M Elias Khan

M Régis Terrier

Jean-Philippe Lenain

Mme Catherine Boisson

Keywords: Cherenkov Telescope Array: Development high-energy gamma observation, supernova remnant, Cherenkov Telescope Array, Galactic cosmic rays, radiative models, multiwavelenth analysis, NectarCAM camera, single photoelectron calibration

for their stimulating questions and support throughout the defense.

Last but not least, in my journey from an impressionable naive girl to a determined young astrophysicist, I met several individuals who knowingly or unknowingly impacted my life and played an important role in shaping me. I would like to express my sincere gratitude towards each of them, for they have aided in expanding my horizon by challenging my beliefs, presented me with opportunities for growth, and

Titre: Cherenkov Telescope Array: Développement d'un système de calibration pour NectarCAM et l'étude des restes de supernova comme candidats PeVatron. Mots clés: observation de gammas de haute énergie, restes de supernova, Cherenkov Telescope Array, rayons cosmiques galactiques, modèles radiatifs, analyse de multi-longeur d'onde, caméra NectarCAM, système de calibration, calibration à photoélectronique unique.

Résumé:

Cherenkov Telescope Array (CTA) promet d'observer l'Univers de haute énergie avec une sensibilité et une résolution angulaire sans précédent encouvrant le domaine multi-TeV. La première partie de la thèse concerne le développement d'un système de calibration à photoélectron unique pour la caméra NectarCAM des télescopes de taille moyenne (MST) du CTA. La deuxième partie vise à comprendre l'origine des rayons cosmiques (CRs) en effectuant une analyse multi-longueurs d'onde (MWL) des données existantes des restes de supernova (SNRs) galactiques. Enfin, la troisième partie présente une étude de la capacité du CTA à détecter les SNRs à la recherche de PeVatrons en simulant les flux predits pour CTA.

Un système d'étalonnage à photo-électron unique (SPE) du plan focal a été conçu par IJCLab pour la caméra NectarCAM des télescopes MST. Le système se compose d'un écran peint en blanc, d'un guide de lumière en queue de poisson et d'un flasher. Les flashs imitent le rayonnement Cherenkov et illuminent le plan focal sous l'écran de manière homogène. Ensuite, grâce à la motorisation XY, l'écran est déplacé sur l'ensemble du plan focal de la caméra NectarCAM. Ce travail de thèse concerne le développement de ce système. En particulier, la conception de l'écran de calibration a été optimisée, et un algorithme pour balayer le plan focal a été écrit. Enfin, les données des calibration MST ont été analysées, et montrent une bonne performance du système de calibration.

Les SNRs sont des sources prometteuses pour les CRs galactiques. Les CR chargés peuvent être détectés indirectement par l'observation de rayons gammas par la production d'un π 0 et de la désintégration consécutive en rayons gammas de haute énergie. Dans ce travail de thèse, nous avons étudier les tendances en faveur des scénarios lepto-hadroniques et rechercher des SNRs qui montrent des preuves d'accélération hadronique jusqu'aux plus hautes énergies. Nous avons réalisé une étude MWL sur 9 SNRs en utilisant des données provenant de différents instruments. Les données ont été ajustées avec des modèles radiatifs. Les résultats de l'ajustement ont été analysés à l'aide de trois méthodes différentes : la comparaison de probabilité, le critère BIC et l'estimation de la contribution hadronique en fonction des bins d'énergie. Les résultats montrent que tous les SNRs étudiés favorisent le modèle lepto-hadronique par rapport à un modèle purement leptonique. Nous avons identifié quatre SNRs, RX J1713, Cassiopée A, HESS J1731, et HAWC J2227, qui ont montré des contributions hadroniques importantes jusqu'à quelques TeV, ce qui en fait des candidats prometteurs pour le PeVatron. La dernière partie de la thèse est consacrée à l'évaluation de la capacité de CTA à détecter les SNRs. Cela implique de répondre à la question de savoir si CTA peut améliorer les observations des sources potentielles de PeVatron précédemment identifiées, détecter différentes valeurs d'énergie de coupure des protons, et identifier la contribution des éléments plus lourds à haute énergie où l'excès de flux a été observé. À cette fin, les flux de CTA ont été simulés par Gammapy à l'aide de modèles physiquement motivés obtenu des résultats de l'étude MWL réalisée précédemment. Les résultats montrent que CTA détectera un flux couvrant une large gamme d'énergie avec une incertitude moindre par rapport aux instruments actuels. Pour la source RX J1713, une contribution des éléments lourds a été introduite. Le résultat montre qu'en utilisant une combinaison d'éléments de type hydrogène et azote, un meilleur ajustement a été obtenu par rapport à celui utilisant uniquement des protons. En plus de l'étude de simulation précédente, nous avons également analysé les résultats de l'étude du plan galactique simulée par le groupe "Galactique" de CTA. L'étude a montré que CTA augmenterait d'un facteur 2 le nombre de SNRs détectés. De plus, les SNRs couvrant une grande distance (jusqu'à 20 kpcs), avec un flux aussi bas que ∼ 10 -14 photons cm -2 s -1 seraient facilement détectés par CTA.

Abstract:

Cherenkov Telescope Array (CTA) promises to see the high-energy Universe with unprecedented sensitivity and angular resolution covering the multi-TeV domain. The first part of the thesis concerns the development of a single photoelectron calibration system for the NectarCAM camera. The second part aims to understand the origin of Cosmic Rays (CRs) by performing a multiwavelength (MWL) analysis of existing data of Galactic Supernova Remnants (SNRs). Finally, the third part studies CTA's role in detecting SNRs in search for PeVatrons by simulating fluxes using Gammapy.

A focal plane single photoelectron (SPE) calibration system has been specially designed by IJCLab for the NectarCAM camera of the MST telescopes. The system consists of a white painted screen, a fishtail light guide, and a flasher. The flashes mimic the Cherenkov radiation and illuminate the focal plane under the screen homogeneously. Then, through the XY motorization, the screen is moved across the entire focal plane of the NectarCAM camera. This thesis work concerns the development of the calibration system. In particular, the design of the calibration screen was optimized, and an algorithm to scan the focal plane was written. Finally, the data from the MST calibration runs were analyzed, and the results show a good performance of the calibration system. SNRs are promising candidate sources for Galactic CRs. The charged CRs can be detected indirectly by the γray observations through the π 0 production and consequent decay to high-energy γ-rays. In this thesis work, we study the trends in favor of lepto-hadronic scenarios and search for SNRs which show signs of hadron acceleration up to the highest energies. We have performed an MWL study on nine SNRs using data from different instruments different. The data were fitted with radiative models to evaluate the hadronic contribution. The fit results were analyzed using three different methods: likelihood comparison, BIC criterion, and the estimation of the hadronic contribution as a function of energy bins. The results showed that all the studied SNRs favor the lepto-hadronic model over a pure leptonic one. We identified four SNRs, RX J1713, Cassiopeia A, HESS J1731, and HAWC J2227, which showed important hadronic contributions up to a few TeV, thus making them promising PeVatron candidates. Additionally, for some SNRs, excess flux was observed at high energies.

The last part of the thesis is dedicated to assessing CTA's capability to detect SNRs. This involves answering if CTA can 1) improve the observations of the potential PeVatron sources previously identified, 2) detect different proton cutoff energy values, and 3) identify the contribution of heavier elements to the excess flux at high-energy observed before. To do so, CTA fluxes are simulated by Gammapy using physically motivated models taken from the results of the MWL study performed earlier. CTA has provided flux covering a wide energy range with less uncertainty compared to current instruments. For source RX J1713, a contribution of heavy elements was introduced. The result showed that by using a combination of hydrogen and nitrogenlike elements, a better fit was obtained compared to the fit using only protons. In addition to the previous simulation study, we also analyzed the results of the Galactic Plane Survey simulated by the Galactic group of CTA. The study showed that CTA would increase the number of detected SNRs by a factor of 2. Additionally, SNRs covering a large distance (up to 20 kpcs), with flux as low as ∼ 10 -14 photons cm -2 s -1 would be easily detected by CTA.

Dedication

I want to dedicate my thesis to my parents, Bhagirathi and Sudhanshu Sharma, who have made several sacrifices and worked hard to ensure that I received the best education and every opportunity possible to achieve all my aspirations. I also owe much gratitude to my sisters and my extended family for their unwavering support and prayers.

I would also like to dedicate my thesis to my partner, Sanat Sogani. Words fail me when I try to encapsulate the emotions I feel when I reflect on your constant presence in my life. I appreciated your practical and emotional support despite the competing demands of your own work. I am grateful for your encouragement when at times, the thesis seemed arduous and insurmountable. Thank you for your unwavering patience, love, and support.

There are a number of people without whom this thesis might not have been written, and to whom I am greatly indebted.

First and foremost, I would like to thank my supervisor Prof. Tiina Suomijärvi, for providing me with constant guidance in the early part of my research career. I am most grateful for our discussions, the emotional support during the covid times, and all the special Christmas lunches you organised. I want to thank my co-supervisor, Dr. Giulia Hull, for sharing her expertise on the calibration part of my thesis. I appreciated the warm encouragement and the autonomy you provided.

As female researchers at high positions, you both certainly are a role model for me. I would also like to thank Dr. Jonathan Biteau for always being there to share his expertise on all parts of the thesis, especially on the calibration studies. Thank you for taking time out of your busy schedule to help me with all my doubts. Your confidence and enthusiasm for astrophysics is surely worth aspiring to.

I want to thank Barbara Biasuzzi, Kevin Pressard, Micheal Josselin, Sami Caroff, and Patrick Sizun for helping me with several technical aspects of my thesis and patiently answering all my questions. I am also grateful for the constant discussions with the NectarCAM Working Group, which provided me with the necessary feedback to perform better.

For the study on PeVatrons, I want to thank the Galactic Working Group of CTA, which provided me with constant feedback. For CTA simulations, I used Gammapy and am indebted to the support provided to me to learn the basics of Gammapy. I would especially like to mention Fabio Acero, Atreyee Sinha, and Luca Giunti for answering all my questions kindly and quickly.

I am indebted to PHENIICS Doctoral School for providing me with the necessary funds to pursue my degree. I am thankful to all the staff at my lab who made my stay at IJCLab comfortable, Laure-Amelie Couturie, David Verney, and Luc Perrot, to name a few.

During my years at IJCLab, I made many friends who played an important role in helping me cross various hurdles, provided me with emotional support by listening to all my rants, and ensured that I had a home away from home. I would have liked to name and thank each of you individually, but the list would be long.

List of Figures

2. [START_REF] Workman | Review of Particle Physics[END_REF] The energy (energy-per-nucleus) spectrum of all particles from various air shower instruments. Credit Particle Data Group [START_REF] Workman | Review of Particle Physics[END_REF] . . . .

Hillas plot

showing the size and magnetic field strength of various astrophysical sources which could be potential accelerators [START_REF] Anthony | The origin of ultra-high-energy cosmic rays[END_REF]. . . .

2.3

TeV Galactic gamma-ray sources with PWN/TeV Halo shown by green dots, starburst shown in dark blue, GRBs AGNs and Blazar shown in light blue, SNRs shown in pink dots, DARK and unid objects represented by black dots and finally, binaries, XRB and Nova given by purple dots. Credit: TeVCat online source catalogue 2. [START_REF] Matthews | A Heitler model of extensive air showers[END_REF] The graph shows the pair production mean free path of VHE γ photons propagating through soft photon background as a function of energy corresponding to different background models. The solid black line represents the contribution from cosmic microwave background radiation. Different EBL models have been represented by dashed and dotted lines. Credits: Tonia M. Venters [START_REF] Venters | Contribution to the extragalactic gamma-ray background from the cascades of very high energy gamma rays from Blazars[END_REF] . . . . . . .

2.5

Illustration of a supernova remnant producing relativistic protons which interact with surrounding molecular clouds to produce gamma rays. Unlike charged protons, gamma rays travel in a straight trajectory toward the Earth. The colourful blob on the top left represents a supernova remnant. The yellow cloud lying between the SNR and the Earth represents a molecular cloud. The orange curved path indicates the path of the charged proton, gamma rays are represented by the blue straight lines. Direct detection of gamma rays is done using the satellite shown in grey and finally, the interaction of protons and gamma rays is indicated by the shower in orange and blue, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . [START_REF] Matthews | A Heitler model of extensive air showers[END_REF]. The squiggly lines represent photons, and solid lines represent electrons/positrons. SNR HAWC J2227+610 modelled using the lepto-hadronic scenario. 104 6.3 Naima MCMC output of a corner plot for the SNR RX J1713.7-3946 modeled using the hadronic scenario. . . . . . . . . . . . . . . . . . 105 6.4 MWL SED of the SNR RX J0852.0-4622 modeled by using the hadronic scenario (left) and the leptonic scenario (right). . . . . . . 107 6.5 MWL SED of the SNR RX J1713.7-3946 modeled by using the hadronic scenario (left) and the leptonic scenario (right). . . . . . . 108

Simplified diagram of an electromagnetic cascade

LIST OF FIGURES 6.6 MWL SED of the SNR Cassiopeia A modeled by using the hadronic scenario (left) and the leptonic scenario (right). . . . . . . . . . . . 6.7 MWL SED of the SNR CTB 37A modeled by using the hadronic scenario (left) and the leptonic scenario (right). . . . . . . . . . . . 6.8 MWL SED of the SNR HAWC J2227+610 modeled by using the hadronic scenario (left) and the leptonic scenario (right). . . . . . . 6.9 MWL SED of the SNR HESS J1731-347 modeled by using the hadronic scenario (left) and the leptonic scenario (right). . . . . . . 6.10 MWL SED of the SNR IC 443 modeled by using the hadronic scenario (left) and the leptonic scenario (right). . . . . . . . . . . . . . [START_REF] Fernandez | Gamma-Ray Telescopes[END_REF].11 MWL SED of the SNR W28 modeled by using the hadronic scenario (left) and the leptonic scenario (right). . . . . . . . . . . . . . . . . 6.12 MWL SED of the SNR W 49B modeled by using the hadronic scenario (left) and the leptonic scenario (right). . . . . . . . . . . . . .

6.13

The value of the magnetic field obtained from the fit as a function of the reference magnetic field. The age and the magnetic field of the SNRs have been taken from Table 6.3, and the references therein. The old SNRs are indicated by blue circles, while the young SNRs are represented by orange circles. . . . . . . . . . . . . . . . . . . .

6.14

The magnetic field as a function of the electron energy cut-off value obtained from the fit. The age and the magnetic field of the SNRs have been taken from Table 6.3, and the references therein. The old SNRs are indicated by blue circles, while the young SNRs are represented by orange circles. . . . . . . . . . . . . . . . . . . . . .

6.15

The magnetic field as a function of the cut-off energy of protons obtained from the fit. The age of the SNRs has been taken from Table 1, and references therein. The old SNRs are indicated by blue circles, while the young SNRs are represented by orange circles. . .

6.16

The magnetic field as a function of the cut-off energy of protons obtained from the fit. The interacting SNRs are indicated by blue circles, while the shell-type SNRs are represented by orange circles.

6.17 The magnetic field as a function of the cut-off energy of protons obtained from the fit. The age of the SNRs has been taken from

Chapter 1 Introduction

Surpassing man-made accelerators by several magnitudes, nature has managed to accelerate particles up to 10 20 eV, making astrophysical particle accelerators a subject of fascination for researchers. In 1912 Victor Hess provided evidence for high-energy radiation entering the Earth from outer space. Identified as Cosmic-Rays (CRs), these are charged particles that indicate the presence of non-thermal high-energy processes. CRs, continuously bombarding the Earth, have been observed by various instruments [START_REF] Workman | Review of Particle Physics[END_REF]. As observed from Earth, the incoming CRs form a steep energy spectrum with a few interesting features out of which the knee, around 10 15 eV, is the focus of this study. Sources that can accelerate particles up to PeV energies are known as PeVatrons. Theory suggests that the spectrum up to the knee can be attributed to Galactic astrophysical sources such as supernova remnants (SNRs). Since CRs are charged particles, we cannot trace back the trajectories to the original astrophysical source due to the deflection by the galactic magnetic fields. However, these CRs while propagating, interact with their surroundings and produce gamma radiations which act as a messenger of the relativistic Universe.

In 1989, when the Whipple telescope detected the first TeV gamma rays from the Crab nebula, physicists found a new way to detect the CRs indirectly. Highenergy gamma rays encode essential physical information about the non-thermal Universe and studying these extreme conditions help understand the physics behind the acceleration of particles up to such high energies.

However, detecting these high-energy gamma rays comes with several challenges. The biggest is that despite the highly penetrative ability of gamma rays, our Earth's atmosphere is opaque to them. Searching for gamma rays amidst the ocean of CRs is like finding a needle in a haystack. Another challenge arises in the interpretation of the observed gamma rays. Two fundamentally distinct processes can produce gamma rays, namely leptonic or hadronic processes, depending on how the gamma rays were produced. Lastly, the gamma-ray flux from astrophys-CHAPTER 1. INTRODUCTION ical sources decreases as a power-law spectrum which implies that as we reach high energies, the flux significantly decreases. Hence to detect more gamma-ray photons per unit area and improve statistics, it's no longer enough to use small space-based detectors. Instead, a shift is required towards detectors with larger surface areas, longer exposure times, and a better understanding of atmospheric air showers and detector response.

After rigorous attempts, space-based instruments such as Fermi-LAT and groundbased Imaging Atmospheric Cherenkov Telescopes (IACTs) such as H.E.S.S., MAGIC, and VERITAS have led to exciting discoveries. Instruments such as HAWC and LHAASO have recently provided very interesting results in their search for PeVatron candidates. With further developments in ground-based high-energy detectors, futuristic instruments such as CTA promise to solve mysteries in the pertinent active branch of Very-High-Energy (VHE) gamma-ray astronomy, aiming to unravel the mysteries of the relativistic Universe. This thesis revolves around studying SNRs as potential PeVatron candidates with the purpose of understanding CTA's contribution in searching for PeVatron sources. Chapter 2 creates the base for the topics discussed in this thesis. It gives a general overview of high-energy particles and delves deeper into their propagation and radiation production. Chapter 3 describes the basics of gamma-ray astronomy and explores the design of Cherenkov telescopes. In this study, the main IACT under focus is CTA and a general overview of CTA with a focus on the Medium-Sized Telescopes (MSTs) of CTA has been provided in Chapter 4. One of the major challenges of IACTs is to minimize the systematic uncertainties to obtain the actual contribution of photons from an astrophysical source compared to the background noise. Chapter 5 focuses on the usage of the photo-multiplier tubes (PMTs) for detecting faint sources and how the NectarCAM camera is calibrated to achieve accurate observations. Weaving together the observations from different instruments allows us to learn a lot about the physical processes occurring inside and around the source. Multiwavelength analysis has been discussed in Chapter 6 in which, through qualitative and quantitative analysis, we try to deduce whether an SNR is capable of accelerating protons up to PeV energies. Despite multiwavelength studies, it is non-trivial to distinguish between the emission processes at the highest energies, mainly because the gamma-ray fluxes are very low in the VHE domain. However, with the increased sensitivity, wider energy range, and better resolution of CTA, abundant data is expected to be found in the TeV range to make the distinction easier. This brings us to chapter 7, which deals with the simulation of fluxes of SNRs to see what CTA will observe in the coming years and how can it help us get closer to answering the century-old questions in high-energy astrophysics. Finally, Chapter 8 summarizes all the main results found during the thesis. Part of the work done in this thesis has been presented at EAS and ICRC

Chapter 2

High-energy particles and radiations

Introduction

To understand information about the Universe, we rely on different high-energy particles such as CRs and neutrinos along with radiations such as photons and gravitational waves. We live in an exciting time where each distinct messenger can be detected through various types of instruments, each leading to phenomenal astronomical discoveries. Photons and CRs have an intricate relation at highenergy and can reveal interesting information about the high-energy processes occurring in the Universe. In the following chapter, we try to understand the spectrum of the CRs as observed on Earth, explore the potential Galactic CR accelerators, and finally, we discuss how the CRs interact to produce γ-rays.

