events, estimated from the MC simulation, is used to optimise the size of the RoI.

The background estimate is done using the atmospheric muon MC and thus, data-MC comparisons are done before starting the optimisation in order to check that the simulation is in good agreement with the data. Figures 11.7 and 11.8 show the data-MC comparison of the Λ and L dusj (N hits,sh ) distributions, for upgoing and downgoing events, respectively. 11.3: Neutrino spectral fluence upper limits (φ 90% 0 ) obtained for the three VHE GRB searches, separately for upgoing and downgoing events. The search window δt is also given. The hyphen indicates that the corresponding GRB was not seen as upgoing during the gamma-ray emission. Assuming that the neutrino spectrum is a power law with spectral index γ = 2, then the spectral fluence at the detector can be expressed as follows:

Event

φ 0 = E 2 ν dN dE ν [GeV • cm -2 ]. (11.2)
Time integrated fluence upper limits can be easily be derived from Eq. 11.2, considering the Poisson 90% confidence level upper limit, N 90 ν = 2.3, leading to the results shown in Table 11.3 for the three GRBs analysed. Since the redshift of the source is known, these fluence upper limits can be converted into upper limits on the total isotropic neutrino emission following:

E ν,iso = 4πD L (z) 2 1 + z E 95% E 5% E -2 ν φ 90% 0 E ν dE ν . ( 11.3)
The results obtained are presented in Table 11.4. These neutrino limits are 2-3 orders of magnitude above to the isotropic energy inferred from electromagnetic observations: E iso,γ = 6×10 53 erg for GRB 180720B, E iso,γ = 2-3×10 53 erg for GRB 190114C according to Fermi-GVM, andE iso,γ ∼2×10 52 erg as measured by MAGIC; and E iso,γ = 2.967×10 50 erg . Therefore, the ANTARES limits do not allow to constrain the potential hadronic component present in the EM signal. However, the next generation detectors will gain almost 2 orders of magnitude in sensitivity. Moreover, combined studies with several detectors might lead to more encouraging results. Additionally, due to he small neutrino flux expected from these sources, a stacking is appropriate in this case. However, this particular study has been done because these were the three GRBs ever detected at O(TeV) energies, after several decades of search by IACTs. For this reason, special attention was put to these sources with a dedicated search.

The results for GRB 190114C are shown in Fig. 11.19 in the form of a differential upper limit as a function of the neutrino energy. MAGIC data in [START_REF]Observation of inverse Compton emission from a long gamma-ray burst[END_REF] (Extended Data Table 1) is used to infer the differential gamma-ray fluence corresponding to the MAGIC flux over the time window ∆t as follows:

E 2 γ dN dE ν (MAGIC) = φ γ 0 × ( E γ E pivot
) -α × ∆t × ×E 2 γ , (11.4) 11.5. Results of the ANTARES search 207 comparison is not fully accurate since this model provides the expected flux for the prompt emission, and the extended emission observed for this GRB may not be modelled in the same way. Moreover, the time variability of the GRB emission should be taken into account for a more precise calculation. However, the prompt time integrated emission already provides an estimate of the total amount of energy emitted during the GRB, and so it gives an order of magnitude for the strength of the expected flux compared to the experimental limit.

Chapter 12

Summary, conclusions and outlook

Neutrino astronomy is a relatively young field which was born with the observations of solar neutrinos and neutrinos from a core-collapse supernova explosion. Recently, the first detections of high-energy cosmic neutrinos and the first sources observed simultaneously through different messengers have marked a new way of conceiving astronomy which goes beyond the classical observation of electromagnetic emission from the cosmos: the era of the multi-messenger astrophysics.

Neutrinos, cosmic rays and gamma-rays can be produced in the surroundings of the same astrophysical source, where particle acceleration up to high energies is possible. However, gamma-rays can also be produced in leptonic processes, in which no neutrino or cosmic rays are produced. Therefore, detecting neutrinos from an identified source would be the proof for a site of hadron acceleration.

The fact that neutrinos interact only through the weak force makes of their detection a challenge. This same fact makes them invaluable cosmic messengers, since they are going to bring unique information and probe the astrophysical mechanisms riding the most energetic phenomena in the Universe. As of today, the blazar TXS 0506+056 is the only evidence for an astrophysical source of high-energy neutrinos. Some other sources also present an indication in the same sense. In addition, a diffuse flux of cosmic neutrinos with TeV-PeV energies has been detected, whose origin is still unknown. The search for the sources producing it should therefore continue.

Neutrinos are neutral particles that can only be detected indirectly, i.e. via the observation of their interaction products. The detection principle of neutrino telescopes is based on the detection of the charged particles produced in neutrino interactions in the detector material. In particular, in the KM3NeT and ANTARES experiments these particles are observed through the detection of the Cherenkov light induced by charged particles crossing the detector at a relativistic speed. The light is detected in the arrays of photomultipliers (PMTs) which constitute the elementary bricks of the detector. Following the amount of photons deposited and the time when they are detected in each PMT along the instrumented lines, one can reconstruct the position and direction of the particles.

In underwater Cherenkov detectors, three types of background are dominant: charged leptons produced in the interactions of cosmic-rays in the atmosphere that produce detectable light (this includes atmospheric muons and atospheric neutrinos), bioluminescence and radioactive decays.

KM3NeT detectors ARCA and ORCA are under construction in the Mediterranean Sea, respectively offshore Sicily (Italy) and Toulon (France). The first will be dedicated to high-energy (TeV-PeV) neutrino astronomy, as ANTARES. The second has as main scientific goal the determination of the neutrino oscillation parameters and the neutrino mass ordering (GeV energies). The key component of the KM3NeT detectors are the digital optical modules (DOMs), composed of 31 PMTs. In contrast, ANTARES has a single large photocathode PMT per optical module. Three PMTs form an ANTARES storey.

In the following, the main results and conclusions obtained during this thesis and some future prospects are presented.