Cosmic rays

Cosmic rays comprise relativistic particles, with the principal constituent being protons followed by smaller fractions of heavier nuclei and electrons that continuously bombard the Earth. Charged CRs get deflected by the galactic magnetic fields, making it impossible to point back to the sources accelerating the CRs [START_REF] Strong | Cosmic-Ray Propagation and Interactions in the Galaxy[END_REF]. The quest to find their origin has been ongoing since 1912. Hess observed that the further his balloon flight went away from the ground, the more ionizing radiation was being detected. This could certainly not be attributed to radioactivity in the ground, but to "penetrating radiation from outer space". The CR energy density measured at Earth is ∼ 1 eV/cm 3 . It is comparable to the energy density of the galactic magnetic field and the thermal gas. This equality cannot be a mere coincidence but implies an interplay between the Galaxy's thermal and non-thermal constituents. Hence, CRs play an essential role in maintaining the dynamical balance of the Galaxy as we see it today [START_REF] Parker | Galactic Effects of the Cosmic-Ray Gas[END_REF]. It is interesting to note CHAPTER 2. HIGH-ENERGY PARTICLES AND RADIATIONS that all the bright stars we see today owe their birth partially to CRs since they majorly contribute to ionizing and heating the dense proto-stellar regions, which cannot be penetrated by ionizing radiation. [START_REF] Hummel | The first stars: formation under cosmic ray feedback[END_REF].

The energy spectrum of CRs reaching the ground has been measured by many instruments and is shown in Figure 2.1. It shows a steeply declining, power-law spectrum (dN/dE ∝ E -α ) covering more than 12 orders of magnitude in energy. The change in the shape of the spectrum reflects in the change of the power-law index with the main spectral features being:

• Knee: Seen as a break around 10 15 eV, it results in the steepening of the spectrum index from ∼ 2.7 to ∼ 3.1. Studies suggest it corresponds to the maximum energy of the protons accelerated by the sources inside the galaxy or to the escape of the CRs from our Galaxy [START_REF] Ormes | On the propagation of cosmic rays in the Galaxy[END_REF].

• Second-Knee: Predominant around ∼ 10 17 eV, the feature leads to a slight steepening of the index. The reason giving rise to this feature is still under discussion and is said to arise due to the presence of heavier elements.

• Ankle: Found around 6 x 10 18 eV, this feature marks the energy where the spectrum gets harder. It signifies the region beyond which the origin of particles is said to be extragalactic. This was confirmed by the Pierre Auger collaboration [START_REF] Auger | Observation of a large-scale anisotropy in the arrival directions of cosmic rays above 8 × 10 18 eV[END_REF].

Below 1 GeV, the spectrum does not follow a power-law since the CRs comprising of charged particles are pushed away by the Solar wind. This suppression depends on the solar cycle, which lasts 11 years. Similarly, at the high-energy end of the spectrum, there is a flux suppression around ∼ 5 x 10 19 eV [START_REF] Kampert | Cosmic rays from the ankle to the cutoff[END_REF]. The origin of this suppression is still unknown and is debated to be due to the GZK effect 1 or exhaustion of acceleration processes in extragalactic sources. This is one of the science questions studied by the Pierre Auger Observatory 2 and Telescope Array [START_REF] Kawai | Telescope Array Experiment[END_REF] measuring CRs at the extreme energies. 1 The Greisen-Zatsepin-Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic ray protons traveling from other galaxies through the intergalactic medium to our galaxy. It occurs due to the interaction of the protons with the microwave background radiation over a long distance 2 https://www.auger.org/news/scientific-highlights/261-most-precise-measurement-of-thecosmic-ray-energy-spectrum-at-ultra-high-energies

Cosmic ray acceleration

A theory that tends to explain the power-law shape of the CR spectrum is given by a shock acceleration mechanism called the Diffusive Shock Acceleration (DSA) or the first order Fermi acceleration [START_REF] Schure | Diffusive Shock Acceleration and Magnetic Field Amplification[END_REF], [START_REF] Hillas | TOPICAL REVIEW: Can diffusive shock acceleration in supernova remnants account for high-energy galactic cosmic rays[END_REF]. DSA postulates that a turbulent magnetic field, moving at a non-relativistic speed is required to accelerate a particle efficiently. The particles are scattered several times by the magnetic field and in this process gain energy. After several cycles, the particle gains enough energy to escape the diffusive process and be accelerated up to the ultra-relativistic energies seen in the CR spectrum. If the particles are injected continuously into the acceleration process, they are expected to undergo diffusion until the particle's Larmor radius 3 becomes larger than the size of the system in which the particle is confined. In the following, we present a simplified picture of CR acceleration that allows explaining the power-law shape of the non-thermal particle spectrum. Shocks represent discontinuities in the physical quantities of the flow such as ve-CHAPTER 2. HIGH-ENERGY PARTICLES AND RADIATIONS locity, pressure, density, and more. Accelerated particles are non-thermal particles i.e., they do not follow a Maxwellian distribution. If a particle encounters a discontinuity, it is forced to change its direction. This event is called a scattering event. Particles gain energy every time a collision occurs at the scattering center. After each collision, the energy of the particle is,

E = βE 0 , (2.1)
where β is the gain and E 0 is the energy before collision. We assume that the particle is moving in a certain volume with a lot of scattering centers. There is always a probability that the particle will escape the acceleration region and hence the particle cannot gain energy infinitely. The number of particles remaining within the accelerating region is given by,

N = N 0 P, (2.2)
where N 0 is the original number of particles, and P is the probability P (< 1) of the particle remaining in the acceleration region.

After k collisions the energy becomes,

E = β k E 0 , (2.3)
and the number of particles leaving the acceleration regions becomes,

N = N 0 P k , (2.4)
with p < 1.

Using logarithm we can eliminate the k in 2.3 and 2.4 and we get,

N N 0 = E E 0 -α , (2.5)
where,

α = lnβ lnP , (2.6)
Eliminating k gives us the form of a power-law distribution of accelerated particles due to collisions with some scattering centers. From this formulation, we can see that the energy of the particle increases with every collision (β > 1). At the same time, the number of particles remaining inside the acceleration region becomes lesser (P < 1) therefore, the higher the energy, the lower the number of particles. This derivation helps to explain, theoretically, the origin of the powerlaw spectrum clearly.

COSMIC RAYS

29

If the shock propagates through a uniform magnetic field, it becomes difficult to achieve acceleration of CRs to PeV energies because charged particles can easily escape the shock region and thus gain less energy. Hence large turbulent magnetic fields are required to trap the particles inside the shock region to force them to scatter multiple times in order to gain more energy before they finally escape. DSA is a simple, robust process that predicts a universal spectrum. Despite all these factors, researchers still search for irrefutable proof of accelerators that can accelerate particles up to PeV energies, only to be confirmed by observations.

The maximum energy of accelerated particles decides the shape of the powerlaw spectrum shown above and depends on a source's ability to confine the particle long enough for acceleration. The particles in the source are expected to have a gyro radius smaller than the size of the source. After several estimations, a relation can be found which gives the limit on the maximum energy of the particle accelerated [START_REF] Anthony | The origin of ultra-high-energy cosmic rays[END_REF]:

E max ∝ ZBR, (2.7)
where Z is the atomic charge of the particle, B is the magnetic field strength (µG) of the accelerating source, and R is the radius (pc) of the accelerating source. Using this limit, Hillas could classify astrophysical objects that could be responsible for accelerating CRs, and the resulting plot is given in Figure 2.2. The plot uses different objects' sizes and magnetic fields to classify them as CR accelerators. The diagonal line in the plot represents a constant E max , and all the objects lying above the line can accelerate particles up to that energy. The line shown in the plot corresponds to an E max of 10 20 eV. The solid and the dashed line represent protons and iron particles, respectively.

For the case of SNRs, if we assume B ∼ 3 µG and R ∼ 1 pc, then E max comes out to be ∼ 3 PeV. The Hillas condition is necessary however, not enough to prove efficient acceleration. The acceleration process needs to be studied in great detail as it involves a careful interplay between the acceleration time and the smallest of the three possible time scales; 1) the age of the accelerator, 2) the time taken for the particle to escape the accelerator and the time taken for the particle to lose energy.

CHAPTER 2. HIGH-ENERGY PARTICLES AND RADIATIONS

Galactic CR accelerators

Our Galaxy is host to various astrophysical sources which emit in the VHE ( up to hundreds of TeV) domain. Until now, over two hundred VHE γ-ray sources, both galactic and extra-galactic, have been detected4 . Figure 2.3 shows the galactic γ-ray sources discovered by current instruments.

Supernova remnants

A Supernova is a cataclysmic explosion of a massive star (M ⋆ > 8M ⊙ ), marking the end of the stellar evolution. What's left behind after the explosion is known as the Supernova Remnant. These rare events caught the attention of humankind even before telescopes were invented. An SNR releases 10% of its rest mass and the remaining part is transferred to the ejected matter expanding into the surrounding ISM [START_REF] Tsirou | Study of Pulsar Wind Nebulae in Very-High-Energy gammarays with[END_REF].

This work focuses on two different types of SNRs: shell-type and interacting SNRs. Shock waves generated by the supernova explosion cause the surrounding ISM to heat up, creating a shell-like structure of hot material in space. The shell-type SNRs are often seen as bright rings since more heated gas exists in our CHAPTER 2. HIGH-ENERGY PARTICLES AND RADIATIONS line of sight at the edges than at the middle. This phenomenon is referred to as limb brightening. The interacting SNRs are the remnants of massive stars which explode and interact with the molecular clouds in which they were born [START_REF] Slane | Supernova Remnants Interacting with Molecular Clouds: X-Ray and Gamma-Ray Signatures[END_REF].

A Typical SNR undergoes various stages of evolution as it expands:

• The first stage is known as the free expansion stage. After the explosion, the ejected material from the dead star sweeps up its weight in the ISM. When the stellar material interacts with the ISM, a forward-directed shock wave is generated in the interstellar gas. A shock in the reverse direction is also produced back into the supernova ejecta. The shocked material can reach a temperature up to millions of degrees Kelvin resulting in the emission of thermal X-rays. Depending on the dense surrounding gas, this expansion can range from a few tens to a few hundred years.

• Once the mass of the stellar ejecta is balanced by the mass of the swept-up interstellar gas, the shock waves begin to slow, and the Sedov-Taylor phase begins. In this phase, the shock's internal energy remains large compared to the loss due to thermal and synchrotron radiation. Therefore, the total energy remains constant. At this stage, the Rayleigh-Taylor instabilities5 arise, which then mix the shocked ISM with the supernova ejecta and leads to enhancement of the magnetic field inside the SNR shell. This phase lasts between 10,000 and 20,000 years.

• Finally, after 30,000 years, we have the radiative phase. When the temperature falls below 20,000 Kelvin, the recombination process is favored, and electrons recombine to form heavier elements. Radiation from this recombination process is more efficient than X-ray and synchrotron emission, which leads to the cooling of the wave and eventual dispersion into the surrounding ISM.

For almost a century, SNRs have been considered the predominant source of CRs. Supporting the SNR paradigm is the fact that only ∼ 10-20 % of the kinetic energy of SN explosion is sufficient to produce the observed CR spectrum up to PeV energies [START_REF] Baade | Cosmic Rays from Super-novae[END_REF].

What makes the detection of PeV CRs so tricky is the fact that SNRs are active PeV CRs emitters only for a few years [START_REF] Cardillo | On the cosmic ray spectrum from type ii supernovae expanding in their red giant presupernova wind[END_REF] after the explosion when they are evolving from the free expansion phase to the Sedov phase. The shock velocity decreases upon entering the Sedov phase and PeV CRs cannot be confined and escape in the ISM [START_REF] Ptuskin | On the spectrum of high-energy cosmic rays produced by supernova remnants in the presence of strong cosmic-ray streaming instability and wave dissipation[END_REF]. The possibility of detecting an SNR in the PeV phase is low; however, even one detection is sufficient to prove SNR as a PeVatron source.

Pulsars and pulsar wind nebulae

At times, what remains at the core of a collapsed Supernova is a rapidly spinning, highly magnetised neutron star, also called a Pulsar. Pulsars are one of the dominant γ-ray sources discovered by the Fermi telescope [START_REF]Fermi Large Area Telescope Third Source Catalog[END_REF]. Powered by the rotational energy of the fast-rotating pulsar, the strong ultra-relativistic wind of particles emitted from the young pulsar forms a synchrotron nebula when the particles interact with the surrounding medium. This forms what we call a Pulsar Wind Nebula (PWNe) [START_REF] Slane | Pulsar Wind Nebulae. Handbook of Supernovae[END_REF]. At the point of interaction, strong shocks form, which results in the acceleration of particles up to a few hundred of TeV due to inverse Compton scattering of 1-100 TeV electrons. Inverse Compton scattering dominates the GeV and TeV γ-ray energies. In its last stages, the pulsar escapes its parent SNR and dims in the lower energy band, leaving behind the TeV halo. PWNes are important candidates for the galactic CR source based on Hillas's criteria [START_REF] Anthony | The origin of ultra-high-energy cosmic rays[END_REF].

X-ray binaries

X-ray binaries derive their power from the accretion of stellar matter onto a black hole or a neutron star. The binaries that can be detected in the γ-ray domain can largely be divided into four classes: γ-ray binaries (power is generated using pulsar rotation), microquasars (power is generated by the accretion onto a black hole or a neutron star), novae ( power is generated by thermonuclear runaway of a white dwarf) and, colliding wind binaries (power is generated by stellar winds of massive stars) [START_REF] Dubus | Gamma-ray emission from binaries in context[END_REF]. Maximum γ-rays can be observed when the object is close to our line of sight. Due to the uncertainty in the position provided by γ-ray telescopes and the complexity of the regions in which they are found, correlating these high-energy sources with objects found in other bands is often tricky. The confusion due to nearby objects can be resolved with the upcoming ground-based instruments such as CTA up to a greater extent due to higher angular resolution and larger collecting area compared to present IACTs.

Giant molecular clouds

Certain middle-aged SNRs are surrounded by dense molecular clouds (MCs). These clouds act as dense targets for CR hadronic interactions, thereby producing γ-rays by the decay of neutral pions. The dense clouds can become highly magnetized and emit non-thermal radiations when CRs from the nearby accelerator interact with them. We expect a correlation between MCs and SNRs in star-forming regions of the galaxy. However, finding an association between the SNR and MC is sometimes difficult as the angular distance between the two can be greater than the field of view of the detector. Studies have shown an enhancement in the emission of γ-rays CHAPTER 2. HIGH-ENERGY PARTICLES AND RADIATIONS in proportion to the mass of the MC, which is not the case for inverse Compton radiation due to accelerated electrons. In addition, the γ-ray emission is seen to depend on the propagation time. Hence, MCs can be visible much longer than in emissions from SNRs, making MCs more easily detectable than SNRs. [START_REF] Gabici | Broad-band non-thermal emission from molecular clouds illuminated by cosmic rays from nearby supernova remnants[END_REF] [START_REF] Gabici | Broad-band non-thermal emission from molecular clouds illuminated by cosmic rays from nearby supernova remnants[END_REF] predict a distinct spectral signature in the form of a concave energy spectrum, and with the aid of joint Fermi and ground-based IACTs, we should be able to observe them.

Galactic center

It is well known that a supermassive black hole resides in the center of our Galaxy. Although only weak X-ray activities have been observed from the galactic center (GC) along with transient events in the MeV/GeV domain, enough evidence can be found which provides proof of the violent history of the GC. In order to accelerate protons up to a few PeV, tens of Gauss of magnetic field is required which can be reached in the GC. Hence, the accretion of stars and gas around the supermassive black hole could have been highly effective in accelerating particles. Accelerated CRs diffusing out of the GC, undergo hadronic interaction with the surrounding ISM to produce γ-rays. VHE γ-rays have already been detected by IACTs in the multi-TeV range e.g., [START_REF] Adams | VERITAS observations of the galactic center region at multi-TeV gamma-ray energies[END_REF]. The Galactic center is the object of observation by all major IACTs, including MAGIC and H.E.S.S. The latter has even helped hint at a possible PeVatron in the vicinity of the Galactic center [START_REF]Acceleration of petaelectronvolt protons in the Galactic Centre[END_REF].

Propagation of radiation and particles

The DSA predicts an α of ∼ 2 for the differential flux of accelerated particles. However, on Earth, we observe a spectrum of slightly higher index α ∼ 2.7. The difference arises from the effects of CR propagation in the Galaxy, such as spallation, energy losses, and escape of particles from the Galaxy. Thus, the source of CRs must be studied through neutrally charged messengers such as γ-rays and neutrinos, which can reach the Earth without several propagation effects described above. This thesis examines further how γ-rays can reveal important information about the CRs produced at the acceleration sites.

CRs undergo several interactions during its propagation to produce γ-rays such as; CRs can produce γ-rays through proton-proton interactions: p CR + p ISM → p + p + π 0 , which decays quickly into γ-rays: π 0 → γ + γ. In addition to this, when relativistic electrons collide with low-energy photon fields, the electrons impart some of their energy onto the photons, exciting them to emit at the γ-ray energy. These processes have been elaborated further in Chapter 6. Primarily, Galactic CR sources have been considered as γ-rays suffer from propagation effects. There is a limit on the observable γ-ray horizon. The cosmic γ-ray horizon is set by the interaction of γ-rays with the Extragalactic Background Light (EBL). EBL encapsulates the energy released by all the stellar objects and galaxies at different redshifts throughout cosmic history. The most important contribution of background radiation comes from the CMB, the optical and the infrared part of the EBL spectrum. The high-energy γ-photon interacts with photons from the ambient EBL to produce electron and positron pair. This process is known as pair production and is responsible for suppressing the extra-galactic γ-rays. Figure 2.4 shows the mean free path (λ) of VHE photons due to pairproduction at different energies [START_REF] Venters | Contribution to the extragalactic gamma-ray background from the cascades of very high energy gamma rays from Blazars[END_REF]. As can be seen, there is a steep decrease in the mean free path down to 10 -2 Mpc as we try to go beyond the energy of 100 TeV. With the galactic radius being ∼ 15 kpcs, it is clear that observing γ-rays above 10 14 eV would be quite challenging.

PROPAGATION OF RADIATION AND PARTICLES

The propagation of charged particles is affected by magnetic fields and there-CHAPTER 2. HIGH-ENERGY PARTICLES AND RADIATIONS fore, cannot point back to their sources unless they are at extreme energies (> 10 19 ) eV. Figure 2.5 shows a pictorial representation of the path of charged particles emitted by an astrophysical source. An SNR emits charged particles like protons which either gyrate along the magnetic field and eventually reach the Earth to produce hadronic showers or interact with nearby molecular clouds to produce γ-rays as secondary particles. These γ-rays can either be directly detected by satellites orbiting around the Earth or indirectly by capturing the Cherenkov radiation emitted from the electromagnetic shower induced by γ-rays interacting with the Earth's atmosphere (More information in Chapter 3). Chapter 3

VHE Gamma-ray observations

Introduction

Gamma rays have been observed over a wide energy range, starting from a few MeVs to a few hundreds of TeVs. Different techniques are required to maximize the detection of γ-rays, which depend on the properties of gamma radiation, such as its differential spectrum, and the background, such as the amount of CR flux. Two main types of instruments which allow us to observe the γ-rays are:

• Space-based detectors -Satellites mainly work on the principle of high-energy γ photons producing e -e + pair inside the detector. Following the path of the pairs inside each detector layer allows for the determination of arrival direction. A calorimeter is used to measure the energy of the incoming photon. Since they are spaceborne, they escape the problem of the atmosphere. However, there is a limitation on the size of the onboard detectors; hence, their collection area is small and, therefore, can detect only a limited flux of γ-rays (tens of GeVs). Fermi1 is an example. Another technique used for gamma-ray detection is the Compton-scattering process (more detail in Chapter 5). Here the incident photon is usually Compton-scattered from one detector into another to register a valid event, e.g., COMPTEL onboard CGRO2 .

• Ground-based detectors -The detection principle behind the IACTs is to use the Earth's atmosphere as a detector to detect high-energy γ-rays. Additionally, large detector arrays sampling the particles reaching the ground also exist. For example, HAWC6 (High-Altitude Water Cherenkov Observatory) uses the water Cherenkov method where the particles created in the atmospheric showers are detected by recording the Cherenkov light produced when the particles enter the tank filled with purified water.

Another instrument worth mentioning in this category is LHAASO7 (Large High Altitude Air Shower Observatory). It consists of an array of electromagnetic particle detectors, muon detectors, water Cherenkov detectors, and electron-neutron detectors, along with air Cherenkov telescopes. These are designed to optimally detect the air showers triggered by γ and cosmic rays.

For more information, refer to LHAASO science book [START_REF]The Large High Altitude Air Shower Observatory (LHAASO) Science Book[END_REF].

In the following chapter, the basics of showers and shower detection are provided with a focus on how IACTs detect the γ-rays. In the end, major IACTS have been mentioned that are pivotal to the growth of γ-ray astronomy.

Extended Air Showers (EAS)

Photon induced showers

High-energy incoming γ-rays from sources interact with the Earth's atmosphere and produce an electromagnetic (EM) shower. First, high-energy γ-rays produce an electron-positron pair. This pair then emits γ-rays in the form of bremsstrahlung radiation. These two processes of successive pair-production and bremsstrahlung lead to a cascade where the energy of the primary γ-ray gets distributed equally amongst the secondary particles produced next. This continues until there is insufficient energy for pair production to occur.