Detection of CCSN neutrinos with KM3NeT

CCSN was the second astrophysical neutrino source identified after the Sun. In fact, the only detection of neutrinos from a CCSN event allowed to consolidate the basis of the astrophysical mechanism, showing the relevance of the role of neutrinos in such explosions. However, a single detection is not enough to constrain all the unknown parameters that allow to explain in details what happens in the different phases of the explosions, and their impact. For this reason, it is of interest to study the perspectives for a future explosion occurring in our Galaxy.

Ideally, sensitive neutrino detectors will be ready for the next Galactic explosion. In fact, current and near-future detectors will only be sensitive to CCSN events up to the Magallanic Clouds. Only one to three events are expected per century in the Galaxy, so we do not want to miss the next one.

We have seen that KM3NeT detectors are not initially designed to detect MeV neutrinos. Even though in these low energy interactions it is not possible to do an event-by-event reconstruction, a CCSN explosion may be identified as an overall increase of the detected rate over background. In fact, the large amount of neutrinos produced in these astrophysical phenomena will produce an increase not only in the total amount of detected photons (hits), but also in the amount of hits seen in coincidence between the different PMTs in a DOM. This is why both ORCA and ARCA detectors can be used for this kind of searches.

KM3NeT detectors will mainly be sensitive to the ν e flux, that will interact with protons in water. Using the number of coincidences in the same DOM (called multiplicity), one can drastically reduce the background from radioactive decays and bioluminescence. Moreover, looking for spatially and temporally correlated photons through different DOMs, it is possible to filter the events produced by atmospheric muons, which show characteristic correlations. These techniques allow to optimise the KM3NeT potential to MeV neutrinos.

A detailed simulation of the KM3NeT detector response to MeV neutrinos has been developed in the framework of this thesis.. From the simulation, it has been estimated that 115 KM3NeT detection lines provide an equivalent effective detector mass for MeV neutrino searches of ∼50 kton. With the multiplicity selection optimised for this kind of analysis, this effective mass in reduced to ∼1 kton. This simulation has allowed for a characterisation of the detector response at low energies, which has been implemented in the form of a parametrisation with the efficiency as a function of the neutrino energy. In this way, it allows to evaluate the KM3NeT signal expectation for any astrophyscial neutrino flux with energies between 1 and 100 MeV, including all the experimental effects.

The coincidence method mentioned above has been put in place and optimised during the thesis, and it has been applied to the first KM3NeT data for the background measurement, as well as to the signal simulation. Finally, it has been used to evaluate the KM3NeT capabilities to detect CCSN neutrinos, including a detailed study of the systematic uncertainties. The results of the study are promising and show that KM3NeT will be able to detect more than 95% of the Galactic CCSN progenitors, contributing to the observation of the next Galactic explosion.

Real-time monitoring and first results

The CCSN selection has been implemented in the data acquisition system in the form of a trigger for real-time analysis, keeping the information of candidate events in a continuous way. The background stability and control achieved with this trigger have allowed the KM3NeT experiment to be part of the SNEWS network, where all the experiments sensitive to CCSN neutrinos send their alerts with a fake trigger rate which is lower than one in eight days. The interest of this network is that on the one hand it allows to lower the threshold of individual detectors by requiring a coincidence detection, and on the other hand it provides the infrastructure for sharing information between the different experiments, which may be relevant to the physics results that may be obtained from the next observation. Moreover, such network will communicate with other observatories, which might be of help for a successful multi-messenger follow-up.

KM3NeT is able to combine in real time the ORCA and ARCA data into a single trigger, with a latency below 20 s. Currently, six ORCA lines taking data can trigger an alert to SNEWS if a CCSN happens closer than 6-9 kpc, depending on the progenitor mass.

One of the main goals of the real-time searches is to be able to identify the signal through different messengers, and determining where and when the event happens. In particular, in CCSN explosions, neutrinos are expected to be detected up to several hours before photons. Moreover, CCSN are believed to be also a source of gravitational-waves. Therefore, a prompt neutrino detection may help for a multi-messenger follow-up.

During their last data taking run (O3), the gravitational-wave detectors triggered two signals, which were potentially originated from a CCSN explosion. At that moment, four ORCA lines were in operation, and a follow-up of these alerts was performed with available data, applying the CCSN analysis. No significant MeV neutrino excess was observed, which allowed to set limit on a possible CCSN emission. In particular, a CCSN source closer than 6 kpc was ruled out, and the total energy emitted in neutrinos could not be larger than 3 × 10 53 erg if the source was at 10 kpc, corresponding to the typical energetic output expected from this kind of events. With these follow-ups, we could test the functioning and performance of the CCSN trigger in a real analysis for the first time, verifying that the analysis could be applied in a real case, and a fast response is achieved.

Study of the properties of the CCSN neutrino flux

In this work, the capability of discriminating between the different models, and determining the spectral properties of the flux has been evaluated. For this, it is crucial to estimate which are the angular, energy and time resolution of the experiment when applying the analysis to the searched signal.

In order to carry out time dependent analysis, a good time resolution is needed. In particular, a millisecond time-scale resolution is required to study fast changes in time in the neutrino flux, and to precisely determine the arrival time of the signal. To achieve this goal, the instrument must be able to detect a large number of signal events. In KM3NeT, this is possible only if all coincidences are used. The high multiplicity selection yields a better background rejection and detection sensitivity, but at the expense of loosing a large amount of signal events.

The main analysis performed using the time profile (lightcurve) has been to develop a method to combine the neutrino lightcurves as detected by different experiments. The aim of this study is to determine the time delay of the arrival of the signal at the different detectors, and the uncertainty of this measurement. For this, a canonical parametrisation of the neutrino flux, and a simple detector response simulation are used to evaluate the performance and feasibility of the method. These results have been used to infer the source localisation by triangulation of the signal at the different experiments. The analysis yields a precision of ∼70 deg 2 in the localisation of a CCSN at 10 kpc which explodes in the direction of the Galactic Centre. The proposed approach will allow to determine the time delay between experiments in a model independent way, in contrast to the methods used in previous works. This analysis is meant as a low latency evaluation, allowing to send fast and preliminary information to other observatories. The result can be improved in a later refined analysis combining additional information and methods.