The energy at which the cascade stops generating new particles is called the critical energy E c . The maximum number of particles can then be given by N max = E 0 Ec . The depth of the maximum of the air shower is proportional to the logarithm of the ratio of the energy of the primary photon to the critical energy. X max = λlog 2 (E 0 /E c ), where λ is the interaction length. After E c has been reached, the energy is dissipated by ionization processes, and hence energy loss is more rapid after the critical energy has been reached. The complete description of shower generation has been given by the Heitler model [START_REF] Heitler | The quantum theory of radiation[END_REF].

Shown in Figure 3.1 is a simplistic representation of a photon-induced shower. A photon, drawn by squiggly lines, interacts with the atmosphere. After each interaction length, shown by dotted lines, new e -e + pairs are produced. These pairs then further generate bremsstrahlung radiation, shown with squiggly lines as the shower depth increases.

Hadron induced showers

When charged particles (hadrons) penetrate the atmosphere, they produce hadronic showers. Here the primary hadron decays into neutral and charged pions. Neutral pions quickly decay into γ-ray photons, which in turn create e -e + pairs, thus leading to the generation of EM sub-showers. On the other hand, the charged pions traverse a certain distance until they decay into a muon and a neutrino. This shower development continues again until it reaches a critical point, and in the end, an air shower that has both a hadronic and an electromagnetic nature is generated. Figure 3.2 outlines the basic mechanism. A nucleus, shown by the thin solid line, interacts with the atmosphere. After each interaction length, shown by dotted lines, new particles, mostly pi-mesons, are produced. The pions can be either neutral pions (decays immediately into two γ photons) represented by dashed lines or charged pions (decay after a longer time, thus colliding with other nuclei before decaying) represented by thick solid lines. The number of particles increases until the shower maximum is reached.

The CR particles entering the atmosphere are present in abundance compared to the incoming γ-ray photons. Therefore, the flux of CRs is much larger (factor of 1000) than that of γ-rays. We need to be able to differentiate between the showers from two different primaries in order to truly understand the signal from the source.

Cherenkov radiation

When the secondary particles produced in the shower travel at a speed faster than the speed of light in the dielectric medium, bluish Cherenkov radiation is produced. The ensemble of radiation emitted by each charged particle takes the form of a uniform circular light pool centered on the shower core. Huygens's principle states that waves are emitted spherically at a velocity equal to the phase velocity of the medium. If the particle velocity is lower than the speed of light in the medium, the radiated waves interfere destructively in the direction of the motion, and no radiation is visible. However, if the speed of the particle exceeds the speed of light in that medium, the emitted waves superimpose constructively to emit Cherenkov radiation. It is emitted at an angle θ c with respect to the direction of the particle motion.

Emitted radiation takes the shape of a cone, as shown in Figure 3.3, with its axis being the path of the particle. The angle θ c is dependent on the velocity (v) of the particle and the refractive index (n) of the medium. Mathematically it can be represented as:

cos(θ c ) = c vn = 1 βn , (3.1)
where

β = v/c
Since cosθ < 1, the necessary condition to be satisfied for the emission of Cherenkov radiation is:

β > 1 n , (3.2)
Using the equations above, we can obtain the threshold velocity of the particle to produce Cherenkov light:

v th = c n , (3.3)
The energy of the particle producing the radiation is proportional to the angle θ c . The blue optical light produced by air showers, apart from Cherenkov radiation, may also be due to fluorescence emission. It occurs when the air-molecules deexcite after being excited by the charged particles of the shower. The photons due to fluorescence and Cherenkov radiation arrive simultaneously and hence are indistinguishable from the ground. However, there are some important differences that we can exploit to differentiate between the two radiations. Fluorescence is less efficient than Cherenkov production and is emitted isotropically. Therefore, if the telescope performs an on-axis observation, then the signal is denominated by Cherenkov radiation as long as the telescope points within the Cherenkov light pool [START_REF] Morcuende | Relevance of the fluorescence radiation in VHE gamma-ray observations with the Cherenkov technique[END_REF].

Shower reconstruction by IACTs

The Cherenkov light is reflected using large mirrors towards a camera, where it is captured by an array of photodetectors. Photodetectors increase the intensity and convert the light into electrical signals, which are then amplified, digitized, and transmitted for further analysis. Owing to the thin and short flashes of Cherenkov radiation, cameras are designed to use a few nanosecond exposure times and ultrasensitive photon detectors, which are optimised to capture the faint signal, as shown in Figure 3.4.

The showers initiated by γ-rays often appear as an ellipse on the camera plane. This image can be analysed to extract interesting physical parameters such as the type of the primary, the particle's energy, and direction. Cherenkov imaging approach can help us to discern the excess events from a source with respect to the overwhelming CR background. Turver and Weekes [START_REF] Weekes | Gamma-Ray Astronomy from 10-100 GeV: a New Approach[END_REF] observed using various Monte Carlo calculations of air shower developments that the lateral distribution of gamma or hadron-induced showers appeared to be significantly different. The γ-ray shower occurs in the form of a compact pool resulting in an elliptical shower image. The major axis of the ellipse represents the shower axis projected onto the image plane. As opposed to this, the image of the proton shower is more scattered and shows a lot of variations due to the hadronic interactions of neutral and charged pions. In 1985, Hillas proved the possibility of distinguishing between background hadronic and γ-ray showers using the width, length, and orientation of the Cherenkov light images of the showers [START_REF] Hillas | Cerenkov Light Images of EAS Produced by Primary Gamma Rays and by Nuclei[END_REF]. These image parameters could be quantified and showed that images of the gamma showers are thinner, more focused, and oriented towards the source. γ-rays are selected depending on the cuts on these parameters. The most important image parameters are:

• Width: It is the root mean square (RMS) spread of the Cherenkov radiation perpendicular to the major axis of the ellipse.

• Length: It is the RMS spread of the Cherenkov radiation parallel to the major axis of the ellipse.

CHAPTER 3. VHE GAMMA-RAY OBSERVATIONS

• Distance: It is the angular displacement of the centroid of the image formed on the plane of the camera from the centre of the FoV.

• Alpha: It is the angle made at the intersection of the major axis and the distance axis.

Shown in Figure 3.5 is the pictorial representation of the important Hillas' parameters, which help determine essential physical information about the incident shower. Additionally, the more energetic the primary γ-ray is, the more particles are produced in the shower, thereby leading to a brighter image. Therefore, it is possible to reconstruct the energy of the incoming γ-rays using the brightness of the image. Hillas' theory for shower reconstruction summarised above can define the energy and the direction of the incoming γ-rays.

Mirrors produce a direct representation of the shower in the form of an image on the camera. If just one telescope is used, only a projection of the Cherenkov shower can be obtained. Stereoscopy is a method of observing the same source using several telescopes. This uniquely allows us to pinpoint the source of the shower by projecting the images from triggered telescopes into one plane. The point of intersection of the major axes of the image gives the shower direction as shown in Fig 3 .7. The use of multiple telescopes gives a better angular resolution, energy resolution, background rejection, and higher sensitivity. Effective tools such as Monte Carlo simulations are required to eliminate the background events from the acquired data. Rejection is done on the grounds of directional information, the geometry of the shower, and the shape of the images.

The complexity of the EAS (electromagnetic and hadronic) makes it hard to infer the properties of the particles which initiated them. Detailed numerical simulations of showers are needed to understand their properties. However, due to the l arge number of particles in a high-energy shower, the lack of complete understanding of interaction cross-sections, and particle production at high energies, this remains a challenge.

CHAPTER 3. VHE GAMMA-RAY OBSERVATIONS

Current IACTs and Science

This thesis would be incomplete without commemorating the present instruments, which increased our knowledge in the domain of γ-ray astrophysics and paved the path for the improved γ-ray instruments. At present, three major IACT systems are in operation, namely:

• The High Energy Stereoscopic System (H.E.S.S.) Observatory: Located in Namibia, currently, it is the only IACT in the Southern hemisphere and thus the only eye pointing towards the inner Galaxy. Phase 1 consisted of an array of 4 telescopes placed in a square layout with a spacing of 120 m between each length, which is a compromise between a good stereoscopic viewing and triggering at least two or more telescopes for shower detection.

Each telescope has a mirror area of 107 m 2 . 960 photomultipliers in the camera make up the FoV of ∼ 5 • . In Phase 2, a huge dish with a mirror area of 614 m 2 , with a camera consisting of 2048 photodetectors, was installed in the middle of the array. This aided in increasing the instrument's overall energy coverage, sensitivity, and angular resolution [START_REF] Becherini | The phase II of H.E.S.S[END_REF]. The camera is 1.5 m in diameter, with the inner hexagonal area consisting of 397 photomultipliers of diameter 1 " and the surrounding area consisting of 180 photodetectors of diameter 1.5 " , making the resultant FoV of 4 • . Its light structure allows for a fast slewing rate, crucial for transient events [START_REF] Baixeras | Commissioning and first tests of the MAGIC telescope[END_REF]. The latest GPS confirmed the detection of 16 new sources emitting VHE γ-rays. This was made possible after a decade of observations amounting up to ∼ 3000 hrs, covering a stretch of the Galactic plane from l = 250 • to 65 • and |b| ≤ 3 • with the energy ranging from 0.2 to 100 TeV. Using the HGPS data, a catalogue of VHE γray sources was created, which boasted 78 VHE sources, out of which 31 have been firmly associated with known SNRs, PWNe, and γ-ray binaries. Furthermore, 36 sources are found to have at least one possible counterpart. However, they have not been clearly identified. The remaining 11 sources are yet to be associated

CURRENT IACTS AND SCIENCE

Chapter 4

Gamma ray observation by CTA

Introduction

CTA 1 is the next-generation ground-based instrument for γ-ray astronomy. Thousands of researchers, technicians, engineers, and program managers are involved worldwide in building CTA and exploring its key science projects. CTA will be the first open observatory in the field of γ-ray astronomy. CTA observatory is spread across the Northern and the Southern hemispheres (Paranal in Chile and La Palma in Spain) and will allow full-sky coverage. The combination of three different sizes of telescopes creates the possibility of covering a wide energy range of 20 GeV to 300 TeV. A wider field of view coupled with improved sensitivity will enable a quick survey compared to its predecessors. Lastly, CTA will provide an unprecedented angular and energy resolution that guarantees detailed imaging of many γ-ray sources. For these reasons, CTA promises to give a view of the highenergy skies never like before and will help bring forth momentous discoveries in astroparticle physics and other related domains.

The Cherenkov Telescope Array

Each type of telescope of CTA is optimized to cover a specific energy range:

Large-Sized Telescope (LST): The flux of γ-rays decreases with increasing energy. LSTs are designed to capture the faint but abundant shower of low-energy γ-rays with the aid of a large mirror with a diameter of 400 m 2 . Its design allows for achieving a high sensitivity at the lowest energies, which provides access to the diffuse Universe. All these telescopes are arranged in a specific array such that there is maximum coverage of showers being detected. The wide energy range, due to LSTs, MSTs and SSTs, is necessary to increase the chances of discovering new sources with unknown spectral characteristics. It is also vital for discriminating between different emission scenarios and identification of new features which may challenge

THE CHERENKOV TELESCOPE ARRAY

53

the conventional power-law forms as it is already very well known for some sources, such as crab nebula, that a power-law spectral shape is too simplistic.

CTA compensates for the rarity of the electromagnetic cascades (one γ-ray photon per m 2 per year from a bright source or one per m 2 per century from a faint source) by employing more than 100 telescopes. Figure 4.2 captures the potential layout of the telescopes. The Northern array will have a limited size, consisting only of LSTs and MSTs, focusing on the low to mid-energy sources in the extragalactic region. The Southern array pointing towards the Galactic center will be equipped with all three types of telescopes to increase the possibility of detecting HE γ-rays.

Currently, in its first construction phase, CTA will consist of a limited number of telescopes based on the results of detailed Monte Carlo simulations organised in the "Alpha" configuration. The Alpha array consists of:

• CTAO Northern Array: 4 LSTs and 9 MSTs covering an area of ∼ 0.25 km 2 .

• CTAO Southern Array: 14 MSTs and 37 SSTs covering an area of ∼ 3 km 2 .

The array may be enlarged in a full-scope configuration (omega) characterized by a greater number of telescopes depending on the available funds.

Science with CTA

CTA seeks to address questions pertaining to three distinct groups [START_REF]Science with the Cherenkov Telescope Array[END_REF]:

• Understanding the origin and role of relativistic cosmic particles -What are the potential sites of acceleration of high-energy particles?

-How are particles accelerated to such high energies? -How do accelerated particles impact star formation and galaxy evolution?

• Probing extreme environments -What is the governing physics close to the neutron stars and black holes?

-What are the characteristics of relativistic jets, winds, and explosions?

-How does the radiation and magnetic fields in the Cosmic voids evolve with time?

THE NECTARCAM CAMERA CONCEPT

• Exploring frontiers in physics

-What is the nature and distribution of dark matter?

-Does a propagating photon feel quantum gravitational effects?

In this thesis, we focus on the first theme of the origin and role of relativistic particles. Relativistic particles are produced in various astrophysical systems ranging from small-sized pulsars to large-scale outbursts from starburst galaxies. The relationship between these particles' interaction with the magnetic and radiation fields remains an open question. CTA, with its ability to precisely measure high-energy γ-rays, will provide valuable insights into the acceleration of protons and nuclei. In order to answer these pressing questions, CTA is gearing towards providing 1) a complete Galactic and extragalactic survey with deep observations of selected key astrophysical sources and 2) precision measurements involving resolved spectroscopy and light curve with high statistics of typical bright sources.

The NectarCAM camera concept

Due to the exponential loss of flux intensity arising from scattering and absorption processes, the faint Cherenkov signal needs to be enhanced to confirm the observation. To achieve this, each of the telescopes of CTA has been equipped with its own variation of a robust camera designed to collect the short-duration faint Cherenkov light deftly. This section explores the design concept of the camera of MST. There are currently two cameras being fit aboard the MST, NectarCAM and FlashCam. While FlashCam uses a digital trigger and readout system, NectarCAM relies on an analog pipeline readout chip. NectarCAM will equip MST telescopes on the Northern site, while FlashCam is planned for the Southern site.

Building on the experience gained by the previous generation of IACTS, the design of NectarCAM aims to be reliable and straightforward. Although Nectar-CAM has been designed for MSTs, the concept can be easily adapted for other telescopes of the Cherenkov Array. The NectarCAM camera has an FoV of 9 • , made possible by the 1855 pixels. Each pixel is a 1.5-inch long PMT from Hamamatsu (R12992-100), with 7 dynodes each [START_REF] Tsiahina | Measurement of performance of the NectarCAM photodetectors[END_REF], having an angular diameter of 0.18 • . In front of each PMT, a Winston cone is attached to ensure maximum light collection at the photocathode [START_REF] Thomas Tavernier | Status and performance results from NectarCam -a camera for CTA medium sized telescopes[END_REF]. Using the pixels, we can retrieve the charge and the arrival time of the incoming photons. The charge deposited from a specific event can be found by integrating the signal acquired from individual PMTs over a particular time window. Although the Cherenkov signal lasts a few nanoseconds, the duration of the signal on the camera can extend up to longer times (tens of ns). The PMTs have been grouped into modules, each containing 7 PMTs (or pixels). This has the advantage of minimizing the electrical connections between different modules and easily creating a trigger system that confirms a signal only when a certain number of neighboring pixels are illuminated. Additionally, a smaller module size allows for more flexibility in production, repairs, and maintenance. In total, there are 265 modules in the camera.

The systematic uncertainty while reconstructing the signal stems from the uncertainty of the gain of the detection chain, which includes photodetectors such as PMTs. Improvement of current or future IACTs requires accurate calibration to extract the arrival direction and energy of the incident photon. A single photoelectron (SPE) calibration system has been designed at IJCLab for the NectarCAM camera of the MST telescopes. This system is integrated into the NectarCAM camera [START_REF] Glicenstein | NectarCAM : a camera for the medium size telescopes of the Cherenkov Telescope Array[END_REF]. The entire camera is enclosed in an aluminium box which is sealed to protect the camera electronics from dirt. Proper temperature controls have been installed inside the camera to increase its reliability. NectarCAM has been assembled using several different individual units shown in Figure 4.5. This flexible design increases the ease with which the camera can be constructed and integrated at the production stage. The camera can be mainly divided into 3 parts: 1) At the entrance of the camera lies a customised roller shutter to cover the camera and protect it from various weather conditions. It is further protected by an acrylic sheet behind the shutter, which helps to seal the camera tightly against dirt. 2) The central part of the camera consists of the tubular frame made up of aluminium along with the module holder, wherein the modules are fit along with the cooling units of the front-end electronics. 3) The back structure is where the trigger, data acquisition, and other services of the camera are located. • When the camera receives a sufficient amount of light in several neighbouring modules within a few ns or even several pixels within a single module, a trigger is sent. First, a module containing a group of pixels is triggered (level 0 trigger or L0), and then the camera is triggered (level 1 trigger or L1). The final decision is taken by an array-level trigger.

THE NECTARCAM CAMERA CONCEPT

• Once the camera is triggered, the front-end electronics system captures the signal and transfers it to the Data Acquisition (DAQ) system using an Ethernet link to be read out. Figure 4.7 shows its layout. In order to support a large dynamic range from 0.2 to 300 p.e., the output of each PMT is divided into 3 linear channels; high gain, low gain, and trigger channels. L0 and L1 triggers provide a fast response every 400 ns, and in the meanwhile, the signal is stored in analogue memory using NECTAr analogue pipeline (ASIC) until the trigger signal arrives. Once the L1 signal is accepted, the data is transferred from the NECTAr chips to the FPGA2 where total charge and time of arrival of the signal is calculated. Finally, after the array level trigger is detected, the data is transferred from the camera to the ground for further analysis.

THE NECTARCAM CAMERA CONCEPT

Chapter 5

Calibration of NectarCAM camera

Introduction

To detect a low-intensity light generated by Cherenkov radiation, we need to follow the conversion of photons to photoelectrons, which are then multiplied to give the detected electrical signal. The gain is the factor by which the photoelectrons have been multiplied, and it is required to estimate the actual intensity of the light.

A focal plane calibration system has been specially designed by IJCLab for the NectarCAM camera of the MST telescopes. This will allow us to measure the gain of the camera's photodetection chain accurately and to constrain the systematic uncertainties on the energy reconstruction of γ-rays detected by the telescope [START_REF] Biasuzzi | Design and characterization of a single photoelectron calibration system for the NectarCAM camera of the mediumsized telescopes of the Cherenkov Telescope Array[END_REF]. This chapter is dedicated to the R&D activity done to design the SPE calibration system to measure the gain of each pixel (PMT) of NectarCAM. In this chapter, a general overview of the PMTs has been provided and then the calibration system designed for NectarCAM has been discussed in detail. Additionally, the method used to analyze the calibration data is explained at length. Finally, the calibration data for the first NectarCAM, soon to be commissioned, has been analysed and results are shown. The calibration system studied during this thesis will be the final version that will be installed and operated on the first MST telescope in La Palma.

Photomultiplier tubes

Due to the large choice of different existing PMTs, the selection of the right one which optimizes the scientific goal is very important. For Cherenkov detection, an ideal PMT should:

-Suppress night sky background (NSB): NSB can be suppressed by choosing PMTs which are only sensitive in the wavelength range where the Cherenkov radi-62 CHAPTER 5. CALIBRATION OF NECTARCAM CAMERA ation dominates. The spectrum of Cherenkov photons is a continuous one ranging from near UV to the visible wavelength, with the intensity being inversely proportional to the square of the wavelength of the photon. Due to absorption by the atmosphere, the Cherenkov spectrum shows a cut-off for wavelengths below 300 nm. The NSB shows bright emission lines above 500 nm resulting from the atomic oxygen, hydroxide, and sodium present in the atmosphere. Therefore, to maximize the detection of Cherenkov photons, the photon detection efficiency of the PMTs should be maximum in the wavelength range from 300 nm to 500 nm and have a cut-off at higher wavelengths.

-Have a short response time: The speed of radiating particles is comparable to the speed of the emitted Cherenkov photons. Therefore, the light emitted at varying depths of the shower arrives at the ground approximately simultaneously [START_REF] Völk | Imaging very high energy gamma-ray telescopes[END_REF]. All photons of an extensive air shower hit the camera within a narrow window. A very short camera exposure time is required, and to achieve such a temporal resolution, PMT must have a short response time. The response time of a PMT can be quantified by the rise time and pulse width of an SPE signal. Rise time is the time elapsed between two points (usually 10% and 90%) on the rising edge of a signal and describes the response of a system when the amplitude of the input signal changes. The pulse width is given by the full width half maximum (FWHM) of the signal formed at the anode.

-Have a low noise: An afterpulse is a spurious pulse that appears, following directly a true pulse, and can be confused as a signal. They have a dominant contribution to the noise level of a PMT. The main causes of an afterpulse are 1) Back-scattered electrons: the incident photoelectron may be scattered elastically by the first dynode, which causes a signal after a short delay. 2) Luminous reactions: the constant bombardment of electrons on the dynodes may cause stimulated emission of single photons. However, emitted photons mostly fall in the infrared regime and can be neglected. 3) Ionization of residual gas: when residual gas in the PMT is ionised by electrons, positive ions are created which get accelerated towards the cathode and can release new electrons. In this case, the afterpulses are dependent on the mass of the ion. However, these noises are less dominant than the constant NSB at the SPE level.

Traditionally, PMTs have been used for the conversion of light to photoelectrons, allowing the detection of faint light on a single photon level. A PMT, as shown in Figure 5.1, is a collection of a photocathode, several dynodes, and an anode, all enclosed within a vacuum tube made out of glass. It works on the principle of the photoelectric effect (p.e.e.). When an incident photon strikes the photocathode, an electron is emitted. This electron is made to accelerate by an electric field across all successive dynodes where, through the emission of secondary electrons, there is an exponential increase in the number of electrons. This amplification 5.2. PHOTOMULTIPLIER TUBES 63 leads to the collection of a measurable current from the initial photoelectron. The probability that an incident photon manages to release an electron using p.e.e. is known as its quantum efficiency (QE). It is highly dependent on the material of the cathode and is usually about 20-30 %. The probability that a photoelectron reaches the first dynode is denoted as a PMT's collection efficiency (CE). CE depends on the dynode's geometry and the resulting electric field and is usually better than ∼ 60 -90 % for modern PMTs. For a fixed incident photons N γ , the number of photoelectrons N P E at the first dynode can be given by:

N P E = N γ • QE • CE, (5.1)
An accelerating field can be created between the dynodes by a high voltage of ∼ 1000-3000 V. Cathode is put at a negative potential which decreases with each dynode, with finally, the anode being very close to the ground potential. The field geometry, strength, and the number of dynodes together decide the Gain (G) of the PMT. The number of electrons at the anode N A is given by:

N A = N P E • G = N γ • QE • CE • G, (5.2)
An avalanche of electrons reaches the anode in the form of a sharp current pulse. The time it takes for the cascade of electrons from the cathode to the anode is denoted as the transit time. Geometrical influences can lead to variations in the transit time, thus causing a spread in the signal. The overall signal shape is an outcome of PMT's inner structure, resulting field geometry and more. Thus the gain represents the mean number of photoelectrons collected at the anode after a single photoelectron was released from the cathode.

NectarCAM PMT specification

The photodetector chosen for NectarCAM is 1.5-inch PMT R12992-100 featuring 7 amplifying stages developed by Hamamatsu1 . It is a head-on type with a concaveconvex borosilicate window and a super-bialkali photocathode. To overcome ageing effects, the PMT is operated at a low gain of 4 x 10 4 , thus allowing the camera to operate during a full moon. However, due to operation at low gain, the output of the PMTs has to be pre-amplified. The PMT has an SPE signal FWHM of 2.5 to 3 ns and can be operated at an ambient temperature range of -30 • C -+50 • C. This information has been provided in the datasheet given by the manufacturer C.1.

The main specification of the PMT R12992-100

SPE calibration method

The gain usually depends on the material and geometry of the dynode and can be varied by varying the voltage applied to the PMTs. When the light illuminating the PMT is very low, i.e., at the SPE level, a sophisticated function is required to model the response of the PMT. The probability of collecting n electrons is given as:

P (n, µ) = µ n e -µ n! , (5.3)
with µ being the mean number of photoelectrons collected at the first dynode. The resultant charge x, after the amplification, also follows a Poisson distribution. However, it can be estimated by a Gaussian distribution provided the gain at the first dynode is sufficient enough (factor > 4) [START_REF] Bellamy | Absolute calibration and monitoring of a spectrometric channel using a photomultiplier[END_REF]. The effect of amplification

SPE CALIBRATION METHOD

65 can be inculcated in the distribution of SPE by assuming that for each incident photoelectron, the amplification process is independent, and this distribution, for n > 0, translates to:

G n (x) 1 σ 1 √ 2πn • exp - (x -nq 1 ) 2 2nσ 1 2 , ( 5.4)
with q 1 being the average charge and σ 1 being the standard deviation. When n = 0, the gain function tends to 0. However, even in the absence of light, we can detect some current which arises in the form of background noise due to processes such as thermonuclear emission, radioactivity, leakage currents, and much more. This leads to the formation of a pedestal signal. The resultant charge due to the background noise can also be modeled as a Gaussian distribution:

B(x) = 1 σ 0 √ 2π • exp - (x -q 0 ) 2 2σ 0 2 , ( 5.5)
with q 0 being the average pedestal charge and σ 0 being the corresponding standard deviation of the pedestal. Finally, the PMT response of the incident photon in the SPE regime can be given by the convolution of the contributions listed above: Experimentally, the gain is determined from the position of the SPE peak of the charge distribution of all the waveforms integrated in a certain window within which the SPE signals lie. The size of the window is chosen such that the complete signal along with the tail of the signal containing tiny fluctuations, is contained within that window length. The pedestal is determined by integrating a window of the same length in front of the signal position or it can also be measured by acquiring data with all light-emitting diodes (LEDs) turned off (explained in section 5.5). The pedestal is subtracted from each of the signal waveform to obtain the charge. For each pixel in a camera, the charge distribution in the SPE regime is of the form shown in Figure 5.2. The charge histogram per pixel often contains two peaks. The first peak is the pedestal position (zero photoelectron) and the second broader peak corresponds to the peak of one photoelectron. Peaks of successive photoelectrons can sometimes be found too but are mostly hidden in the tail of the first SPE peak. This distance between the two peaks gives the gain of the PMT. In order to find the gain of a PMT accurately, dedicated algorithm is used to fit the SPE spectrum and provide the output parameter values which help calculate the gain of the PMT.

F (x) = N n=0 • µ n e -µ n! 1 2π(nσ 1 2 σ 0 2 ) • exp - 1 2 (x -nq 1 -q 0 ) 2 nσ 1 2 + σ 0 2 , ( 5.6)
A dedicated algorithm has been designed to reconstruct the charge distribution of a single photoelectron using low-intensity charge distribution. Up till now, a simple Gaussian model has been used to fit an SPE curve. However, a new model has been proposed that fits the data better [START_REF] Caroff | Determination of the single photo-electron spectrum and gain measurement for the Cherenkov Telescope Array camera NectarCAM[END_REF].

The charge distribution resulting from the response of a PMT in the SPE regime consists of several peaks representing photoelectrons. The charge distribution of n p.e. is produced by a convolution of n SPE distributions along with a pedestal distribution, as shown below:

q(x|n) = q ped * (Q SP E 1 * (Q SP E 2 ... * (Q SP En )(x), (5.7)
where q ped and Q SP E represent the charge distribution of the pedestal and SPE, respectively. As the number of p.e. collected increases, the charge distribution takes the form of a Gaussian shape owing to the central limit theorem 3 . However, when the distribution is measured at the SPE level, as discussed above, it follows a Poisson distribution. Then the contribution from n p.e. is summed according to Poisson law and fitted to the output charge distribution with the aid of the maximum likelihood method. A precise fitting was obtained for a model which consists of a sum of two Gaussians with one always centered at 0. The model considered four free parameters:

• µ high -mean of the highest charge Gaussian.

• σ high -width of the highest charge Gaussian.

• µ low -width of the lower charge Gaussian.

• p -the distance between the two Gaussians.

The two-Gaussian model takes into account the losses occurring inside the PMT. For example, in the path of the electron from the first dynode to the second dynode, the electron can take a non-ideal trajectory. Additionally, there may be a possibility that the electron does not originate from the photocathode, but the incident photon produces the p.e. at the first dynode, thus leading to a lower gain. Such losses contribute to the low charge component in the resultant SPE distribution. The presence of a pedestal includes two more parameters to the fit, independent of the SPE model. The pedestal is fit using a Gaussian model with a certain mean and width. Lastly, the mean number of p.e. is also considered a free parameter. The resultant two-Gaussian model provides a better fit and thus gives a lower gain value to the charge distribution than a simplistic single Gaussian model. The two-Gaussian model can effectively account for the intermediate region between the pedestal and peak of the first p.e. Each PMT signal varies due to either difference in the production of a PMT or the avalanche stage leading to the output signal. Due to this, a simple statistical effect cannot explain the variability in the model of different PMTs. Therefore, the determination of gain using a dedicated SPE software should be obtained on a PMT-by-PMT basis to suppress systematic uncertainty.

SPE calibration system

The SPE calibration system designed at IJCLab is multifaceted and can also be used for two important processes; mirror alignment and the study of the point spread function (PSF).

When a telescope forms an image of a point source, such as a star, the image is always blurred. The response of a telescope to a point source is defined as the PSF. The main reasons for blurring are aberration and diffraction effects. Great efforts have been made to reduce the size of the PSF to achieve near-diffraction-limited performance so that better resolution can be achieved. The MST consists of 90 hexagonal-shaped mirrors which reflect light onto the camera. These segments need to be aligned deftly to create a uniform reflector such that the best possible PSF can be achieved.

In order to align the mirrors and perform PSF studies, a uniformly painted, reflective target is required. For SPE studies also, a reflective target is required with different paint specifications such that low-intensity measurements, as low as a single photon level, are possible. A two-in-one target has been designed where CHAPTER 5. CALIBRATION OF NECTARCAM CAMERA one side of the target will allow for PSF studies, and the other side will allow for SPE studies. The target has been designed such that it can also move along the focal plane with the help of a motor for a complete scan of the camera. The calibration system mainly consists of a:

• Screen: It is a 10 mm thick block of Poly(methyl methacrylate) (PMMA) painted with a white diffuse reflective material. Its surface can cover 51 PMTs at once. Attached to it, there is a fishtail light guide which helps to guide the light injected into the screen. This calibration screen has been depicted in Figure 5 • Motors: They allow the movement of the calibration screen across the camera with the help of XY rails. The screen is painted with highly reflective paint, which causes the light to be reflected several times, thus spreading the light uniformly throughout the screen. It is painted to serve dual purposes. The side of the screen facing the mirror dish of the MST is painted with three homogeneous layers of paint for PSF and alignment studies. The other side is divided into 3 regions, each with layers of paint of varying thickness to allow for efficient spreading of light, whose transmissivity is used to measure the gain of the photodetection chain in the SPE regime. This calibration system is mounted inside the camera at a distance of 15 mm from the Winston cone on a system of XY rails attached to the motors, which will move the system over the entire focal plane. When idle, the screen rests at the parking position, i.e., on the bottom right corner of the camera, where it does not cast a shadow on any of the pixels (see Figure 5.5).

Diffuse-reflective screen

Prior to the thesis work, various screens were examined [START_REF] Biasuzzi | Design and characterization of a single photoelectron calibration system for the NectarCAM camera of the mediumsized telescopes of the Cherenkov Telescope Array[END_REF] to see which configuration provided maximum coverage of light across the screen within a given percentage of maximum intensity. The analysis included the study of 1) different shapes of the screen, namely square, rectangular, round, and octagonal, 2) two different reflective materials, namely polytetrafluoroethylene and reflective paints, 3) three coating methods, namely brush, airbrush, and dip coating and finally 4) different paint patterns for different prototypes.

An ideal screen should ensure the homogeneous spreading of light so that each PMT receives an equal amount of light during the scan. To obtain the calibration screen with optimum homogeneity, we need to study:

• Paint specification: This involves the careful study of painting patterns to ensure high reflectivity and homogeneous spreading.

To obtain homogeneity, the screen needs to be coated with a paint of varying thickness by applying different layers of paint, as shown in Figure 5.6. To do this, masks of different sizes have been used to cover the part of the screen which was not required to be painted. The width of the layers has been decided by analysing the light profiles along the central longitudinal axis and, if necessary, the lateral one.

• Screen geometry: The screen should be as large as possible to enable a fast scan and small enough to be integrated within the camera without casting a shadow on the focal plane when in the parking position.

• Coating method: Dip-coating method is used to paint the screen and the fishtail. To ensure homogeneity and reproducibility of the screen performance, a careful study of the dip-coating procedure needs to be performed to optimise the thickness of the paint layers on the screen. To test the homogeneity of the calibration screen, a dedicated test bench inside a dark room has been set up at IJCLab. One PMT (Hamamatsu R12992-100 used in NectarCAM) is placed 15 mm from the surface of the calibration screen enclosed in an aluminium frame which serves to protect the screen and maintain its planar position. A Winston cone is attached at the bottom of the PMT to ensure maximum collection of light at the entrance of the PMT. The PMT is then connected to a NectarCAM front-end board (FEB), originally developed by a consortium involving Institut de recherche sur les lois fondamentales de l'Univers (IRFU), Laboratoire de physique nucleaire et de hautes énergies (LPNHE), Instituto de Ciencias del Cosmos, Universitat de Barcelona (ICCUB), and LUPM. The entire system is moved over the screen, using motors, on a system of rails to perform light intensity measurements. The intensity of LEDs can be adjusted using a dedicated labview software interface. Several screens were tested using a high voltage of 1200 V for the PMTs and with appropriate voltage for LEDs to avoid saturation of light in bright spots of the screen. A picture of the test bench is shown in Figure 5.7.

Screen test setup

In order to paint the screen, a dedicated dip coating system has also been CHAPTER 5. CALIBRATION OF NECTARCAM CAMERA assembled at IJCLab and is shown in Figure 5.8. The main components of the dip coating apparatus are:

• Aluminium tank: It is a rectangular container with a 'V-shaped' bottom used to store the paint.

• Rail-belt system: It is a system of trolleys onto which the screen is attached and is used for the vertical dipping of the screen into the tank.

• DC motor: It is used to drive the rotation of the belt system.

• Rubber tube: It is electronically moved with the help of a pump and is used to stir the paint inside the tank.

This entire setup is mounted on a table for mechanical support and is connected to a computer that can control the withdrawal speed, the stirring rate, and more. The procedure for the dip coating is given in Appendix C. The system must be automated as much as possible to ensure the calibration screen is reproducible, as many more MSTs are to be built. Currently, there are a few issues that need to be solved before the dip coating process can be finalized, such as:

• Discontinuation of the adhesive tape: A strong adhesive tape is required to apply the mask on the screen to paint different layers. However, the present one leaves a sticky residue that is quite cumbersome to clean from the screen's surface. A new tape needs to be found which has strong adhesion on smooth surfaces and leaves no residue behind when peeled off.

• Single stirring tube: At present, only one stirring tube has been installed in the bottom left corner. For the proper mixture of the paint in order to avoid bubble formation, another rubber stirrer needs to be added in the bottom right corner.

• Production of new screens: For now, it is quite a tedious task to cut the PMMA block into the octagonal shape of the calibration screen. Furthermore, it is futile to clean and re-paint the existing screens because 1) it is a tedious job that requires quite a lot of time 2) constant cleaning and reusing of the screen tends to make the homogeneity tests unreliable as the degradation of the screen, due to scratches while cleaning, occurs. It has been decided that an external company needs to be contracted to produce at least 10-15 screens.

Although we are near finalizing the calibration system for the NectarCAM, a few critical tasks remain, with the biggest challenge being the assurance of reproducibility and the ability to follow this process to ensure smooth commissioning.

RESULTS

Results

The final configuration of the calibration screen was painted with Eljen paint with 18% dilution. For the PSF measurement, one side of the calibration screen was painted with three layers, while for the calibration measurements, the other side of the screen has been painted with the paint configuration 3-2-1. The side of the screen painted for calibration studies has 3 layers of paint between 0 and 16 cm from the direction of light injection, 2 layers between 16 and 26 cm, and 1 layer between 26 and 39 cm, which is the farthest region from the injection point. A dipcoating machine was developed specifically to paint the screen. The PMMA target to be coated was attached to vertical motorization atop of the tank. The dipping speed, rest time, and withdrawal speed of the screen from the tank filled with paint were regulated manually. The thickness of the painted layer depends on various factors, with the two most important ones being 1) the dip-coating procedure, such as the speed of withdrawal, and the temperature of the room, 2) the parameters of the paint, such as its density, viscosity, and surface energy [START_REF] Faustini | Preparation of Sol-Gel Films by Dip-Coating in Extreme Conditions[END_REF]. A dedicated mask was made to cover different regions of the screen while immersing it in the paint tank. For the final geometry, a flat octagonal screen of area 1338 cm 2 , with a flat fishtail light guide and a bent groove (30 • ), has been selected. The bending allows the light to enter at an angle that results in more internal reflections and increased homogeneity. Dedicated work on the dip-coating procedure has allowed for obtaining a reliable and reproducible dip-coating process. The final screen was painted with a withdrawal speed of 2 mm/s. In order to determine the homogeneity of the calibration screen, light intensity measurements were performed in a highintensity regime (> 100 p.e. produced at photocathode) using the darkroom setup. It was done by measuring the photon counts and producing histograms of charge integrated over 30,000 signals, for a fixed time window (60 ns), at various points on the screen. The procedure for high-intensity measurement is given in Appendix C.

Shown below in the Figure 5.9 are a few chosen examples of the results of the homogeneity tests done for various screens produced in the R&D phase, each differing in the painting procedure or the geometry of the calibration screen. Different colours represent the intensity of light within a certain percentage of the maximum intensity. In the few examples provided below, one can see that for different painting procedures and geometries, we obtained different intensity maps. Our goal was to choose the procedure which yields the most homogeneous light output. It should be noted that the result for screen number 13 seems quite good as well, however, it was rejected as we were not able to reproduce it. This further motivated the automation of the dip coating process. A table representing different configurations of screens is shown below in Figure 5.10 and 5.11. Here the area of the screen represents the effective area after the application of black tape to reduce the loss of light from the edges. We first started with a screen geometry in which the screen's fishtail was bent by 6 • and the groove (a block of PMMA used to join the screen with the flasher) was flat. However, this geometry proved problematic during the dip coating procedure, and so the geometry was changed to have a flat fishtail. The new geometry aided in bending the light right at the point of light injection and therefore led to a more homogeneous spreading of light. After Saint Gobain paint was discontinued, all the screens were painted with Eljen paint. For the test, mostly the percentage of dilution, order of masking, layers of paint, and the orientation of the screen during the dip coating process remained constant. Studies varied mostly due to the withdrawal speed of the motors during dip coating. It had a significant consequence on the thickness of the paint deposited on the screen and, thus, the spreading of the light. The homogeneity map of the best-obtained screen with the homogeneous spreading of light is shown in Figure 5.12. The map of the screen is plotted using 10 contours ranging from half down to a tenth of the maximum screen emissivity. We can see that light is satisfactorily spread across the screen within 10 contours. The cumulative area covered by each contour, along with the intensity lying within a given percentage of the maximum intensity for each contour is reported in the

Temperature measurements

The cameras of the MST, installed in the Northern and Southern hemispheres, will operate in an open environment, and the calibration system designed will have to withstand the extreme temperature fluctuations at both sites. Based on the information on the weather conditions defined for the CTA observatory, a temperature test was made at IJCLab to check if temperature fluctuations can affect the coating of the paint and thus affect the homogeneity of the calibration screen.

A climatic chamber (Vtsch Industrietechnik VC4034) was used, which allows working with a temperature ranging from -42 • C to 180 • C. In order to do the testing, we created three temperature models using the control panel:

TEMPERATURE MEASUREMENTS

79

The calibration system consisting of a screen, frame, and optical box, along with the cables, was put inside the climatic chamber for a selected amount of time. We also put a temperature sensor inside the chamber to check if the climatic chamber worked well. Shown in Figure 5.13 is the plot of the model in a solid blue line and the temperature observations from the sensor in orange/red points. Through the plots, we can see that the temperature change inside the climatic chamber followed the temperature set in the climatic chamber for all the models except for the high-temperature model. The high-temperature test was interrupted after 24 hrs instead of continuing up to 48 hrs which was attributed to a power outage in the laboratory during the weekend. After the completion of each temperature test, a homogeneity test was performed on the calibration screen. Figure 5.14 shows the homogeneity maps of the screen tested at different temperature conditions. From the tests, we concluded that the temperature has no significant impact on the screen's homogeneity of the paint pattern. However, after each test, water droplets formed on the screen, CHAPTER 5. CALIBRATION OF NECTARCAM CAMERA which may have led to slight thinning of the paint, thus resulting in a slight variation of the contours. This problem can be overlooked as MST will be enclosed in an overpressurized, nearly air-tight camera body with its cooling system [START_REF] Emmanuel Moulin | Cooling Tests of the NectarCAM camera for the Cherenkov Telescope Array[END_REF], and hence it will be easy to control humidity on site.