The different hydrodynamical processes and instabilities taking place during the CCSN may also impact the time evolution of the neutrino flux, in particular, by producing oscillations in the neutrino lightcurve. A spectral analysis has been carried out to evaluate the detection capability of such oscillations in KM3NeT. The results obtained conclude that KM3NeT will be able to detect this oscillatory signature (with a significance of 3σ) if the source is near-by (between 3 and 5 kpc distance).

Additionally, the possibility to access the neutrino spectrum information using the correlation between the neutrino energy and the multiplicity rates has been investigated. Even though the three parameters describing the CCSN neutrino spectrum are not independent in our measurement, a statistical analysis based on a χ 2 minimisation method has been performed, allowing to set confidence level intervals. In case the other two parameters are measured with an uncertainty of about 10%, KM3NeT could reach an ∼0.5 MeV resolution in the mean neutrino energy.

Comparison with other experiments

Table 12.1 shows the number of expected events in each detector for a CCSN explosion at 10 kpc, for three different progenitors and the two NMO hypotheses: NO on the left, IO on the right. All of the detectors in the Table will be part of SNEWS2.0, and are sensitive to a Galactic CCSN. Four of them (IceCube ICSN, Super-Kamiokande [START_REF]Search for Supernova Neutrino Bursts at Super-Kamiokande[END_REF], Hyper-Kamiokande [206], and JUNO [START_REF]Neutrino physics with JUNO[END_REF]) can reach a 5σ detection of sources up to the Magallanic Clouds. No current or near-future detector will be sensitive to explosions further away. The currently operating KM3NeT detector, with 6 ORCA lines taking data, is already able to cover CCSN events up to ∼6 kpc in case of a low mass progenitor (11 M ⊙ ) and beyond the Galactic Centre for higher-mass stellar collapse (27 M ⊙ ).

For what concerns time-dependent analyses of the neutrino lightcurve, IceCube and Hyper-Kamiokande, provide the best opportunities. They will be the only experiments able to detect the SASI oscillations at 15-20 kpc for the 27 M ⊙ progenitor model [START_REF] Tamborra | Neutrino signature of supernova hydrodynamical instabilities in three dimensions[END_REF][START_REF] Migenda | Detecting Fast Time Variations in the Supernova Neutrino Flux with Hyper-Kamiokande[END_REF]. KM3NeT, Super-Kamiokande, JUNO and DUNE may contribute to close-by (∼5 kpc distance) and failed CCSN explosions [START_REF] Walk | Neutrino emission characteristics of black hole formation in three-dimensional simulations of stellar collapse[END_REF].

In terms of localisation, using the ES channel information in Super-Kamiokande with Gd doping may provide the most accurate pointing [START_REF] Tomàs | Supernova pointing with low-and high-energy neutrino detectors[END_REF]. Other possibilities such as triangulation, anisotropic interactions or the first events can also be used for a fast time response involving several high-statistics detectors, which may also be helpful [START_REF] Vogel | The angular distribution of the reaction: ν e + p → e + + n[END_REF][START_REF] Linzer | Triangulation pointing to core-collapse supernovae with nextgeneration neutrino detectors[END_REF][START_REF] Coleiro | Combining neutrino experimental light-curves for pointing to the next Galactic Core-Collapse Supernova[END_REF].

Regarding the resolution of the spectrum, scintillator detectors like JUNO will be the ones achieving the best results, with an energy resolution of the order of 1% [START_REF] Lu | Getting the most from the detection of Galactic supernova neutrinos in future large liquid-scintillator detectors[END_REF]. However, the combination of various detectors may help involving more independent measurements and breaking the degeneracy between the different parameters, hence reducing the uncertainties [START_REF] Gallo Rosso | What can we learn on supernova neutrino spectra with water Cherenkov detectors?[END_REF][START_REF] Köpke | Improved Detection of Supernovae with the IceCube Observatory[END_REF].

Experiments

Type [START_REF] Mirizzi | Supernova neutrinos: production, oscillations and detection[END_REF] that form neutron stars and s40 from [START_REF] O'connor | An Open-Source Neutrino Radiation Hydrodynamics Code for Core-Collapse Supernovae[END_REF] which forms a black hole. The two numbers given are the total events over all channels using SNOw-GLoBES [START_REF] Beck | SNOwGLoBES: SuperNova Observatories with GLoBES[END_REF] assuming adiabatic MSW oscillations only for the normal mass ordering (left number) and the inverted mass order (right number).

Outlook and perspectives

At the end of this thesis, a new project has started which aims at exploiting the combination of the information coming from different experiments sensitive to different interaction channels (neutrino flavors). This is done in collaboration with theory experts and people from the DUNE and Darkside Collaborations, which are sensitive to ν e and all flavors, respectively, while KM3NeT is sensitive to ν e . First work has been done to extend and implement the CCSN simulation for these argon detectors, in the same framework as for KM3NeT, and evaluate the expected number of events as well as the detected lightcurve for different models. In this way, the final goal is to evaluate the model discrimination power using the synergies between these experiments, and determine the flux properties thanks to this combination.

Moreover, a time-dependent analysis of the spectrum would be of interest for the discrimination between the different models. In fact, determining the spectrum at different times of the emission may reveal the time evolution of the spectral parameters.

The possibility of using machine learning techniques to achieve a better discrimination between signal and background, by identifying patterns as the signature of the bioluminescence and radioactive decay processes, is going to be studied. This could allow to enhance the sensitivity, specially in time dependent analyses.

In addition, the neutrino mass ordering, and in general neutrino flavor conversion effects, will impact the observables of the core-collapse supernova neutrino emission. Therefore, CCSN neutrinos can also provide a measurement of the neutrino mass ordering. A very preliminary study has been started on this topic, but it should be mentioned that the change in the observed neutrino flux induced by the neutrino mass ordering is a tiny effect, so the experimental systematic effects of the NMO study using the neutrino lightcurve would need to be evaluated in an accurate way. Moreover, a precise knowledge of neutrino physics in such extreme media is required for a realistic estimate of the expected signal. For these reasons, this was kept outside of the scope of this thesis.