Calibration scan

With the design of the calibration screen finalised, the focus was shifted towards optimising the scanning procedure for performing calibration tests. The optimal screen positions required to scan the entire focal plane need to be determined to ensure coverage of all pixels with reasonable redundancy and minimise the time required for calibration. To achieve this, screen and camera geometry based on the Python library, Sympy was used. The screen is displaced across the camera horizontally with a fixed step h and vertically with a fixed step v . The values of the steps have been chosen such that there is sufficient overlap between two successive screen coverages to account for edge effects. The limits of the movement are set by the edges of the camera's internal frame. Once these limits had been set, the time taken for each translation was computed. To estimate this, the total time has been divided into different parts. Figure 5.15 shows the representation of the various time periods considered for the movement of the screen, along with the equation of motions used for transition from one position to the next one. In the equation provided in Figure 5.15, a 1 , a 2 represent the ramp-up and ramp-down acceleration respectively. The transition from one position to the next one is given by accounting for:

• t 1 -Time taken for the speed of the motor to ramp up.

• t 2 -Time taken for the screen to move from one position to another.

• t 3 -Time taken for the speed of the motor to ramp down.

In addition to this, the horizontal (step h ) and vertical (step v ) translation of the screen has been fixed as 0.261 m and 0.313 m respectively. These values have been fixed so as to ensure the least overlap between the successive screens and full coverage of all PMTs. •

t 1 = | v a 1 | • t 2 = (step h/v -|( 1 2 × a 1 × t 2 1 )|-|( 1 2 × a 2 × t 2 3 )|)/v • t 3 = | v a 2 |
The total time estimate also accounts for the time taken for the screen to move from the parking position to the first position on the camera, transit time from one column to the other, and the time required to return back to the parking position once the scan is over. With the assumption that 10,000 SPE flashes are shone upon the PMTs at a 1 kHz rate for each position, a rest time (t stop ) of 10 s can be obtained. The minimum and maximum velocity and acceleration of the motors have been set based on mechanical tests in the laboratory and are listed below:

• v -constant velocity: [START_REF] Kawai | Telescope Array Experiment[END_REF][START_REF] Faustini | Preparation of Sol-Gel Films by Dip-Coating in Extreme Conditions[END_REF] mm/s

• a 1 -ramp-up acceleration: [START_REF] Kawai | Telescope Array Experiment[END_REF][START_REF] Faustini | Preparation of Sol-Gel Films by Dip-Coating in Extreme Conditions[END_REF] mm/s 2

• a 2 -ramp-down deceleration: [START_REF] Kawai | Telescope Array Experiment[END_REF][START_REF] Faustini | Preparation of Sol-Gel Films by Dip-Coating in Extreme Conditions[END_REF] mm/s 2 Finally, having considered all these factors, the total time taken for a complete scan is estimated to range from 17 to 28 minutes, for a total of 55 successive positions.

By using the information about the coordinate of the centroid of each translated position of the screen we can represent the screen positions on the camera geometry as shown in Figure 5.16. The edges of the screen are shown in red, the coordinate of the centroid of each position of the screen is marked as a plus sign and the path of the screen is illustrated by the dotted line. The limits imposed by the camera's internal frame are signified by the black lines. 5.9 Test run with the calibration system

MST prototype and calibration run in Adlershof

In 2019, a mini NectarCAM camera consisting of 427 pixels was installed to the MST prototype telescopes in Adlershof (Germany). The main aim was to perform functional and mechanical interface tests. A detailed study of the transport strategy and environmental constraints was also conducted. The very first data was acquired along with proper testing of the trigger and SPE system. The SPE screen was moved over all pixels with 4 LEDs powered at 10V. Data were acquired at 2kHz, for 20 seconds per position.

Data analysis with Ctapipe

The Ctapipe software was used to analyse the SPE calibration data. Ctapipe 4 is a low-level data processing framework for CTA that includes analysis and processing of air shower images such as the reconstruction of incident air showers and discrimination between gamma-ray and hadronic showers [START_REF] Kosack | on behalf of the CTA Consortium. ctapipe: A Low-level Data Processing Framework for the Cherenkov Telescope Array[END_REF]. In Ctapipe, EventSource

TEST RUN WITH THE CALIBRATION SYSTEM

83

class iterates over all events and reads an event source that contains the various sub-runs in the dataset. Then EventSeeker is used to seek a particular event and access information about all events in one sub-run. For each event, a timestamp, identifying when a certain event occurred, is obtained. The time difference between consecutive timestamps is calculated. Finally, events with a time difference greater than 0.5 seconds are used to flag a change in the position of the screen during the scan.

Results

The charge of each event, reconstructed after pedestal subtraction for every pixel, is shown in Figure 5.17. The reconstructed charge pattern on the camera corresponds to the emission pattern of the screen used to calibrate it (see [START_REF] Thomas Tavernier | Status and performance results from NectarCam -a camera for CTA medium sized telescopes[END_REF]). All events up to the event corresponding to the first time flag have been selected and the charge for each event is extracted and displayed on the camera plane. Events that fall between consecutive transit periods are identified as corresponding to a specific position of the screen during the scan. For a particular stop position of the screen, the waveforms of all events per pixel are summed to give a combined waveform. The average waveform in each pixel is used to determine the time when the signal is maximum (T max ). For the study an integration time of T max -5ns : T max + 15ns has been used to select the window where the signal is strong and the noise is less. A similar window length is also used to subtract the pedestal from the waveform. The pedestal is calculated before the peak of the signal in the acquisition window. The integration window has been optimised by accounting for the position of the maxima of the waveform for each pixel in a given window and selecting the integration widow around this maxima. The integrated waveform then gives the charge per event per pixel. Once the position of the screen is found, we select only the illuminated pixels as is shown in Figure 5.18. For each illuminated pixel, a histogram of the charge distribution is stored.

The charge distribution of each pixel is modeled by a multi p.e. spectrum, accounting for a pedestal contribution corresponding to noise, represented by the first peak in Figure 5.19 and Figure 5.20. Subsequent peaks correspond to photoelectrons modeled by a two-gaussian SPE response. This spectrum can be reconstructed either in the high-intensity region (Figure 5. [START_REF] Kampert | Cosmic rays from the ankle to the cutoff[END_REF] or in the low-intensity region (Figure 5.20) of the screen. Blue markers represent data points and the orange curve is the fit. As discussed above, the gain of the PMTs can be computed by measuring the distance between the pedestal and the first p.e. peak. Ideally, the gain should be the same between all the PMTs in order to correctly reproduce the real observations. The width of the final gain distribution of all the pixels would give the variation in the gain measurement. From the analysis, a mean gain of 56 ADC/p.e. ± 2.1 ADC/p.e has been found over the mini camera. The accuracy of the calibration varies with different PMTs and can be calculated for each PMT using the data obtained from the SPE fit. For the SPE spectrum in Figure 5.19 and Figure 5.20 an accuracy of ∼ 2% can be found.

A histogram of the gain distribution of ∼ 21k events in all the illuminated pixels was also studied. This allowed us to constrain the pixel variation in gain to ∼ 4%. Using the scan algorithm detailed in section 5.7, a list of different screen positions required to cover the camera was obtained. This list of positions was then used to move the calibration screen effectively over the entire focal plane for the calibration scan. At each position, 10,000 events were acquired at a nominal rate of 1kHz (10 s). The data collected was then analysed using the algorithm detailed in section 5.7. The algorithm helped to easily identify the illuminated pixels, obtain the charge of each illuminated pixel and finally produce a fit to determine the gain of each PMT. At the moment, due to mechanical constraints, only 80 % of the camera could be covered by the motors. Once the XY rails of the motors are updated, a complete SPE scan can be made for each pixel, and a more accurate value of the gain and its uncertainty is expected. Shown below are the SPE calibration results for the first scan position. For this particular calibration scan run at CEA, the integrated reconstructed charge after pedestal subtraction is shown in Figure 5.22 and the selected pixels are shown in Figure 5.23. The charge distribution of two pixels is shown in Figure 5.24 and 5.25. Once the first MST of CTA will be fully functional, the SPE runs are expected to be taken at least twice per month (before and after the full moon) with LED and PMTs configuration as used during in-house tests to be able to make calibration of each PMT. In the previous SPE fit using Adlershof data, the pedestal has not been subtracted, whereas for the SPE fit using the CEA data, the pedestal has been subtracted. This shows that the SPE fitting algorithm works, with and without pedestal subtraction. It relies only on the relative difference between the pedestal and the first SPE peak.

Conclusion

Chapter 5 covers the tasks undertaken during the thesis to participate in the design and characterization of the SPE calibration system. It also contains a detailed description of the analysis tools developed to perform the SPE calibration. The final octagonal calibration screen was coated with varying layers (3-2-1 from the light injection point) of Eljen paint. The geometry of a flat fishtail was selected, which ensured the effective spreading of light across the screen to enable measurements at the SPE level.

Several homogeneity and temperature tests were conducted to ensure the efficiency and prolonged durability of the calibration screen. Homogeneity tests revealed that in up to ten contours, the light covered 100% of the calibration screen. Temperature tests on the calibration screen showed no significant difference in the homogeneity when the temperature was varied between -15 • C to +35 • C. Few updates are required in the dip coating system, which consists of automatizing the painting process of the calibration screen to assure reproducibility. Once done, mass production of the calibration screens can be initiated.

A new method developed to optimize the scan positions to reduce the time taken to scan all PMTs during a calibration run has also been discussed. After several estimations, the total scan time for acquiring 10,000 data points at a 1 kHz rate per position was estimated to range between 17-28 minutes.

Additionally, to understand the acquisition process of calibration data on-site, data acquired in Adlershof, using the SPE system integrated into the mini Nectar-CAM prototype, was analyzed. Finally, the calibration data from the first MST camera at CEA, soon to be commissioned, has also been incorporated into this study. An algorithm was written to analyze the calibration data, which found a robust way to identify only those pixels that are illuminated by the screen to allow for a quick and precise estimation of the gain of the selected PMTs. The variation of the gain determination using the mini camera at Adlershof was estimated to be ∼ 4%. The typical calibration accuracy for PMTs was about ∼ 2%. The data obtained from the full scan of the fully equipped camera will determine whether a homogeneity of gain better than 4% can be achieved in the near future.

Introduction

Different sources that make up our Universe radiate at varying wavelengths. Detecting sources in different energy bands can provide a wealth of information about the source during its evolution. An infant SNR radiates mostly thermal and nonthermal X-rays due to the accumulation of hot material behind the shock wave. Filaments in the optical region are present in the cooler and hence older SNRs. Radio emissions can be detected in all the evolutionary stages from the shocked parts and the cooling filaments. Finally, when the expanding SNR interacts with the ISM, γ-rays are emitted. A single source emitting photons of varying energies indicates a complex phenomenon of material heated over a wide range of temperatures and the existence of high-energy electrons, protons, and other nuclei.

The multiwavelength analysis is the focus of this chapter. This technique is used to constrain the physical parameters and find the global parameters which will be used in Chapter 7 to make a simulation of fluxes of selected SNRs as would be seen by CTA. To study the sources of Galactic cosmic rays, we need to focus on the γ-ray energy domain and try to deduce if the emission is of leptonic or hadronic origin. This chapter provides a blend of observational, analytical, and statistical tools to ascertain the nature of emissions at very high energies.

Multiwavelength studies

The plot of the flux of a source at different energies is known as a Spectral Energy Distribution (SED). An example is shown in the left-hand side of Figure 6.1. Every physical process happening inside or around a source leaves its characteristic imprint, which governs the overall shape of the observed spectrum. The highly 90 CHAPTER 6. MULTIWAVELENGTH ANALYSIS energetic phenomenon, such as the death of a massive star, leads to the acceleration of relativistic charged particles. We know that when charged particles accelerate in a magnetised environment, they radiate energy. Theoretical radiative models are built for different radiative mechanisms such as synchrotron, bremsstrahlung, inverse Compton and pion-decay to get the expected flux at different energies as shown in the right-hand side of Figure 6.1. These theoretical models are fit to the observed flux to extract the physical information about the source such as the magnetic field, the maximum energy of accelerated particles, and much more. shown the possibility of detecting galactic PeVatrons that extend beyond 10 TeV [START_REF] Cristofari | On the search for Galactic supernova remnant PeVatrons with current TeV instruments[END_REF]. The high-energy observations will be further complemented by upcoming observatories such as CTA. Due to their higher sensitivity, accuracy, and wide energy coverage, we expect a significant increase in the quantity and the quality of the observations at the very high-energy γ-ray domain. In this domain, the γ-rays are either produced by hadronic or leptonic interactions, however, any firm conclusions cannot be drawn with the present observations.

Three main ways of disentangling between leptonic and hadronic components are 1) studying the γ-ray spectra well beyond ∼ 10 TeV, where there is a decline of inverse Compton radiation due to the Klein-Nishina effect [START_REF] Longair | High Energy Astrophysics[END_REF]; 2) studying older SNRs (≥ 100 yrs) where electrons are expected to have exhausted their energy and hence cannot reach the multi-TeV energies; 3) studying SNRs which are known to be near high density (> 10 cm -3 ) Molecular Clouds (MC) which increase the production of π 0 due to the hadronic interaction and consequent production of γ-rays. All observations together allow us to perform MWL analysis which helps us understand the physical processes taking place at the site of acceleration. It also allows us to study the possibility of hadrons being accelerated by SNRs.

Radiative models

Non-thermal radiations at different wavelengths are produced at different evolutionary stages depending on the surroundings and regions. A detailed description of these interactions can be found in [START_REF] Longair | High Energy Astrophysics[END_REF]. The major radiative processes that have been considered in the study are given in brief below.

Synchrotron

Electrons encountering the magnetic field near the SNR shock emit non-thermal Synchrotron radiation. This radiation is detected in the radio band but extends up to the X-ray domain. A high-energy electron moving in a uniform magnetic field follows a spiral path having a constant pitch angle α. The pitch angle α is random and can change depending on the fluctuations in the magnetic field or the streaming instabilities. The average loss rate is given by [START_REF] Longair | High Energy Astrophysics[END_REF]:

- dE dt = 4 3 σ T cU mag v 2 c 2 γ 2 , (6.1)
where σ T is the Thompson cross-section and U mag = B 2 /2µ 0 is the energy density of the magnetic field. For this study, the Synchrotron radiation has been modeled using the results found by F.A. Aharonian et al. [START_REF] Aharonian | Angular, spectral, and time distributions of highest energy protons and associated secondary gamma rays and neutrinos propagating through extragalactic magnetic and radiation fields[END_REF].

Bremsstrahlung

At times, a moving charged particle may be deflected by another charged particle due to a change in the momentum when entering the Coulomb field of another charged particle, causing it to decelerate. The moving particle loses kinetic energy, which is converted into bremsstrahlung radiation. The Klein-Nishina effect7 needs to be added when the energy of the emitted photons is similar to that of the accelerated electrons. Hence, complete quantum mechanical treatment is required. Bremsstrahlung is mostly a result of the electron-electron and electron-ion (majorly protons and He) interactions. In the γ-ray regime, the cross-sections of e-e and e-p are similar and have similar contributions to the emission, while in the X-ray domain, the bremsstrahlung is dominated by the interaction of the non-relativistic electrons with ambient ions. In a fully ionised plasma, the rate at which electrons lose energy through bremsstrahlung radiation is given by [START_REF] Longair | High Energy Astrophysics[END_REF]:

- dE dt = Z 2 e 6 N E 12π 3 ϵ 3 c 4 ℏ ln 192 Z 1/3 , (6.2)
where Ze is the charge of the nucleus, N is the space density of nuclei and E is the energy of the electron. In this study, the spectrum of Bremsstrahlung is computed using the approximation by Baring et al. [START_REF] Baring | Radio to Gamma-Ray Emission from Shell-Type Supernova Remnants: Predictions from Nonlinear Shock Acceleration Models[END_REF].

Inverse Compton

When relativistic electrons interact with the ambient low-energy photons (∼ CMB and IR fields), such as discussed above, they up-scatter the low-energy photons to γ-ray energies. There is a gain in the energy of photons at the expense of the kinetic energy of the electrons. This process gives rise to the inverse Compton radiation. It is the primary channel for the γ-ray production for electron population [START_REF] Blumenthal | Bremsstrahlung, Synchrotron Radiation, and Compton Scattering of High-Energy Electrons Traversing Dilute Gases[END_REF].

In this study, we have considered two dominant sources of background radiation: Cosmic Microwave Background (CMB) radiation and Cosmic Infrared Background (CIB). The amplitude of CMB dominates the cosmic background spectrum. It is the remnant of the early Universe when the temperature after the Big Bang cooled sufficiently to allow coupling between protons and electrons to form neutral atoms. This marked the recombination epoch and the formation of atoms led to the decoupling of photons. These photons traveled freely through space and are now visible as the ambient 2.7 K CMB radiation. The EBL 8 consisting majorly of CIB and COB radiation closely follows CMB radiation. The CIB is emitted by the reheated dust surrounding stars inside a galaxy and red-shifted light from a distant Universe [START_REF] Lagache | Dusty Infrared Galaxies: Sources of the Cosmic Infrared Background[END_REF]. FIR is an important part of the CIB arising from the cold gases or MC embedded in our galaxy. For this study, we have assumed that the inverse Compton radiation arises solely due to the interaction between energetic electrons and the photon seed field from the CMB and from the FIR 9 . Although other fields exist, FIR radiation due to dust emission in Milky Way-type galaxies provides the most important contribution for γ-ray photons ranging from GeV to TeV [START_REF] Popescu | A radiation transfer model for the Milky Way: I. Radiation fields and application to high-energy astrophysics[END_REF].

For electrons having energy < 10 TeV, the seed photon energy in the rest frame of electrons is less than the electron's rest energy. In this energy range, the classical Thompson limit can be applied. However, quantum mechanical treatment is required for higher energies, and the Klein-Nishina effect drastically decreases the cross-section as energy increases. The rate at which the electrons lose energy is approximated by:

- dE dt = 4 3 σ T cU rad v 2 c 2 γ 2 , (6.3)
where σ T is the Thompson cross-section and U rad is the energy density of the radiation.

It is interesting to note the similarity between Equations (6.1) and (6.3). This indicates that the rate of energy loss only depends on the electric field responsible for accelerating the electron in its rest frame. It does not depend on the origin of the field. For synchrotron radiation, the electric field is generated due to the motion of the electron through the magnetic field, and in comparison, for inverse Compton radiation, the electric field arises from the electromagnetic waves incident on the electron.

In this study, we have used the analytical approximations to IC up-scattering of black body radiation developed by Khangulyan et al. [START_REF] Khangulyan | Simple Analytical Approximations for Treatment of Inverse Compton Scattering of Relativistic Electrons in the Blackbody Radiation Field[END_REF]. In order to compute non-thermal seed photon fields, a differential cross-section illustrated by Aharonian & Atoyan [START_REF] Aharonian | Compton Scattering of Relativistic Electrons in Compact X-Ray Sources[END_REF] has been used. These radiations together form the leptonic scenario where the radiation is due to electrons and positrons.

Pion decay

Another process that also leads to γ-ray emission at high energies is the pion decay. It occurs when accelerated protons interact with protons of the surrounding medium. The proton-proton collisions produce π 0 mesons which subsequently decay into two γ-rays (π 0 → γ + γ). Each of the γ-ray produced has an energy of 94 CHAPTER 6. MULTIWAVELENGTH ANALYSIS m π 0 c 2 /2, which in the rest frame of neutral pion is equal to 67.5 MeV. Additionally, charged pions (π + and π -) are also produced, which give subsequent rise to secondary leptonic radiation mechanisms. Charged pions also produce neutrinos which can act as an indicator of hadron acceleration. In the frame of π 0 , the loglog representation of the γ-ray spectrum (dN/dE) is symmetric around 67.5 MeV. The minimum energy of the incident proton needed to produce π 0 particle is 280 MeV. This threshold energy can be seen in the photon spectrum (E 2 dN/dE) as a steep rise above ∼ 200 MeV. The decrease of the π 0 spectrum is due to the cutoff imposed by the maximum energy of protons. Ervin Kafexhiu et al. [START_REF] Kafexhiu | Parametrization of gamma-ray production cross sections for p p interactions in a broad proton energy range from the kinematic threshold to PeV energies[END_REF] have provided a parameterization of the pion-decay spectrum, resulting from inelastic p-p kinematics, by combining the experimental data on the π 0 production below 2 GeV and the publicly available Monte Carlo codes at higher energies.

Leptonic and lepto-hadronic scenarios

To truly understand the nature of particles accelerated by the source at TeV energies, we need to disentangle two high-energy processes depending on whether or not there is ambient material surrounding the expanding SNR. TeV photon emission is expected from SNRs if they accelerate hadrons up to PeV energies [START_REF] Cristofari | On the search for Galactic supernova remnant PeVatrons with current TeV instruments[END_REF]. However, most SNRs also emit non-thermal electrons which glow in the multi-TeV domain. As discussed above, these electrons can often upscatter the photons of the CMB and FIR fields and emit TeV γ-rays via the inverse Compton scattering process [START_REF] Reynolds | Supernova remnants at high energy[END_REF].

The magnetic field plays an important role in particle acceleration and radiation processes. It could be used to get an indication of hadronic emission. An SNR with more than 10 µG magnetic field would produce less TeV inverse Compton emission. If the magnetic field is approximately 10 µG, then the number of electrons required to explain the X-ray emission can sufficiently describe the entire TeV spectrum [START_REF] Gabici | Gamma ray astronomy and the origin of galactic cosmic rays[END_REF]. Observing thin (few arcseconds) synchrotron X-ray filaments around an SNR shock usually implies the presence of a strong magnetic field (100 µG or more). The presence of a strong magnetic field indirectly supports hadronic emission because, as mentioned above, for a magnetic field stronger than a few ten µG, the emission due to inverse Compton scattering becomes negligible, allowing the hadronic emission to be the dominant γ-ray production channel [START_REF] Gabici | Gamma ray astronomy and the origin of galactic cosmic rays[END_REF]. Additionally, Bell [START_REF] Bell | Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays[END_REF] showed that shocks that are efficient CR proton accelerators are host to instabilities that would amplify the magnetic field. This amplification value for the magnetic field, supported by X-ray observations, provides the desired condition for proton acceleration up to PeV energies.

Another way to discriminate between the two γ-ray emission processes is to perform an MWL analysis and focus on the TeV range. Data points pertaining to different observations at varying wavelengths allow us to constrain different physical parameters. This is done by comparing the predicted radiative models to the MWL observations spanning from the radio to the TeV range. The synchrotron emission model can constrain the electron parent particle distribution and the magnetic field. The resulting electron spectrum in the presence of synchrotron losses can be used to derive the consequent inverse Compton emission off photons in the permeating radiation. The pion-decay radiation model, which fits the observations in the MeV to TeV domain, provides information about the proton parent particle distribution and helps to constrain the properties of the surrounding medium.

According to our current understanding, hadronic models provide a satisfactory fit to the X-ray and the γ-ray domain observations. In comparison, the leptonic models cannot sufficiently fit the measured TeV spectrum at the lowest energy. Artificially enhanced leptonic emission by infrared background enhancement or the addition of a second electronic component may be possible; however, based on spectral information, it seems unlikely compared to the natural hadronic scenario [START_REF] Tanaka | Study of Nonthermal Emission from SNR RX J1713.7-3946 with Suzaku[END_REF]. Additionally, the spectrum of young SNRs (a few thousand years) exhibits a significantly different characteristic shape depending on the leptonic or hadronic origin. Usually, for hadronic origin, a much harder spectrum is expected. Fermi telescope over long observation years can provide enough statistics to point towards hadronic or leptonic component; however, Fermi alone cannot provide insight on whether the SNR source can efficiently accelerate ions up to PeV energies.

Selecting SNRs lying in close vicinity to MC can help probe γ-ray observations from CRs. If emission was ascribed to be hadronic compared to leptonic, it would mean that mostly protons and nuclei are accelerated by the source or surrounding medium. However, studies indicate that given the normal interstellar medium conditions, the hadronic contribution would dominate only if electrons are less than approximately 0.1 % abundant compared to protons [START_REF] Gabici | Gamma-ray emission from young supernova remnants: Hadronic or leptonic[END_REF]. Hence it is not straightforward to attribute VHE γ-ray emission from SNRs to hadronic processes.

The possibility of mixed lepto-hadronic models also has been discussed [START_REF] Zirakashvili | Nonthermal Radiation of Young Supernova Remnants: The Case of RX J1713.7-3946[END_REF]. The observations of combined GeV and TeV spectra of the SNRs surely possess the ability to break the degeneracy of leptonic or hadronic origins of the γ-ray emission. The thesis aims to use the MWL analysis method to study the possibility of breaking the degeneracy of the leptonic or hadronic nature of high-energy γ-ray emissions.

Data selection

In this study, all the shell and interacting-type SNRs listed in TeVcat [START_REF] Wakely | TeVCat: An online catalog for Very High Energy Gamma-Ray Astronomy[END_REF]) (29 sources) were added to a preliminary list of SNRs. Table 6.1 gives information about all the SNRs present in the preliminary list. From this list, the SNRs were further divided into different datasets, silver(only high-energy) and golden (low and high-energy), depending on the availability of MWL observations. The final dataset contained the SNRs for which high-energy data was available in gammacat [START_REF] Nigro | Towards open and reproducible multi-instrument analysis in gamma-ray astronomy[END_REF], additional data were found in ASDC10 , Green catalog [START_REF] Green | A revised catalogue of 294 Galactic supernova remnants[END_REF], Chandra X-ray catalog 11 and literature. The complete table consisting of the origin of multiwavelength data for the chosen sources is shown in Table 6 Int. 1000-4000 [START_REF] Thoudam | Cosmic-ray energy spectrum and composition up to the ankle: the case for a second Galactic component[END_REF] 200 [START_REF] Brogan | Very large array HI Zeeman observations toward the W49 complex[END_REF] Table 6.3: List of the chosen SNRs along with their type (Int. refers to SNRs interacting with the surrounding medium), age, and magnetic field.

Source ASDC Chandra [71] [70] [72] [73] [74] [66] [75] Cassiopea A X X X X X _ _ _ _ CTB 37A X X X X _ _ _ _ _ HAWC J2227+610 X X X X _ _ _ _ X HESS J1731-347 X _ X X _ _ _ _ _ IC 443 X X X X _ _ _ _ _ RX J1713.7-3946 X _ _ X _ _ X X _ RX J0852.0-4622 X X X X _ X _ _ _ W28 X X X X _ _ _ _ _ W49B X X X _ _ _ _ _ _
Table 6.2: Origin of the data points for the selected SNRs.

For choosing the observations for the SNRs listed in Table 6.2, a few selection criteria were applied. First, the latest observations or surveys were favoured. Hence observations from the newest available catalogues were chosen. Second, we have eliminated observations from the UV or IR bands in order to avoid contamination from nearby stars and dust. Third, we have only chosen instruments for which the FoV was comparable or larger than the size of the chosen SNR.

After all these considerations we were left with the 9 SNRs. For each SNR, in Table 6.3, we provide information about its type which can be found in TeVcat, age, and magnetic field along with the references.

Finally, for each of the selected SNRs, its flux and its uncertainty were collected and an MWL spectral SED was constructed. Dedicated software has been used to fit these SEDs using the theoretical models discussed above to extract the physical information for the observed flux. 98 CHAPTER 6. MULTIWAVELENGTH ANALYSIS

Analysis and tools

In our attempt to understand which scenario is supported by the available observations, we have fitted the observed SEDs of all the chosen SNRs. The fit was done using two different models: a lepto-hadronic model where the photons are assumed to be produced by a mixture of leptonic and hadronic processes and, a purely leptonic model where photons are assumed to be produced only through leptonic processes.

In the study, we have considered only protons for hadronic processes and electrons for leptonic processes. The energy distribution of both proton (f p (E)) and the electron (f e (E)) distributions have been assumed to follow an exponential cutoff power-law (ECPL). The equations for protons and electrons are given below:

f p (E) = A p × ( E E 0 ) αp × exp(-E/E cop ) β , (6.4
)

f e (E) = A e × ( E E 0 ) αe × exp(-E/E coe ) β , (6.5) with :
• A p : the amplitude of the proton particle distribution

• A e : the amplitude of the electron particle distribution

• α e : the electron spectral index

• α p : the proton spectral index

• E coe : the electron energy cut-off

• E cop : the proton energy cut-off

• β: the cutoff exponent

The reference energy has been set as E 0 = 1 TeV. The parameter K ep = A e /A p describes the ratio of electrons with respect to protons at 1 TeV.

Since π 0 production depends on the density of protons in the surrounding medium N H and the synchrotron radiation depends on the magnetic field B in the radiating region, we need to add these two parameters to obtain the overall fit. Finally, 8 free parameters are required to theoretically build the SEDs: A, α e , α p , E COE , E COP , K ep , B, N H .

In contrast to the lepto-hadronic model, the leptonic model only considers bremsstrahlung, inverse Compton and synchrotron processes. Defining the electron energy distribution as equation (6.5), we find that only four free parameters are needed to theoretically build the SEDs: A e , α e , E COE , B.

Since electrons suffer radiative losses, one would expect electron distribution to differ from a simple ECPL. To account for this behaviour, we have first studied the effect of using an ExponentialCutoffBrokenPowerLaw function for electron distribution using the parameters found in the references [START_REF] Abdalla | observations of RX J1713.7-3946 with improved angular and spectral resolution: Evidence for gamma-ray emission extending beyond the Xray emitting shell[END_REF], [START_REF] Abdalla | The supernova remnant W49B as seen with H.E.S.S. and Fermi-LAT[END_REF], [START_REF] Ackermann | Detection of the Characteristic Pion-Decay Signature in Supernova Remnants[END_REF]. Additionally, we studied the effect on the fit by using a more general form for the electron distribution. This was done by varying the value of β as 0.5, 1, and the effect of leaving it free. Statistical analysis of the results of both studies showed that there was no significant qualitative or quantitative impact on the overall results. Hence, in the following, we have used ECPL with β = 1 for both electron and proton distributions. The details of this study can be found in Appendix B.

Monte Carlo Markov Chain (MCMC)

To build theoretical SEDs, we have used Naima [START_REF] Zabalza | Naima: a Python package for inference of particle distribution properties from nonthermal spectra[END_REF]. It is a Python package consisting of radiative models which allow us to compute the non-thermal emission from populations of relativistic electrons and protons and perform MCMC [START_REF] Foreman-Mackey | emcee: The MCMC Hammer[END_REF] fitting to the observed spectra. In a Markov process, a particular step only depends on the previous step and not on the previous state of the system. Monte Carlo is used to imbue randomness in the process. Therefore, MCMC technique implies a random sampling of space such that each step depends only on the previous one. MCMC samples a set of parameters from the posterior distribution (probability of our model given data) and generates a model which best fits the data.

All the models take as input the parent particle distribution function. Since MCMC is Bayesian, a set of parameters, called priors, need to be initialised to sample the spectral model parameters' space. The priors encode our knowledge about the probability distribution of the model parameters. The run returns two sets of parameters: the best-fit parameters along with their uncertainties and the median value of each parameter obtained at the end of the chain of the different initial sets. Naima gives the option to choose between two priors; normal and uniform priors. After studying the fit using both types of priors we concluded that the uniform prior is a better option yielding a better fit to the observations. Supporting our decision is the fact that the uniform prior assigns equal probability to each point in the wide range of parameters whereas the normal prior maximises the probability of values around the mean represented by initial parameters, yielding lower probabilities for the parameters at the edge of the parameter range. Thus using normal priors would require us to have more precise knowledge about physical parameters in contrast to uniform priors which only require a wide enough range to effectively explore the parameter space. Additionally, using normal priors increases the risk of getting stuck in a local minimum.

Naima assumes that the measurements and uncertainties provided for SED building are correct, Gaussian, and independent 12 . The likelihood of a set of parameters is thus computed using the equation (6.6):

L = N i=1 1 2πσ 2 i exp (- (S(⃗ p; E i ) -F i ) 2 2σ 2 i ), (6.6)
with N being the total number of measurements, F i the measured flux at the energy E i and σ i the associated uncertainty. S(⃗ p; E i ) is the theoretical flux at a particular energy E i given the assumed spectral model and the set of parameters ⃗ p.

Calculations can be significantly simplified by studying log(L) instead of L. This gives the equation 6.7:

log(L) = N i=1 - (S(⃗ p; E i ) -F i ) 2 2σ 2 i . (6.7)
The log(L) can be related to χ 2 parameter using the equation:

χ 2 = -2 log L. (6.8)
This makes the maximisation of log-likelihood to be equivalent to minimization of χ 2 .

In order to compare the pure leptonic and lepto-hadronic models additionally, we make use of the Bayesian Information Criterion (BIC) to see which model is better at explaining the observed spectrum [START_REF] Schwarz | Estimating the Dimension of a Model[END_REF]. The BIC quantity is defined using the equation (6.9):

BIC = k log(n) -2 log(L best ), (6.9)
with k being the number of parameters estimated in the model, n being the number of data points, and L best the likelihood associated with the best-fit parameters for a given model.

BIC has the advantage of being independent of the prior and measures the efficiency of the parameterized model in terms of predicting the data. However, it is limited by the fact that a valid sample much larger than the number of parameters in the model is required.

When comparing two models, the model with a lower BIC is preferred. The BIC value increases with an increasing value of k. Thus lower BIC implies either fewer explanatory variables, better fit, or both. We have decided to consider two different models, leptonic and lepto-hadronic and the magnitude of the ∆BIC = BIC leptonic -BIC lepto-hadronic will allow us to determine which model is better. The resulting ∆BIC value is to be interpreted as evidence against pure leptonic being the better model. If the resulting ∆BIC value is larger than 2 then the model with the lower BIC value is slightly preferred. If the ∆BIC value is greater than 6 then the model with a lower BIC value is highly favoured. In between the two values, no firm conclusion can be drawn but would tend towards favoring the model with a lower BIC value.

Naima modeling

For this study, the synchrotron emission model has been used to fit the low-energy contribution of the observed SED. At high energy, either purely leptonic consisting of bremsstrahlung and inverse Compton radiation or a mixture of lepto-hadronic models consisting of bremsstrahlung, inverse Compton & pion-decay have been considered.

For modeling the bremsstrahlung radiation, the default values of the solar system abundance were chosen as provided by Naima. During the modeling of the inverse Compton radiation, CMB and FIR fields have been considered, and the default values set by the Naima package have been used i.e. a temperature of 2.72 K, 26.5 K, and energy density of 0.261 eVcm -3 , 0.415 eVcm -3 for CMB and FIR radiations, respectively. The information about the models used in the Naima package has been mentioned in section 6.3.

Model constrains

Having short-listed the SNRs which had sufficient data points, in order to start SED fitting, we first need to limit the range of possible values that parameters can take. This is done to avoid biased results and to ensure that the output parameters lie within the physically acceptable range. Experimental results have shown that the spectral index of CRs usually lies between, -1.5 ≤ α ≤ -3 both for electrons and protons. Therefore, we have chosen α to vary between these values. The natural constraint on the K ep value also arises from the fact that it is easier for electrons to be absorbed compared to protons while traversing through the medium. Hence we put a constraint of 0 < K ep ≤ 1. In order to constrain B and N H values, we studied various articles 13 and decided to choose as an upper limit the value that was greater than all those found in the literature. Zero was chosen as a lower limit for both variables. Finally, for the amplitude, which is a re-normalizing constant with no obvious constraints, the boundary was chosen to allow the fit to converge, given all the other constraints. The constraints applied to each parameter are listed in Table 6.4.

Parameter

Naima plots

A random sampling of space does not yield quick useful results hence the algorithm is optimised to go to regions of higher posterior to avoid searching regions of the parameter space which poorly fit the data. To begin MCMC sampling, we start with defining walkers, which specify a set of parameter combinations that are then perturbed slightly and vary within the prior range set by us. Every update prompts the walker to explore the parameter space. Each walker, steps towards a new set of permitted parameter values within the given range and outputs a model with those parameters. Then a comparison is made between the model with best-fit parameters and the data, and if the likeliness ratio between the new model vs the current model is better, then the walkers move in that direction. This is repeated until it finds the region in the parameter space where the posterior distribution peaks and the model most likely generates the data. During a run, the set of chosen parameters is called a chain, with each step representing a link in that chain. Walkers should be set such that their number is two times the initial free parameters. For this study, 50 walkers have been used to ensure more coverage of the parameter space. During the beginning of the MCMC run, some iterations can be thrown away. This is called the burn-in period. Since a Markov chain has no memory, hence burning initial samples would not alter the calculations. Burn-in is simply done to enter the region with high probability. In this study, 50 steps have been used for burn.

Shown in Figure 6.2 is the example of the output of the Naima MCMC run. It is the chain plot for the N H value obtained from the fit of the SNR HAWC J2227+610 with the lepto-hadronic model. The plot on the top-left shows the walker traces where each line represents a walker. We can see how the walker varies with the number of steps around the maximum value. On the right-hand side, the posterior distribution of the parameter is shown. The dashed line represents the median value, uncertainty is shown by the grey region at the confidence level of 1σ. Information about the number of walkers, run, the mean acceptance fraction, the median value, and the uncertainty is summarised in the bottom left. To get an estimate of whether a good convergence has been reached or not, the mean acceptance fraction can be read. A low value of acceptance fraction ( < 0.25) suggests poor functioning of the chain. Through these figures, we can see that walkers are equally distributed around the median and that the distribution on the right roughly follows a Gaussian distribution. These are indicators of a wellbehaved run.

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A so-called corner plot can be very useful to get a quick glimpse of the covariance 14 between the different parameters. The marginalised distribution, which is a distribution focusing on only one variable while ignoring the rest of the variables in a dataset, for each parameter is in the histograms. The contours represent the 1σ, 2σ, and 3σ uncertainty around the most likely parameter value. The dashed lines in each one-dimensional distribution indicate the 16%, 50%, and 84% quantiles. All the plots illustrate that the fit is good.

Naima fit results for selected SNRs

In this section, we show all the SNR fit results obtained by using both the leptohadronic and leptonic scenarios. For each source, we show the SED plots, and the obtained fit parameters and give a brief discussion of the results, together with a comparison to the literature. In all the SED plots, the black dots represent the observations (Table 6.2) from several instruments for which the value of the flux measurement at a given energy is known with a precise uncertainty. Red triangles are used to differentiate those observations for which the flux measurements are uncertain and hence have been plotted as an upper limit.

In the following figures, the contribution of the radiative emissions from the sources is shown using different curves and colors. The solid yellow curve depicts the synchrotron theoretical flux, the green dot-dash curve represents the theoretical flux due to bremsstrahlung radiation, the orange curve with a dotted pattern gives the theoretical flux pertaining to inverse Compton, and the red dashed curve corresponds to emission due to pion-decay. The combined contribution of all these emissions is given by the blue solid curve.

It must be pointed out that exact comparison to other results is often difficult due to several reasons. In various literature, the authors have invoked their own fitting models each with its own set of assumptions, in order to reproduce the observed flux. Additionally, in each case, different datasets have been used thus making direct comparison difficult. In the following discussion, the information on the type and age of SNRs has been referred from various papers shown in Table 6.3. • RX J0852.0-4622: Also referred to as RX J0852.0-4622, this source is a young shell-type SNR.

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107

It was extensively studied by the H.E.S.S collaboration [START_REF] Abdalla | Morphology studies and resolved spectroscopy[END_REF]. The authors conclude that both leptonic and hadronic emission scenarios remain plausible. The lack of thermal X-ray emission is in favor of the leptonic scenario. Conversely, it was suggested that a highly inhomogeneous clumpy environment could increase γ-ray emission from hadronic interactions (similar to the case of SNR RX J1713. .

In this study, Fermi data points starting from 2 x 10 8 eV have been included using the ASDC data archive. Their inclusion leads to a pronounced hadronic bump around 10 9 eV, similar to that of HAWC J2227+610. The ∆BIC being ∼ 94 favors the lepto-hadronic scenario. Through this SNR, we can see that a fit with the pure leptonic model will not be sufficient to cover the entire γ-ray domain. Whereas, with the help of pion-decay radiation in the lepto-hadronic scenario the increased emission in the GeV domain can be accounted for. • RX J1713.7-3946: Among all the shell-type SNRs, the young SNR RX J1713.7-3946 is one of the brightest TeV sources [START_REF] Abdalla | observations of RX J1713.7-3946 with improved angular and spectral resolution: Evidence for gamma-ray emission extending beyond the Xray emitting shell[END_REF]. The HESS collaboration performed an MWL study but neither hadronic, leptonic nor both could explain the data unambiguously. However, the paper of ref.

[?] suggests that the γ-ray emission from RX J1713.7 -3946 could be explained by the π 0 decay produced in hadronic CR interactions with a dense, clumpy gas embedded in the SNR shell.