For what concerns the real-time analysis, there is still some work to be done/improved in the near future. As an example, defining the arrival time of the CCSN signal from the real-time trigger, implemented over 500 ms, is ongoing work. This arrival time will be part of the information to be provided in case of an alert. In particular, it is of interest also to see which is the response of the KM3NeT DAQ to a very intense flux expected from a close explosion (below one kpc), e.g. in case Betelgeuse explodes. The idea to be put in place is to inject a real simulated signal at such distance into the DAQ, and look if such high amount of data can be processed without stalling or showing problems, with a proper behavior of the filters.

Moreover, there is a plan to develop a full run-by-run simulation of the data taking conditions for the CCSN data stream, with and without an inclusion of the signal. Up to now, all the background evaluation has been done directly on data, and a separate signal simulation. The purpose is to evaluate the signal detection efficiency in a more accurate way, incorporating the varying conditions in real data.

ANTARES search for high-energy neutrinos in coincidence with GW events and GRBs detected at TeV energies

Cosmic neutrinos and high energy cosmic rays are expected to have a same origin, yet unknown. Among the possible source candidates, gravitational-wave and TeV gamma-ray sources may also produce high-energy neutrino emission. For this reason, we have dedicated part of the work of this PhD to the search for high-energy neutrinos observed in coincidence with EM or GW detected sources.

When looking for high-energy neutrinos in neutrino telescopes like ANTARES, space and time correlations between the detected photons are used to identify different event topologies characteristic of the interaction of charged particles in water: long tracks induced by muons produced in the atmosphere and in muon neutrino charged current interactions releasing detectable Cherenkov light, that can come from outside the detector; and quasi spherical light deposited inside the detector emitted by particles produced in neutral current interactions of all-flavor neutrinos and in charge current electron neutrino interactions (shower-like). These correlations are exploited in an optimal way and implemented in the form of triggers, which tag candidates of these particle interactions and help reducing part of the background. In fact, events marked by bioluminescence or radioactivity will not active the triggers by themselves. Thus, the dominating background component for high-energy neutrino searches is the atmospheric background.

The most usual way to get rid of the atmospheric background is to look for events that come across the Earth (seen as upgoing in the detector), since only neutrinos can travel through the Earth. Moreover, atmospheric and cosmic neutrinos are expected to have a different energy spectrum. Therefore, by selecting the most energetic events, one can filter most of the remaining miss-reconstructed muons and the atmospheric neutrino contribution.

Another possibility is to look for time and space coincidences with a confirmed detection of a transient source, observed through any messenger. This is part of the multi-messenger approach. A small space region and a short time window where to look at, allow for a significant background reduction and lead to an increase of the discovery potential. In fact, background can be reduced enough to also allow for searches above the detector horizon (downgoing events, which are most probably muons). In this way, the search can be extended to the full sky, an including all neutrino flavors. 12.2. ANTARES search for high-energy neutrinos in coincidence with GW events and GRBs detected at TeV energies 215

Part of the thesis work has been devoted to the development of an event selection for showerlike events to be applied to these multi-messenger/transient searches. This selection is based, as for track events, on searching for the cuts in the quality parameters of the reconstruction so that one event passing the cuts, which is found inside the search time window, and reconstructed with a position compatible with the source location, leads to a 3σ detection. This strategy allows to keep a good sensitivity (fixed at 3σ) while obtaining an optimal upper limit at the same time, since the cuts are chosen to maximise the signal expectation. This analysis has been applied during this thesis to the search for a neutrino counterpart in ANTARES data to the GW events from the O2 catalog, and to the first detection of GRB events at TeV energies. These are all-flavor and full-sky neutrino searches. Including shower events in the analysis leads to an improvement of about 30% for upgoing events, and up to 200% for downgoing searches, compared to using only tracks. However, both searches result in no neutrino detected in coincidence with any of the GW and GRB signals analysed.

Outlook and perspectives

The prospect is now to perform the analysis on the new GW candidates from run O3. For binary blackhole mergers, a stacking analysis using a more sophisticated likelihood method will be carried out, following the same strategy as for O2.

Outside of the content of the manuscript, some work has been done to evaluate the sensitivity of the future KM3NeT-ARCA detector to these same transient sources by using the same method as in ANTARES, which allows for a fast response analysis, which can be applied to the full-sky and all neutrino flavors. The conclusion of these preliminary studies is that the same method is still applicable in an efficient way to KM3NeT-ARCA, even if it is a larger detector with a higher background rate. The expected improvement compared to ANTARES is going to be evaluated.

The KM3NeT detectors will offer the opportunity of a common multi-messenger program using ORCA and ARCA, covering a large energy range that will go from O(GeV) up to tens of PeV energies. Moreover, they will be operating in the same timeline as new space missions (e.g. SVOM), new Cherenkov ground-based telescopes (CTA), new GW instruments (run O4 with four GW interferometers, LISA), and the next generation neutrino detectors (IceCube-Gen2, Hyper-Kamiokande).

Figure 1 . 21 :

 121 Figure 1.21: Illustration of the two different classifications of active galactic nuclei. The dashed line separates the radio-low and the radio-quiet regions. The different names of the object depending on the orientation of the jet with respect to the line of sight are shown. Figure from [63].

Figure 2 . 8 :

 28 Figure 2.8: A picture of a DU deployment, where the detection unit is furled into the LOM.

Figure 4 . 1 :

 41 Figure 4.1: Time distributions of neutrino events observed by the three observatories from SN 1987A. Figure extracted from[START_REF] Burrows | Neutrinos from SN 1987A[END_REF]

Figure 4 . 2 :

 42 Figure 4.2: The differential (top) and cumulative (bottom) probability distribution of the distance to a supernova in the Milky Way from the model in [142].

4. 2 .

 2 Phases of a Core-Collapse Supernova: the explosion mechanism 77 mechanism.With the revival of the shock, the final explosion takes place (Fig.4.4 lower right). During the cooling phase, which lasts a few tens of seconds, the luminosity and temperature gradually decrease. The corresponding luminosity time evolution along this phase is shown in Fig.4.5 (right). This final phase is dominated by all-flavor neutrino pair productions. The so-called neutrino-driven wind is launched by neutrino-energy deposition in the NS which has just born. This wind is essentially a spherical flux of baryonic matter going out from the NS surface, and favours the nucleosynthesis of heavy elements (Fig.4.4 lower right). An overall feature of the neutrino flux at this stage is the luminosity being roughly equal for the three neutrino flavors.

Figure 4 . 4 :

 44 Figure 4.4: Dynamical phases of stellar core collapse and explosion by the neutrino-driven mechanism: infall, core bounce, stagnation of the bounce shock, accretion and neutrino heating, shock revival, and outward acceleration of the neutrino-powered SN shock front (from top left to bottom right). Figure taken from [147].

Figure 4 . 5 :

 45 Figure 4.5: Simulations of the neutrino burst (left), the accretion phase (middle) and the cooling phase (right) of a CCSN are shown here. The notation ν x includes all the non-electronic neutrino flavors that in this case can be considered as one for what concerns their evolution. The middle plot comes from the 3D simulation of the 27M ⊙ progenitor in [148]. The right and left plots come from the 1D simulation of an 8.8M ⊙ in [149].

  3 as pessimistic and optimistic models of fast time variations in the neutrino light-curves in case of a normal CCSN. The duration of the simulated emission is of 543 ms for the 27 M ⊙ simulation, 340 ms for the 20 M ⊙ and 11 M ⊙ progenitors, and 572 ms for the failed CCSN (40 M ⊙ ).

Figure 4 . 8 :

 48 Figure 4.8: Neutrino flux as a function of the energy at different times of the core collapse, for the 27 M ⊙ progenitor simulation. Figure built with data from [148].

Figure 4 . 9 :

 49 Figure 4.9: Neutrino fluence for the accretion phase of a core-collapse supernova at 10 kpc for the Garching 3D simulation models of 40 M ⊙ (right), 27 M ⊙ (middle) and 11 M ⊙ (left) over a time of 543 ms and 340 ms, respectively.

Figure 4 . 10 :

 410 Figure 4.10: Schematic level crossing diagram in CCSN, for normal (left) and inverted (right) mass hierarchies. The circles shows the resonance points. Figure from [159].

Figure 5 . 1 :

 51 Figure 5.1: Cross sections of neutrinos in water for the different interaction modes.

Figure 5 . 4 :

 54 Figure 5.4: IBD (left) and ν e ES (right) interaction rates in a 100 kton water detector.

Figure 5 . 5 :

 55 Figure 5.5: Interaction rates in a 100 kton water detector. Distribution for ν e + 16 O, (left) and ν e + 16 O (right) interactions.

Figure 5 . 7 :

 57 Figure 5.7: Example of background lightcurves measured from raw data, sampled with a 1 ms binning. On the left for ARCA, on the right for ORCA. They are generated with a selection of 5 ns L1 coincidences. The spikes observed in ORCA data (not observed in ARCA due its deeper location and the larger distance between the DOMs, which prevent to detect such coincidences) are correlated at sub-ms scale and thus may be induced by correlated muon coincidences.

Figure 6 . 3 :

 63 Figure 6.3: Highest multiplicity coincidence of single-muon events versus the distance of closest approach, determined from atmospheric muon Monte Carlo. The black lines show the 10%, 50% and 90% quantiles.

  10 5 N gen (115 × 11) = 6.4×10 7 ×0.2×0.001×π×400×38×27055 10 5 ×10 8 = 2091 N 2+1 = N MC ×N SN ×V gen 10 5 N gen (115 × 11) = 6.4×10 7 ×0.2×0.001×π×400×38×5946 10 5 ×10 8 = 455

Figure 7 . 10 :

 710 Figure 7.10: The detected lightcurve in ARCA including signal and background. For two different CCSN progenitor masses considered: 27 M ⊙ (top left) and 20 M ⊙ (top right). The failed CCSN of 40 M ⊙ is shown on the bottom plot. The source is considered at 5 kpc.

Figure 8 . 1 :

 81 Figure 8.1: Time evolution of the neutrino luminosity in the considered simplified model.

Fig. 4 ,

 4 left]. The ARCA and ORCA detectors consist of 4140 and 2070 optical modules, respectively. The coincidence selection translates into a lower effective CCSN detection volume for KM3NeT/ARCA compared to IceCube, even if both have an instrumented volume of ∼1 km 3 . The effective mass and the background rate for the different detectors used in this work are summarised in Table 8.1. The examples of the simulated experimental lightcurves are provided in Figure 8.2.

Figure 8 . 2 :

 82 Figure 8.2: Expected neutrino lightcurves obtained with the described simulation, showing the number of event in 50 ms bins. On the left for IceCube (black) and ARCA (red), on the right for Hyper-Kamiokande (black) and Super-Kamiokande, zoomed vertically 10 times for visual purposes (red). The error bars for each bin correspond to the original statistical (Poisson) uncertainty on the number of events, scaled accordingly to the bin size.

Fig. 8 .

 8 [START_REF] Czakon | Are neutrinos Dirac or Majorana particles?[END_REF] shows an example of the T match 0 -T 0 distribution from pseudo-experiments of the χ 2 fit between IceCube and Hyper-K.

Figure 8 . 3 :

 83 Figure 8.3: Distribution of the difference T match 0 -T 0 obtained applying the χ 2 fit between IceCube and Hyper-K to a set of realisations of the real (observed) T 0 .

3 .

 3 The confidence area skymaps shown in Figures 8.4 and 8.5 are drawn assuming the fitted delays as true positions. Additionally, the fitted CCSN location distributions for the same realisations are shown in Figures 8.4, 8.5.

4 Figure 8 . 7 :

 487 Figure 8.7: Schema of the DOM geometry. The left/right Figures indicate the upper and lower hemispheres of the DOM. The 6 simulated directions are pointed with colored circles, showing the PMTs closest to the interaction vertex in each case.