Our study reveals the ∆BIC of ∼ 6 which tends towards favoring the leptohadronic model. The prospect of observing RX J1713.7-3946 by CTA was studied in ref. [START_REF] Acero | Prospects for Cherenkov Telescope Array Observations of the Young Supernova Remnant RX J1713[END_REF]. The study predicts that measurements at high energy by CTA will yield further constraints on leptonic or hadronic scenarios using spectral and morphological studies. The fit of SNR RX J1713.7-3946 provides a stark contrast to the previous one. Looking at these figures, we can see that both lepto-hadronic and leptonic scenarios seem to reproduce the observations well. This is further confirmed by the similarity of the obtained likelihood value. It is difficult to conclude which scenario is favoured. • Cassiopeia A: Also known as G111.7-2.1, this young shell-type SNR has been previously studied by the MAGIC collaboration ( [START_REF] Ahnen | A cut-off in the TeV gamma-ray spectrum of the SNR Cassiopeia A[END_REF] and references therein). It has been observed to expand supersonically, producing a shock wave where its high magnetic field can be amplified, leading to the possibility of CR acceleration up to PeV energies. A year-scale variability in the X-ray filaments suggests a magnetic field in the order of mG. The authors combined Fermi -LAT and MAGIC data and concluded that γ-ray emission from 60 MeV to 10 TeV can be attributed to the population of high-energy protons with an energy cut-off at 10 TeV. The ∆BIC of ∼ 3895 obtained from our MWL fits tend to favor the leptohadronic scenario. In our case, the proton energy cut-off was found to be ∼ 20 TeV, which agrees with the paper referred to above. Furthermore, the fit result using the lepto-hadronic model gives us a magnetic field of ∼ 960 µG. • CTB 37A: Also referred to as G348.5+0.1, this source was detected by the Fermi collaboration [START_REF] Brandt | A view of supernova remnant CTB 37A with the Fermi Gammaray Space Telescope[END_REF]. This complex source is interacting with several dense MC ( [START_REF] Abdollahi | On the Origin of the Gamma-Ray Emission toward SNR CTB 37A with Fermi-LAT[END_REF] and references therein). Previous studies conclude that the MWL observation is mostly due to the re-acceleration of pre-existing cosmic rays by radiative shocks in the adjacent clouds.

In our study, the ∆BIC value of ∼ 147 favors the lepto-hadronic scenario. Hadronic contribution is most prominent around the GeV energy domain.

In addition to this, in our study, additional data points from HESS indicate leptonic contribution above 10 TeV (Figure . 6.20). CTA will provide a better angular resolution to resolve the complex source into individual components. 6.9: Parameters obtained from the fit for HAWC J2227+610 using Naima.

• HAWC J2227 + 610: Also known as G106.3+2.7, this source is a cometary medium-aged SNR with a tail in the Southwest and a head containing the PSR J2229+6114 in the Northeast [START_REF] Bao | On the hard γ-ray spectrum of the potential PeVatron supernova remnant G106.3+2.7[END_REF]. In a recent paper by the HAWC collaboration [START_REF] Albert | HAWC J2227+610 and Its Association with G106.3+2.7, a New Potential Galactic PeVatron[END_REF], γ-rays above 100 TeV were reported. Despite combining results from VERITAS and HAWC, the authors could not confirm the origin of high-energy photons.

The instrument ASγ has also reported observation of high-energy gamma rays up to 100 TeV [START_REF] Yang | A Possible Hadronic Origin of TeV Photon Emission from SNR G106.3+2.7[END_REF]. MWL Fit with data from the instrument Tibet AS+MD [START_REF] Amenomori | Potential PeVatron supernova remnant G106.3+2.7 seen in the highest-energy gamma rays[END_REF], show a spectral index of 1.79 and an exponential cut-off at 499 TeV. These parameters are similar to the parameters found in this study. Additionally, the authors correlate the γ-ray emission above 10 TeV with a MC which further supports the hadronic scenario. Furthermore, a recent paper by LHAASO collaboration [START_REF] Cao | Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ-ray Galactic sources[END_REF] confirms HAWC J2227+610 to be a PeVatron. In our study, the ∆BIC obtained was ∼ 40 which favors the leptohadronic scenario. All these facts lead towards making HAWC J2227+610 CHAPTER 6. MULTIWAVELENGTH ANALYSIS the most potential PeVatron candidate amongst all the SNRs in this study. • HESS J1731-347: Also called G353.6-0.7, this source is a shell-type medium-aged SNR. It has been studied by the H.E.S.S. collaboration using MWL emission detected in radio, X-ray, and γ-rays [START_REF] Abramowski | A new SNR with TeV shell-type morphology: HESS J1731-347[END_REF]. The authors conclude that a large fraction of the kinetic energy of the explosion is transferred to accelerated protons. In a more recent paper, [START_REF] Cui | Is the SNR HESS J1731-347 Colliding with Molecular Clouds[END_REF], the observed high-energy domain of the MWL SED indicates a hadronic contribution that can be explained using a shock-cloud collision model. In our study, the ∆BIC of ∼ 11 also supports the lepto-hadronic scenario with a strong contribution from hadrons in the high-energy domain extending up to 10 14 eV. • IC 443: Also known as SNR 189.1+03.0, this source is a shell-type medium-aged SNR. The characteristic pion-decay feature in the γ-ray spectra of the two SNRs, IC 443 and W44, has been reported by the Fermi collaboration [START_REF] Ackermann | Detection of the Characteristic Pion-Decay Signature in Supernova Remnants[END_REF] providing evidence that CR protons are accelerated in these SNRs. In both sources, the spectra exhibit a break at ∼ 200 MeV that is related to the π 0 production threshold. For our study, only IC 443 was considered due to insufficient data available for W44. The MWL study yields the ∆BIC of ∼ 16, which seems to favor the lepto-hadronic scenario. The SED shows a hadronic contribution dominating around 10 9 to 10 11 eV. Table 6.12: Parameters obtained from the fit for W28 using Naima.

RESULTS

• W 28: W28, also known as SNR G006.4-00.1, is a mixed morphology old SNR. In its vicinity, various sources are present yielding TeV gammas [START_REF] Aharonian | Discovery of very high energy gamma-ray emission coincident with molecular clouds in the W28 (G6.4-0.1) field[END_REF]. In the paper, the authors conclude that the association of W28 with nearby MC could yield high-energy γ-rays of hadronic origin. This SNR was also studied in ref. [START_REF] Hanabata | Detailed investigation of the gamma-ray emission in the vicinity of SNR W28 with Fermi-LAT[END_REF]. The authors suggest that the interaction between the nearby MC and CRs escaping the SNR could explain emission from the source.

In our study, we have used the high-energy data available in gamma-cat corresponding to HESS J1801-233. The Fermi LAT counterpart taken from the ASDC catalogue coincides with the coordinates of the same source. We obtain the ∆BIC of ∼ 35 which tends towards favoring the lepto-hadronic scenario. The SED shows a strong hadronic component around 10 9 eV corresponding to the π 0 threshold.

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115

Figure 6.12: MWL SED of the SNR W 49B modeled by using the hadronic scenario (left) and the leptonic scenario (right).

Parameters Lepto-hadronic Leptonic log10(Amplitude)

49.90 • W 49B: Also known as G043.3-00.2, this source is an old SNR with mixed morphology observed to be interacting with MC. The Fermi -LAT collaboration jointly with the H.E.S.S. collaboration [START_REF] Abdalla | The supernova remnant W49B as seen with H.E.S.S. and Fermi-LAT[END_REF] found the spectral features to be indicative of the hadronic origin of the γ-ray emission.

Our study gives the ∆BIC value of ∼ 873, strongly favoring the leptohadronic scenario. The best fit is obtained when the pion-decay component is present at around 10 9 eV.

Obtained fit parameters

The range of obtained fit parameters for all the studied SNRs, assuming the two different scenarios, can be found in Table 6.14. The following observations can be made. For the lepto-hadronic scenario, higher magnetic fields are needed to match the observed flux compared to the leptonic scenarios, which consistently predict a lower magnetic field irrespective of its ability to fit data well. Overall, the parameters are within the acceptable values recorded in various papers.

Assuming the lepto-hadronic scenario, the cut-off value of electron (coe) and proton (cop) distributions for different SNRs have been tabulated in Table 6.15. The maximum cut-off value for protons is ∼ 447 TeV for the SNR HAWC J2227+610. This value is still below 10 15 eV required for a PeVatron source. However, it looks very promising. Figure 6.13 shows the magnetic field reported in the literature for various sources as a function of the magnetic field obtained from the fit. A rather good correlation between these two values is observed. However, in the present study, the scarcity of data around the synchrotron peak limits the accurate determination of the magnetic field. On the other hand, the fit at the highest energies is rather well constrained with existing data which allows us to determine the contribution of inverse Compton and indirectly constrain the electron distribution and therefore also estimate the B-field values.

RESULTS

Figure 6.13: The value of the magnetic field obtained from the fit as a function of the reference magnetic field. The age and the magnetic field of the SNRs have been taken from Table 6.3, and the references therein. The old SNRs are indicated by blue circles, while the young SNRs are represented by orange circles. The radiative losses of electrons should depend on the age of the SNR, the younger the SNR, the shorter the cooling time for electrons. In Figure 6.14, one can observe that the young SNRs have higher cut-off energies compared to old SNRs. This could indicate either a shorter cooling time or a more powerful acceleration for young SNRs. We have also studied the correlation between the magnetic field and the cut-off energy of protons, as shown in Figure 6.15. We can observe that the proton energy cut-off value increases with an increasing magnetic field. On the top right corner of the plot, we can see the SNRs RX J1713.7-3946, Cassiopeia A, HESS J1731-347, and HAWC J2227+610, which are identified as potential PeVatron candidates in our study, as will be discussed later. Additionally, contrary to electrons, we don't see any trend as a function of the age of the SNRs.

In Figure 6.16, we have studied the correlation between the magnetic field and the cut-off energy of protons along with the dependency on the type of SNR. No correlation was observed between the magnetic field and the type of SNR or the proton energy cut-off and the type of SNR.

Finally, we saw no correlation between the number density and the type of SNR. Similarly, no correlation was observed between the magnetic field and the type of SNR nor between the proton energy cut-off and the type of SNR. We have also positioned the studied SNRs in the Hillas plot, as shown in Figure 6.17. The magnetic field is the one obtained from the fit and the size of each SNR CHAPTER 6. MULTIWAVELENGTH ANALYSIS is obtained from TeVCat. This figure indicates that most of the studied SNRs would be able to accelerate protons above 1 PeV.

Lastly, for a few sources, the Naima fit results provided quite hard spectral indices. These indices lie within the acceptable range provided by CR measurements. It is difficult to understand the precise physical reason since a CR spectrum is a result of several different sources, each accelerating different elements. However, a hard index generally implies that the particular SNR is an efficient accelerator.

Joint observations from the experiments such as CTA, HAWC, and LHAASO would allow us to observe much higher energy photons and give more constrain to sign hadron acceleration up to higher energies. The parameters obtained in this study for the radiative models can be used to simulate data for these instruments to study their detection capability of observing PeVatron sources (more in Chapter 7).

Quantitative analysis

Three different methods were used to quantify the hadronic contribution: likelihood comparison, BIC criterion, and flux contribution as a function of energy bins.

Likelihood comparison

A method that can be used to distinguish which model describes the observations better is the likelihood comparison. Naima returns the likelihood of the best-fit parameters as an output of the fitting process. Likelihoods were obtained for fits using the two different models, pure leptonic and lepto-hadronic models.

We have compared the likelihood of each leptonic and lepto-hadronic model with the sum of the likelihood of both models, given by r. The equations used are given by Eq. 6.10 a and Eq. 6.10 b.

r lepto-hadronic = 1 - χ 2 L+H χ 2 L + χ 2 L+H . ( 6
.10 a)

r leptonic = 1 - χ 2 L χ 2 L + χ 2 L+H . (6.10 b)
The results of this comparison can be found in Figure . 6.18. In the figure, for each source fitted with a particular model, the blue bar corresponds to Eq. 6.10 a and the yellow bar corresponds to Eq. 6.10 b. The total length of the bar is constrained to 1. The bar tends to +1 if the likelihood of the lepto-hadronic model is greater than that of the leptonic model and to -1 otherwise. criterion to determine which scenario is favored for each source. The ∆BIC value for different sources is shown in Table 6. [START_REF] Hummel | The first stars: formation under cosmic ray feedback[END_REF].

Recalling that for ∆BIC > 2 the model with the smaller BIC is slightly favored, and for ∆BIC > 6 the model with the smaller BIC is clearly favored, we can see that the lepto-hadronic scenario is favored for the majority of the sources given our initial assumptions for radiative models.

However, for the SNR RX J1713.7-3946, we get a ∆BIC value of 6. Although it appears to favour the lepto-hadronic scenario, it is difficult to obtain a firm conclusion. .

Hadronic contribution as a function of energy

In the previous studies, only the overall shape of the SED resulting from various radiative contributions was taken into account. However, a hadronic contribution can become more important when focusing on specific energy ranges. Hence using a lepto-hadronic scenario for each SNR, an integration over the flux ranging from 10 7 to 10 15 eV was performed. This method allows us to compare the relative importance of the leptonic and hadronic processes at different energies. Figure 6.19 depicts how a certain energy range of fixed width is selected as shown by the peach bar. The bar is moved along the energy axis and the amount of flux in that energy bin is integrated. Figure . 6.20 shows the results of this binned integration for each source. We can conclude that in the range of E ∈ [10 9 -10 11 ] eV, the hadronic process dominates for every source. Additionally, most sources show a contribution from the leptons up to the highest energies (TeV range). An interesting result that can be highlighted from this plot, is that the SNR RX J1713.7-3946, HESS J1731-347, 6.8. QUANTITATIVE ANALYSIS 123 HAWC J2227+610, and Cassiopeia A show fit results dominated by hadronic contribution up to the high-energy range. This opens up a promising possibility for these four sources to eventually be PeVatrons.

General features

All the sources show important hadronic contributions, and in most cases, a simple leptonic model fails to explain the observed spectrum. All the SNRs modeled using the lepto-hadronic scenario show a pion-decay bump peaking at different energies. This is due to the varying cut-off energy of the proton particle distribution. This led us to divide SNRs into two groups. The first group contains SNRs in which the high-energy component peaks at 10 9 eV. This group includes W28, RX J0852.0-4622, IC 443, CTB 37A, and W49 B. Clear proof of hadronic contribution can be found if data around the pion-decay threshold is available. Inverse Compton processes cannot explain the hard rise of the photon flux. Therefore more data around the π 0 threshold energy would be valuable to provide a signature of a hadronic contribution. The second group contains the SNRs where the pion-decay bump peaks at 10 12 eV. This group comprises Cassiopeia A, HESS J1731-347, HAWC J2227+610, and 6.9. GENERAL FEATURES 125 RX J1713.7-3946. This important hadronic contribution at high-energy may be attributed to the harder slope of the parent proton distribution or the presence of heavier elements. In the case of SNRs CTB 37A, RX J1713.7-3946, W49 B, and W28 the model predicts a softer spectrum above 10 13 eV, which clearly deviates from the observations. This excess flux at high-energy is highlighted when using the pure leptonic scenario. This may imply the presence of hadronic processes since leptonic processes at such high energies are strongly attenuated. In order to confirm this observation, more data would be required at energies beyond 10 13 eV. The rise of the flux at high-energy compared to the declining radiative model may imply a change in the acceleration process possibly due to the re-acceleration of particles or the effect of the enhanced magnetic field. Furthermore, it may also be a signature of acceleration of heavier elements which although less in number can contribute significantly at higher energies. In order to fit data points that follow this trend, we may have to consider a pion-decay model which is an outcome of elements heavier than just protons. This hypothesis needs to be tested which can only be done once more data is available beyond 10 13 eV.

PeVatron candidates from this study

Referring to Figure 6.20, where the high-energy contributions at different bins are shown, we can see that Cassiopeia A, HESS J1731-347, HAWC J2227+610, and RX J1713.7-3946 have important hadronic contributions up to the highest energies. This could hint toward the possibility of these SNRs being PeVatron sources. Figure 6.21 shows the sensitivity curves of CTA North and CTA South together with the fluxes of the four SNRs mentioned above. The CTA sensitivity curves have been calculated by using CTAO Instrument Response Function (IRF) -prod5 version v0.1 [START_REF]Cherenkov Telescope Array Observatory and Cherenkov Telescope Array Consortium[END_REF] 15 . The telescopes have been assumed to be pointing parallel to each other. The performance has been estimated for a zenith angle of 20 degrees North or South, depending on the source location, with an observation time of 50h. The so-called Alpha configuration has been used for array layout, which includes 14 MSTs and 37 SSTs in the Southern site and 4 LSTs and 9 MSTs in the Northern site. The figure shows that CTA will clearly be able to add data to these four sources at high-energy, allowing us to confirm emission processes at those energies. CTA will provide flux with much less uncertainty compared to the present instruments and hence will help constrain the spectral characteristics of the SNRs better. This will be studied in detail in Chapter 7.

It should be noted that all these results are an outcome of an assumption that the parent particle distribution consists of a single proton energy distribution. We can also take into account the parent distribution which includes heavier particles which will be discussed in detail in Chapter 7. Including heavier particles would lead to particles accelerated to energies higher than those of protons [START_REF] Thoudam | Cosmic-ray energy spectrum and composition up to the ankle: the case for a second Galactic component[END_REF].

In the next section, the output parameters obtained from Naima have been used to get a set of physical input parameters to simulate synthetic SNRs' spectra at high energies, to check if CTA does in fact increase the chances of detecting a PeVatron. With an optimal sensitivity between 10 11 and 10 14 eV and acute angular resolution in this energy range, CTA is expected to bring further clarity about whether or not a particular SNR is a PeVatron [START_REF]Science with the Cherenkov Telescope Array[END_REF].

Conclusions

In this study, we performed an MWL analysis of 9 galactic SNRs using publicly available data from recent experiments. To build MWL SEDs, we assumed that the observed SED was due to the synchrotron, bremsstrahlung, inverse Compton and pion-decay processes. A lepto-hadronic scenario and a pure leptonic scenario were considered to model the observed flux. The Naima package was used to fit the observations. The fit results were analysed using three different methods: likelihood comparison, BIC criterion, and the estimation of the hadronic contri-6.10. CONCLUSIONS 127 bution as a function of energy bins. Furthermore, the results for each source were discussed in light of previous studies reported in various publications.

The Likelihood method used to compare the two scenarios showed more confidence in the lepto-hadronic scenario than in the purely leptonic scenario for most sources. Further proof of inclination towards the lepto-hadronic scenario was provided by determining the ∆BIC value. However, solely based on ∆BIC values, no firm conclusions can be drawn for the SNR RX J1713.7-3946.

The results obtained for binned energy contribution show that none of the sources have a proton distribution with cut-off energy ≥ 10 15 eV, and therefore none can be classified as PeVatrons. However, four sources (SNR Cassiopeia A, RX J1713.7-3946, HAWC J2227+610, and HESS J1731-347) have shown important hadronic contributions at high energies. This opens up a promising possibility for these sources to be PeVatrons. Additionally, the observations for the SNR RX J1713.7-3946, CTB 37A, W49B, and W28 seem to show higher flux than predicted by the model above 10 13 eV when continuing to higher energies making them an interesting study for the possible acceleration of heavy elements. In the future more data at high energy from instruments such as CTA, HAWC and LHAASO would allow us to constrain better the hadronic contribution in the high-energy region.

Most SNRs modeled using the lepto-hadronic scenario have a pion-decay bump appearing above ∼ 200 MeV. This corresponds to the π 0 production threshold (280 MeV) for the incident protons. Here the hard rise of the photon flux cannot be explained by leptonic processes. Therefore more data around π 0 threshold energies would be valuable to provide a signature of hadronic contribution.

With an optimal sensitivity between 10 11 and 10 13 eV and acute angular resolution in this energy range, CTA will be able to further clarify whether a particular SNR is a PeVatron or not [START_REF]Science with the Cherenkov Telescope Array[END_REF].

Apart from SNRs, several other Galactic PeVatron candidates also exist, as enlisted in Chapter 1. HAWC Collaboration has reported various highest energy γ-ray sources detected up till now by the instrument [START_REF] Abeysekara | Multiple Galactic Sources with Emission Above 56 TeV Detected by HAWC[END_REF]. With nine sources identified as pulsars showing high-energy emissions > 56 TeV and three pulsars showing emissions > 100 TeV, with two (eHWC J1825-135 and eHWC J1907+063) of them being very close to an SNR (composite SNR G015.4-00.1 and interacting SNR W49B respectively). 6 of these sources will be in the detection realm of H.E.S.S and the upcoming Southern CTA FoV. In addition, LHAASO has announced the discovery of 12 Galactic γ-ray sources with emissions extending up to several 100 TeV with only one year of observation and a half-completed array [START_REF] Cao | Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ-ray Galactic sources[END_REF]. Out of these sources, γ-ray emission from a region where shell-type SNR HAWC 2227+610 is located has also been identified. However, due to poor angular resolution, the sources have not been spatially resolved sufficiently to pinpoint the source of acceleration. It can be foreshadowed that CTA South, once fully functional, will be able to declare with the highest certainty a PeVatron candidate compared to the aforementioned instruments. Based on the present results, however, CTA can benefit from focusing on a reduced list of potential candidates and preparing a scientific proposal dedicated to the PeVatron key science project with high priority.