8. 2 . 155 Figure 8 . 8 :

 215588 Figure 8.8: On the left, the 1D PMT pattern for dir1 on the top, dir2 on the middle and dir3 on the bottom. On the right, the 2D pattern for the same directions. The z-axis is the number of expected detected events per PMT from a CCSN signal at 10 kpc, without background. The circled PMTs in the 2D patterns correspond to the closest PMTs to the incoming neutrino direction, matching well with the PMTs receiving more hits.

Figure 8 . 9 :Figure 8 . 10 :

 89810 Figure 8.9: On the left, the 1D PMT pattern for dir4 on the top, dir5 on the middle and dir6 on the bottom. On the right, the 2D pattern for the same directions. The z-axis is the number of expected detected events per PMT from a CCSN at 10 kpc. The simulation does not include background. The circled PMTs in the 2D patterns correspond to the closest PMTs to the incoming neutrino direction, matching well with the PMTs receiving more hits.

Figure 10 . 1 :

 101 Figure 10.1: An schematic illustration of a Michelson interferometer. The main principle is drawn comparing the two Figure cases: (1) when no GW passes through the detector and a destructive interference is observed (top) and (2) when a GW crosses the detector and the interference is measured to be constructive (bottom).

10. 3 .Figure 10 . 2 :

 3102 Figure10.2: GW skymap for all the events detected during O1 and O2. Top: GW events observed during O2 for which a real-time alert was released. Bottom: GW detections from O1 and the two O2 events that were not triggered online. Figure from[START_REF]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].

3

 3

  and 10.4 show the skymaps with the 90% confidence level (CL) GW area and the visibility of ANTARES at the time of the alert in equatorial coordinates. Rigt plots inFigures 10.3 and 10.4 provide the number of events in ANTARES data together with the 90% error box in local coordinates.

11. 5 .

 5 Results of the ANTARES search205 Table

Table 5 .

 5 2: Effective mass for a KM3NeT detection block as a function of the multiplicity for the 11 M ⊙ (< E ν >=13.7 MeV), 27 M ⊙ (< E ν >=15.7 MeV) and 40 M ⊙ (< E ν >=18.2 MeV) progenitors.

	Multiplicity	2	3	4	5	6	7
	11 M ⊙ 27 M ⊙ 40 M ⊙	40±4 12±3 5±1 2.5±0.6 1.3±0.4 0.6±0.2 53±5 16±3 7±1 4.0±0.9 2.0±0.6 1.0±0.4 67±7 21±4 9±2 5±1 2.7±0.8 1.5±0.5

Table 6 .

 6 1: Expected number of signal events as a function of the multiplicity for one building block. Statistical uncertainties from the Monte Carlo simulation are reported in parentheses.

	Multiplicity	2	3	4	5	6	7	8	9	10	11
	1119(3) 4806(9) N ev 40M ⊙ (572 ms) 15 240(30) 3650(10) 1449(8) 723(6) 258(1) 100.4(8) 48.9(5) N ev 11M ⊙ (340 ms) 1120(5) 442(3) 218(2) 116.0(15) 64(1) 35.2(8) 19.4(6) 25.8(4) 13.3(3) 7.2(2) 3.4(1) N ev 27M ⊙ (543 ms) 399(4) 226(3) 127(2) 69.5(18) 36.6(13) 15.0(8) 1.29(8) 0.50(5) 8.0(4) 1.9(2)

Table 6 .

 6 2: Rejection efficiency of the coincidence correlation filter in ARCA2 and ORCA4.

	Multiplicity	4	5	6	7	8	9	10	11	12
	ARCA2	0.4% 2%	9% 21% 24% 24% 24% 24% 25%
	ORCA4	4%	21% 67% 90% 95% 95% 96% 96% 96%

Table 6 .

 6 3: Rejection efficiency as a function of the multiplicity for the triggered events based filter in ARCA2 and ORCA4

	Multiplicity 4	5	6	7	8	9	10	11	12
	ARCA2	0.4% 2%	10% 22% 26% 27% 28% 29% 31%
	ORCA4	4%	22% 70% 94% 98% 99% 99% 99% 99%

Table 6 .

 6 4: Systematic uncertainties in terms or relative deviation in the number of neutrinos in the selection multiplicity range.

	Variable	Uncertainty	Syst. err.
	PMT efficiency Active PMTs Generation radius Absorption length Water density as function of depth IBD/ES cross sections	±5% ±3% ±5 m ±10% ±10% < 1%	(S) ± 10% (S, B) ±3% (S) <1% (S) ± 1% (S) <1% (S) <1%
	Filter efficiency	data -MC	(B) +15%

Table 7 . 1 :

 71 Lower limits at 90% confidence level on the CCSN distance, for three different progenitors. The Galactic coverage is underlined in the last column.

	Progenitor d 90% [kpc] (lower limit) Galactic coverage
	11 M ⊙ 27 M ⊙ 40 M ⊙	6.1 11.5 21	10-15% ∼65% ∼98%

Table 7 .

 7 2: Sensitivity results with the combination of ORCA and ARCA, for the three different stellar progenitors considered. The distance horizon and the corresponding coverage are also provided.

	Progenitor d [

kpc] Method 1: Search for Method 2: Search for Coverage of peak in spectrum power excess around f SASI Galactic CCSN

	27 M ⊙ 20 M ⊙ 40 M ⊙	3 5 8	2.8±0.7σ 3.2±0.7σ 3.8±0.7σ	4.1±0.9σ 4.5±0.9σ >5σ	3% 10% 35%

Table 8 .

 8 1: Simplified detector characteristics used as input for the simulation: effective mass in water equivalent units and total background rate.

		IceCube	ORCA	ARCA	Super-Kamiokande Hyper-Kamiokande JUNO
	M eff [kton] R bg [Hz] Reference	3500 ∼3e6 [170]	90 ∼1e6 [203, 119] [203, 119] 180 ∼2e6	22.5 0 [186, 204, 205]	560 0 [186, 206]	22.5 0 [197]

Table 8 .

 8 6: Time delay for each detector pair, assuming the signal emission coming from the three different sources. The time delay uncertainty for each detector pair from Table8.3 is given in the last column.

		Galactic Centre Betelgeuse Cygnus	δt
	IceCube -KM3NeT/ARCA	-21.7 ms	9.4 ms	28.2 ms 6.65±0.15 ms
	IceCube -Hyper-Kamiokande	-27.4 ms	17.4 ms	8.6 ms	0.55±0.01 ms
	Hyper-Kamiokande -KM3NeT/ARCA	5.7 ms	-8.0 ms	19.6 ms 6.70±0.15 ms
	IceCube -JUNO	-29.6 ms	21.0 ms	4.9 ms	1.95±0.04 ms
	JUNO -KM3NeT/ARCA	8.0 ms	-12.3 ms	23.3 ms	7.4±0.2 ms
	Hyper-Kamiokande -JUNO	-2.3 ms	4.3 ms	-3.7 ms 1.99±0.04 ms

Table 10 .

 10 2: Trigger and follow-up information of the events.

	Event (GW) LVC alert Follow-up (TAToO) GCN number Event (GCN)
	GW170608	YES	YES	21223	G288732
	GW170729	NO	NO	-	-
	GW170809	YES	YES	21433	G296853
	GW170814	YES	YES	21479	G297595
	GW170818	NO	NO	-
	GW170823	YES	YES	21659	G298936
	Fig 10.2 (top)

Table 10 .

 10 4: Data quality information for each run.

	GW run Baseline (kHz) Burst fraction (%)	Operating triggers	Qbiolum
	85148	60	42	3N+2T3+K40+GC+TS0	1
	85306	66	39	3N+2T3+K40+GC+TS0	3
	85340	62	41	3N+2T3+K40+GC+TQ+TS0	1
	85351	54	24	3N+2T3+K40+GC+TQ+TS0	3
	85361	66	57	3N+2T3+K40+GC+TS0	1
	85374	53	18	3N+2T3+K40+GC+TQ+TS0	4

Table 10 .

 10 5: Time and run information about the events.

	Event	UTC Time	MJD Time	Run number Run duration (s)
	GW170608 02:01:16.5 57912.08421875	85148	37119.20771
	GW170729 18:56:29.3 57963.78922801	85306	43202.439722
	GW170809 08:28:21.8 57974.35303009	85340	35947.104986
	GW170814 10:30:43.5 57979.43800347	85351	29351.012496
	GW170818 02:25:09.1 57983.10079977	85361	40215.559592
	GW170823 13:13:58.5 57988.55137153	85374	43203.383444

Table 10 .

 10 6: Size (in deg 2 ) of the 90% CL GW error box viewed as downgoing and upgoing events for ANTARES at the time of the alert.

	Event GW170608	A 90% up ( • ) 2 A 90% down ( • ) 2 226 170
	GW170729	553	475
	GW170809	245	95
	GW170814	87	0
	GW170818	0	39
	GW170823	878	771

Table 10 .

 10 7: Pre-selection of events for the shower sample. Additional parameters are used to optimise the cuts for the shower selection. The result of a Random Decision Forest (RDF) classifier, output of the Dusj shower reconstruction

	Criterion	Condition
	Trigger	T3 or N3
	Track veto	Not selected as a track
	Containment ρ Sh < 300m && |z| < 250m M-estimator Mest < 1000

Table 10 .

 10 11: Final cuts applied to the shower sample.

	GW event L dusj cut L µ down L µ up GW170608 0.1 -31 -20
	GW170729	0.1	0	-20
	GW170809	0.1	no cut	-19
	GW170814	0.0	-	1
	GW170818	0.1	-30	-
	GW170823	0.2	-16	-27

Table 10 .

 10 [START_REF] Clay | Penetrating radiation[END_REF]: Average upper limit inside the 90% CL contour for the previous GW-neutrino follow-up analyses.

	GW event GW150914	sky region IceCube downgoing [249]	φ 90% 0	(GeV cm -2 ) 1.2±0.3
	GW151226 GW151226	IceCube upgoing [250] IceCube downgoing [250]		∼0.06

Table 11 . 2 :

 112 Information about the GRB event and the corresponding run.

	GRB event Run ID	MJD Time	Run duration [s] (RA,dec) source [deg]
	180720B	86371	58319.59837558	43237	(0.53, -2.9)
	190114C	86915	58497.87295139	43252	(54.5,-26.9)
	190829A	87564	58724.83047454	43237	(45.6, -7.1)

Table 11 .

 11 4: Upper limits in the total energy emitted in neutrinos (E 90% ν,iso ) for the three VHE GRB searches, separately for upgoing and downgoing events. The 5-95% energy range of the analysis (E 95% ) is also given. The hyphen indicates that the corresponding GRB was not seen as upgoing during the gamma-ray emission. Last column shows the isotropic photon energy measured, E γ,iso .

	up 5-95% and

Table 12 .

 12 1: Estimated number of detected events in the different detectors from a CCSN at 10 kpc, for three different models, s11.2c and s27.0c from

	Super-K Hyper-K IceCube	H 2 O/ νe H 2 O/ νe String/ νe	Mass [kT] 32 220 51600	Location Japan Japan South Pole	11.2M ⊙ 4053/4068 28K/28K 321K/332K 662K/659K 818K/626K 27.0M ⊙ 40.0M ⊙ 7771/7544 7597/4904 53K/52K 52K/34K
	6 KM3NeT-ORCA lines String/ νe	2.5	France	309/313	670/650K	834/660
	KM3NeT (3 blocks)	String/ νe	150	Italy/France	18K/18K	38K/38K	47/38
	KamLAND Borexino JUNO SNO+ NOνA HALO HALO-1kT DUNE MicroBooNe DarkSide-20k	C n H 2n / νe C n H 2n / νe C n H 2n / νe C n H 2n / νe C n H 2n / νe Pb/ν e Pb/ν e Ar/ν e Ar/ν e Ar/any ν	1 0.278 20 0.7 15 0.079 1 40 0.09 0.02	Japan Italy China Canada USA Canada Italy USA USA Italy	189/188 52/52 3798/3769 132/131 2849/2827 4/3 54/47 2750/2485 6/5 100/100	363/349 101/97 7276/6995 254/244 5457/5246 9/8 117/102 5652/5133 12/11 300/300	350/233 97/64 7018/4661 245/163 5263/3496 10/9 128/123 6075/5910 13/13 400/400

A Majorana particle is a fermion which is its own anti-particle. Contrary to Dirac particles for which an antiparticle with opposite quantum numbers exists.

https : //indico.cern.ch/event/800827/contributions/3429831/attachments/1863050/3062552/NovaSN_SNEWS2_0_slides.pd f

This window was used as a compromise between the simulation durations of the 11 M ⊙ and

M ⊙ . After discussion, these window has been set to 500 ms, which is motivated in case of failed CCSN and covers the window with more than 80% of the expected emission. Larger windows might result in a worsening of the result.

https : //gracedb.ligo.org/superevents/S191110a f /view/

https://docs.gammapy.org/dev/stats/feldman_cousins.html

https : //gracedb.ligo.org/superevents/S200114 f /view/

The chirp mass of a compact binary system is defined as a combination of the two merging object masses, and determines the GW signal evolution in frequency. This observable can be measured in gravitational-wave data analysis more easily and with more precision than the individual masses of the two binary components.

This analysis makes use of the ANTARES data set from June until September 2017, which covers all GW events that are analysed here. These data were processed using dedicated offline calibrations.

Part II

Detecting Galactic core-collapse supernova neutrinos with KM3NeT

of the time delay between the signal arrival at the two detector sites.

Table 8.2: Uncertainty δt in milliseconds obtained with the chi-square method using ideal normalization of the detector neutrino lightcurves. The detector pairs are listed in row and column names. The arrow points to the detector name that is used for the lightcurve peak definition, which is also shifted during the χ 2 scan. For KM3NeT, the effective mass corresponding to the ARCA detector is used for the performance estimation. The maximum signal time delay between the ARCA and ORCA sites, (∼3 ms), is on the same order as the estimated uncertainties for any of the combinations involving the ARCA detector. This prevents a simple merging of the two KM3NeT lightcurves.

KM3NeT-ARCA Super

The results of the chi-square method shown in Tables 8.2 and 8.3 are computed using the optimized step and effective bin sizes of 50 ms. Using 10 ms for the step and the bin size for ARCA/IceCube and ARCA/Hyper-Kamiokande combinations provides slightly better results, reaching the value of 6.20±0.15 and 6.30±0.15 ms, respectively. Adding up to 3 Hz of background rates does not decrease the performance for Super-Kamiokande and JUNO detectors.

The performance of the cross-correlation method using the same search time window as for the chi-square method is shown in Table 8.4. The optimal effective bin size is found to be 10 ms for all combinations. The results are compatible with the chi-square method, so cross-correlation represents a viable alternative.

Part III

Searching for high-energy neutrino emission from TeV gamma-ray bursts and gravitational wave sources with ANTARES

Chapter 11

Follow-up of very high-energy gamma-ray bursts with ANTARES

In this chapter, the general context concerning the very high-energy (VHE) gamma-ray bursts detections by Imaging Air Cherenkov Telescopes (IACTs) is discussed and the results of the ANTARES follow-up of these VHE gamma-ray bursts are presented.

Introduction to the GRBs under study

As mentioned earlier in section 9.2, the emission of very high energy (VHE) gamma rays, in the O(TeV) range during the GRB afterglow phase violates the maximum photon synchrotron energy limit. Interestingly, this could be a hint for an additional hadronic component needed to model the full EM lightcurve, motivating a high-energy neutrino search.

The detection of these O(TeV) gamma rays by space instruments remains challenging due to their limited effective area. However, large ground-based Cherenkov detectors observing the showers induced in the atmosphere by high-energy gamma rays are well suited for these kind of observations. Examples of these kind of detectors are the H.E.S.S, MAGIC and VERITAS telescopes.

Three GRBs have lead to the detection of >300 GeV photons in IACTs: GRB 180720B, observed by H.E.S.S, GRB 190114C, detected by MAGIC, and GRB 190829A, also detected by the H.E.S.S telescope. Even though the observed VHE photons can be explained by leptonic models and the synchrotron self-Compton (SSC) scenario [START_REF] Wang | Synchrotron self-Compton emission from external shocks as the origin of the sub-TeV emission in GRB 180720B and GRB 190114C[END_REF][START_REF] Fraija | Modeling the observations of GRB 180720B: From radio to sub-TeV gamma-rays[END_REF] fits the data of these observations [START_REF]Teraelectronvolt emission from the gamma-ray burst GRB 190114C[END_REF][START_REF]Observation of inverse Compton emission from a long gamma-ray burst[END_REF][START_REF] Collaboration | A very-high-energy component deep in the γ-ray burst afterglow[END_REF], these sources remain of interest as potential high-energy neutrino emitters. In fact, some attempts have been made to model the data with a different hypothesis, showing that the high-energy photons could be produced in photohadronic interactions [START_REF] Sahu | Origin of sub-TeV afterglow emission from gamma-ray bursts GRB 190114C and GRB 180720B[END_REF]. Indeed, a subdominant hadronic component is not ruled out by the available data. Therefore, a particular study is carried out for these events to investigate a possible small hadronic component that could be present in the EM data.

GRB 180720B

The GBM (Gamma-ray Burst Monitor) instrument on board the Fermi satellite triggered the gammaray emission from GRB 180720B at UTC time T 0 = 14:21:39.65 (GCN #22974). This event is the 6th brightest GRB observed in Fermi-GBM and the second GRB with the highest energy flux observed by Swift (GCN #22973) in the afterglow (11 h after T 0 ), with a very long X-ray plateau. The source has been estimated to be at a redshift of z=0.653 (measured by the VLT [START_REF] Collaboration | A very-high-energy component deep in the γ-ray burst afterglow[END_REF]). The time at which 90% of