Chapter 7

Simulations for CTA

Introduction

Finally, nearing the end of this thesis, let us recall the major points which have motivated this final chapter. This thesis aimed to answer the riddle of the origin of the "knee" feature of the CR spectrum, around 10 15 eV. In our study, we selected SNRs as a potential PeVatron candidates. Various SNR SEDs were fit to determine whether hadronic contribution can be seen at the highest energies. The four SNRs RX J1713.7-3946, Cassiopeia A, HESS J1731-347, and HAWC J2227+610 were then identified as potential PeVatron sources (to recall, refer to Figure 6.20 in Chapter 6).

After seeing the fit results of the selected SNRs, two questions stood out:

1. How will CTA observe these four potential PeVatron sources?

2. Can CTA detect the potential contribution of heavy elements in the flux at high energies?

More data points are required in the high-energy domain to answer these questions. This motivated the simulation of the CTA flux for the four potential PeVatron sources. The output parameters from the fit results of the multiwavelength analysis done using Naima in Chapter 6 are used as input parameters for CTA flux simulation. Using the Naima library in Gammapy allows data simulation of physically-motivated models instead of plain functional forms.

In section 7.3, first, the fluxes for the four SNRs are simulated using several physically-motivated models. Then using Naima, a re-fit of the SEDs of the selected sources is made after adding the simulated CTA data points along with the set of the observed data. With this analysis, we try to deduce whether adding CTA data points changes the fit results. For the SNR HAWC J2227+610, observations from LHAASO up to hundreds of TeV are available. Therefore, in section 129 130 CHAPTER 7. SIMULATIONS FOR CTA 7.4, different CTA fluxes are simulated for HAWC J2227+610 with varying proton energy cut-off values. Using the simulated CTA flux, a fit of the SNR is made using Naima for each cut-off value. The fit results are compared to deduce information about CTA's capability to detect the fluxes with a different high-energy proton cut-off. Lastly, a detailed analysis has been done for RX J1713.7-3946 in section 7.5 to answer question no. 2, the effect of adding heavier elements. To do so, we explore the effect of using a modified pion-decay model to fit RX J1713.7-3946 using Gammapy.

Science analysis tools

A high-level analysis is required to obtain useful information from the ground-based γ-ray instruments. Instruments such as H.E.S.S, MAGIC, and VERITAS have already provided us with analysis tools required to get detailed images and spectra of objects in the high-energy sky (although not publically available). CTA aims to operate as an open observatory in the future and therefore, it is of paramount importance to construct easily accessible open software to analyse this data. At first, raw data is captured from the cameras of the telescope arrays and injected into a pipeline for initial processing. This involves calibration of data, reconstruction of events, and performing analysis for selecting gamma-ray-like events. The last step also includes providing the Instrument Response Functions (IRFs), a mathematical function, or a set of lookup tables that relates the measured event to the incoming 7.2. SCIENCE ANALYSIS TOOLS 131 photon. For more information, check Appendix D. The final data products of the pipeline contain event lists (EVT), IRFs, and auxiliary data such as pointing information. They are transmitted via the Data Dissemination unit to the entire scientific community for further analysis. Now any observer can download the data and use the dedicated software of their choice for high-level analysis, such as generating spectra and more. Currently, there are two software packages that allow us to analyse CTA data: ctools [START_REF] Knödlseder | GammaLib and ctools -A software framework for the analysis of astronomical gamma-ray data[END_REF] and Gammapy [START_REF] Nigro | Towards open and reproducible multi-instrument analysis in gamma-ray astronomy[END_REF].

ctools

ctools is a software inspired by Fermi's science tools (ftools1 ). It is based on Gam-maLib which is an open-source C++ library allowing high-level scientific analysis of γ-ray data independent of any instrument. Similar to ftools, ctools provides several building blocks, each performing a well-defined task for data analysis such as observation selection or model fitting. It can be used as command-line executables allowing easy analysis even with users without any programming skills. The tools have also been made accessible through dedicated Python modules as an alternative user interface with the software.

Gammapy

Gammapy is an open-source analysis package that has been developed to provide a high-level analysis of IACT data. High-level data analysis is any operation that yields physical results (level ≥ DL3) such as maps, spectra, and catalogs.

The various steps that the data follow (in both ctools and Gammapy)are shown in Figure 7.2. At the DL3 stage, we prepare the data for high-level analysis. DL3 data is exported from a particular storage format (which is instrument-specific) into a common format such as a flexible image transport system (FITS) which has flexible storage units called header-data units (HDU). Moving from DL3 to DL4 involves reducing the data from event lists to high-level containers known as Datasets in Gammapy. Finally, DL5 is the highest level which contains endproducts such as maps, spectra, and lightcurves. Gammapy has been recently selected as the official analysis software for the CTA Observatory2 . It has already been used to analyse data from present instruments and provided great results. Furthermore, the H.E.S.S. collaboration officially supports gammapy for high-level analyses as well 3 . Gammapy has been used for the simulations presented in this

Flux simulation for selected sources

Our studies in Chapter 6 showed that the lepto-hadronic models are preferred over the pure leptonic models. For the four selected SNRs, we see a major contribution from the pion-decay radiation with smaller contributions from the bremsstrahlung and the inverse Compton radiations at high energies. For the simulation of the CTA fluxes, it is necessary to check which radiative models help generate the fluxes that accurately match the present instruments' observations.

Using Gammapy, a 1D binned analysis was done to simulate the spectra of the sources. Spectral analysis allows us to consider all the events inside a source region and bin them in energy only, providing a 1D dataset. Extraction of γ-ray spectrum involved several steps. First, the observational parameters were defined, which include the livetime, the source coordinates, the offset 4 , the integration-radius 5 , and the energy range for which data needs to be simulated. Following that, we chose a spectral model based on which the flux for the source was generated. Then an in-memory observation was convolved with the IRFs, to obtain the predicted number of counts. IRF was chosen according to the location of the source. Finally, counts for each observation were generated using the fake() function. With the dataset ready, a SkyModel was defined, which contains the spectral model and the dataset on which the model is to be applied. It is necessary to define a SkyModel because the Gammapy fitting tool can only access the Sky-Model, not its individual components. With all the necessary ingredients ready, a gammapy.modeling.Fit object was created and run to fit the model parameters. In the end, gammapy.estimators.FluxPointsEstimator was applied, which computed the flux points for the spectral part of the fit.

Gammapy allows us to choose from several models depending on the scientific goal. Since we are only interested in simulating the spectral shape of the observed fluxes, in our case, a simple spectral model was chosen. To simulate the flux of different physical models, we used the Naimaspectralmodel library, which provides an interface with the physical models defined in Naima. For this study, we created a spectral model that convolves an ExpCutoffPowerLawSpectralModel, defining the parent particle distribution of electrons and protons with different radiative models such as bremsstrahlung, inverse Compton, and pion-decay. To account for contribution from more than one radiative model, a CompoundSpectralModel was defined, which allowed combining different radiative components to provide the final flux. For the simulation, we have used the Naima fit results as input parameters for models in Gammapy. The list of parameters for SNR RX J1713.7-3946, Cassiopeia A, HESS J1731-347, and HAWC J2227+610 can be found in Chapter 6 in the Tables 6.6, 6.7, 6.10, and 6.9, respectively.

The SEDs combining the simulated and observed data were then fitted using Naima, similar to what was done in Chapter 6. The theoretical models used were inverse Compton, Bremsstrahlung, and pion-decay. It is important to note that the simulated flux, for which the flux error was significantly larger than the flux itself, has been neglected. 134 CHAPTER 7. SIMULATIONS FOR CTA

RX J1713.7-3946

To simulate CTA flux for RX J1713.7-3946, three different spectral models were created:

• A proton pion-decay model (PD).

• A combined model of inverse Compton and pion-decay radiations (IC+PD).

• A combined model of bremsstrahlung, inverse Compton and pion-decay radiations (BRE+IC+PD).

For the flux simulation using Gammapy, the procedure discussed previously was followed. RX J1713.7-3946 was simulated using 200 hrs of livetime (based on study y Gaia et al. [START_REF] Verna | HAWC J2227+610: a potential PeVatron candidate for the CTA in the northern hemisphere[END_REF]) and the CTA South Prod5 IRF with a zenith angle of 20 • . The on-radius was set as 0.65 • with the offset of 1 • . The values for the on-radius and the offset were taken from TeVCat. TeVCat has been used for the remaining sources as well. These fluxes were then combined with the real observations. The resulting SED was then fit by Naima using the theoretical radiative models. Combining the observed data with the simulated data can increase systematic uncertainties due to a lack of knowledge about the inter-instrument calibration, and hence the fitting has been performed by removing those observations in the energy range which are covered by simulated CTA data points. The radio and the X-ray data points have been included for a fair comparison with the MWL analysis done in Chapter 6. show the fit results of Naima for the combined observations of real data (black points) in the lower energy region and simulated CTA data points at the higher energy region using the three different spectral models. The solid yellow curve depicts the theoretical synchrotron flux, the green dot-dash curve represents the theoretical flux due to bremsstrahlung radiation, the orange curve with a dotted pattern gives the theoretical flux of the inverse Compton radiation, and the red dashed curve corresponds to emission due to the pion-decay radiation. The solid blue curve gives the combined contribution of all these emissions. Figure 7.3 shows the Naima fit result of the radiative models with the combined observations of real observations in the low-energy region and the simulated CTA data points in the high-energy region. The CTA flux has been simulated using a spectral model of only pion-decay radiation. We see CTA's capability of providing flux which covers a wide energy range starting from 30 GeV to ∼ 150 TeV. Table 7.1, lists the output parameters of the fit of the theoretical models against the observed flux (computed in Chapter 6) and the combined data of real data at low-energy and simulated data at high-energy.

Parameter

Real Observations Combined Observations log10(Amplitude) 47.060 The Naima fit parameters obtained from the fit for the lepto-hadronic model of RX J1713.7-3946 with the real observations, and combined data of the observed data at low-energy and the CTA simulated data points at high-energy generated using the PD model.

In Figure 7.4, the CTA flux has been simulated by using a combined spectral model of inverse Compton and pion-decay radiations spanning the same wide energy range mentioned above. Table 7.2, lists the output parameters of the fit of the real observations and combined observations of real and simulated CTA data. It can be seen that the parameters only slightly vary from the previous fit result.

Parameter

Real Observations Combined Observations log10(Amplitude) 47.060 The Naima fit parameters obtained from the fit for the lepto-hadronic model of RX J1713.7-3946 with the real observations, and the combined data of the observed data at lowenergy and the CTA simulated data points at high-energy generated using the IC+PD model.

Table 7.4 lists the MaxLogLikelihood and the BIC values to allow for model comparison. The fit result of the real observations based on present instruments (original data, see Chapter 6) is compared with the fit results after replacing the high-energy points with only the simulated CTA flux generated by considering different physical models (PD, IC+PD, and BR+IC+PD). This table shows that the absolute MaxLogLikelihood value after using only the simulated CTA data is lower compared to that obtained for the original data. This shows that CTA will allow us to constrain better the model parameters compared to present observations. The MaxLogLikelihood is the smallest for the flux simulated with only the pion-decay model. Therefore, simulations using only the pion-decay model will be generated to analyze the remaining SNRs since all chosen SNRs have similar radiative contributions at high energies.

.

Model

HESS J1731-347

The flux for HESS J1731-347 has been simulated using 200 hrs livetime and the CTA South Prod5 IRF with a zenith angle of 20 • . The on-radius has been set as 0.27 • with the offset of 0.70 • . In Figure 7.7, the CTA flux was simulated by using a spectral model of the pion-decay radiation. Table 7.6 lists the output parameters of the fit of the theoretical models against the real observations (as in Chapter 6) and a combined data of the real flux and the simulated CTA flux. For HESS J1731-347, CTA could produce additional points outside the energy domain of the current instruments. The value of the MaxLogLikelihood is slightly larger when simulated CTA data points are added. This may arise due to the fluctuation in the simulated flux at the highest energies. The Naima fit parameters obtained from the fit for the lepto-hadronic model of HESS J1731-347 with the real observations, and combined data of the observed data at lowenergy and the CTA simulated data points at high-energy using the PD model.

HAWC J2227+610

HAWC J2227+610 has been simulated using 200 hrs livetime and the CTA North Prod5 IRF with a zenith angle of 20 • . The on-radius has been set as 0.20 • with the offset of 0.60 • . In Figure 7.8, the CTA flux has been simulated by using a spectral model of the pion-decay radiation in the energy range mentioned above. Table 7.7 lists the output parameters of the fit. The Naima fit parameters obtained from the fit for the lepto-hadronic model of HAWC J2227+610 with the real observations, and combined data of the observed data at lowenergy and the CTA simulated data points at high-energy using the PD model.

As a conclusion for the studies above, we may say the following:

1. It is clear that CTA data points cover a wide energy range (30 GeV to 150 TeV) and have much lower uncertainties compared to the current telescopes in this range.

2. Due to the wide energy coverage, replacing observations at high-energy with only CTA data points yields a lower absolute MaxLogLikelihood value for all sources except HESS J1731-347. Therefore, CTA will be able to better constrain the parameters compared to the current data. The higher MaxLog-Likelihood value of HESS J1731-347 may be attributed to random fluctuation during simulation.

3. Dedicated deep observations for these four sources can be made as they have indicated signs of hadron acceleration up to the highest energies. This study revealed that more than 200 hrs of observation time would be required to increase the possibility of observing photons up to ∼ 300 TeV. Additionally, using IRFs extending up to 300 TeV may also prove useful in understanding the emission processes at high energies.

Varying maximum proton energy

Until recently, the limited sensitivity at the highest energies has prevented us from clearly constraining the proton cut-off energy. For the source HAWC J2227+610, very-high-energy observations were provided by HAWC and LHAASO [START_REF] Verna | HAWC J2227+610: a potential PeVatron candidate for the CTA in the northern hemisphere[END_REF]. This data extends up to 10 14 eV. Therefore, this source was chosen to study the effect of different proton cut-off values.

We have simulated CTA spectra for different cut-off values of the proton distribution. For the simulation, only the pion-decay model was used. In Gammapy, we used the Naimaspectralmodel to create a spectral model that convolves an Ex-pCutoffPowerLawSpectralModel proton particle distribution consisting of different values of the proton cut-off energy (with E cut,p = 300, 500, and 700 TeV) with pion-decay radiation. To define the remaining parameters of the spectral model, we have used the obtained Naima fit results as input parameters in Gammapy. The list of parameters for HAWC J2227+610 can be found in Chapter 6 in Table 6.9. A similar process as mentioned previously, was followed to simulate the γ-ray spectrum. The flux of HAWC J2227+610 was simulated in the energy range of 30 GeV to 150 TeV, using 200 hrs livetime and the CTA North Prod5 IRF with a zenith angle of 20 • . The on-radius has been set as 0.20 • with the offset of 0.60 • . Figure 7.9 shows the pion-decay model of the photon flux generated by Gammapy for different proton energy cut-off values. The pion-decay model with E cut,p = 300, 500, 700 TeV are represented by blue, orange, and green curves, respectively. The observations from current instruments have also been plotted for comparison and are represented by black dots. We can see from this figure that the piondecay models start varying significantly from each other at the energies ∼ 300 TeV. Therefore, sufficient data around 300 TeV are required to disentangle between pion-decay models with varying cut-off values. Shown in Figures 7.10 -7.12 are the Naima fit results for HAWC J2227+610 for different proton cut-off values. All the figures shown below depict a zoomed version of the high-energy part of the SED fitted with various theoretical models. We can see qualitatively that the simulated flux follows the injected model well (compare to Figure 7.9). For this simulation, to study CTA's sensitivity to high-energy cutoffs, a fit has been done only on the CTA simulated data points. The parameters determining the electron contribution have been fixed to the values obtained in the MWL fit described in Chapter 6 (refer to Table 6.9). The fit has been performed using only the theoretical model of pion-decay and is represented by the red dashed curve. The simulated CTA data points are represented by dots in aquamarine. It is important to note that the simulated data points for which the flux error was significantly larger than the flux itself have been neglected. Figure 7.11 shows the zoomed-in Naima fit for a maximum proton energy cut-off value of 500 TeV. The simulated flux shows much less uncertainty than the present instruments. The cut-off begins at the limit of the energy range available for CTA simulations and therefore the simulated data points have larger uncertainties around that energy. The resulting best-fit parameters of the Naima fit have been tabulated in Table 7.9.

Parameter

Lepto-hadronic log10(Amplitude) 47.019 7.9: Parameters obtained from the fit of HAWC J2227+610 using Naima. Figure 7.12 shows the zoomed-in Naima fit for a maximum proton energy cutoff value of 700 TeV. Similar trend as seen above is followed by data simulated by CTA. Hence, not much can be deduced due to the limited statistics around the energy where the cut-off begins. The resulting best-fit parameters of the Naima fit have been tabulated in the table 7.10.

Parameter

Lepto-hadronic log10(Amplitude) 47.021 +0.002 -0.002

Proton spectral index 1.75 From the fit results of HAWC J2227+610 at different proton cut-off energies, we can notice very slight changes in the proton spectral index and the N H value. A compilation of the MaxLogLikelihood and the BIC values along with the proton cut-off energy are shown in Table 7.11. A significant difference is noticed between the BIC value of the model with proton energy cut-off at 300 TeV compared to models with higher cut-offs.

The pion-decay models for which the E cut,p values are 500 TeV and 700 TeV, show a very similar MaxLogLikelihood value, making it hard to disentangle between the two. We see that the values for the input E cut,p and the output E cut,p parameter resulting from the fit match well for PD 300 -model and PD 500 -model. However, for the PD 700 -model, the output E cut,p parameter takes a value ∼ 600 TeV, which clearly differs from the value of 700 TeV provided as input during model simulation. This reflects the limit on the photon counts that can be generated for a given maximum proton energy simulated using the present IRF.

The fit results for the three pion-decay models mentioned above, with varying proton energy cut-off values applied to the dataset containing only the simulated CTA data having proton energy cut-off of 300 TeV, are compared in Figure 7.13. The PD 300 -model is shown by the orange curve, the blue curve depicts the PD 500model, and the PD 700 -model is represented by the pink curve. The shaded area shows the uncertainties in the fit. The simulated data points are shown in dark blue. The fit has been performed in Gammapy using the optimizer called Minuit, with proton spectral index and amplitude as free parameters and keeping proton energy cut-off fixed at 300 TeV. We can see that the simulated data coincides with the PD 300 -model quite well, which proves good reconstruction of fluxes given the model.

The fit results have been tabulated in

True

Table 7.12: The fit results of the different proton energy cut-off models and the simulated data for HAWC J2227+610 generated using proton energy cut-off value = 300 TeV.

From the loglikelihood values, we can clearly deduce that the PD 300 -model is preferred as the loglikelihood value is smaller compared to the other models.

To compute the level of agreement of the two hypotheses models, H0 and H1, to a particular data, one can use the ∆TS-value.

∆T S = T S H1 -T S H0 ∝ -ln(L H0 /L H1 ).

(7.

2)

The ∆TS value for the models PD 300 (H0) and the PD 500 (H1), fit to the dataset is 36.75. Similarly, the ∆TS value for PD 300 (H0) and the PD 700 (H2), fit to the dataset is 75.69. From these values, we can see that with CTA we can clearly distinguish the different proton cut-off values for data having a cut-off of around 300 TeV. However, a limit is seen as we increase the cut-off value, which is evident by the fit results shown in Figure 7.14. The fit is again performed between the three piondecay models with varying proton energy cut-off values and the dataset containing the simulated CTA data generated using the proton energy cut-off of 500 TeV. As above, the PD 300 -model is shown by the orange curve, the blue curve depicts the PD 500 -model, and the PD 700 -model is represented by the pink curve. The shaded area shows the uncertainties in the fit. The simulated data points are shown in dark blue. The fit has been performed using the optimizer Minuit with proton spectral index and amplitude as free parameters and keeping proton energy cut-off fixed at 500 TeV. The fit results have been tabulated in Table 7 The fit results of the different proton energy cut-off models and the simulated data for HAWC J2227+610 generated using proton energy cut-off value = 500 TeV.

The ∆TS value for the models PD 500 (H0) and the PD 300 (H1), fit to the dataset 7.4. VARYING MAXIMUM PROTON ENERGY is 25.60. Similarly, the ∆TS value for PD 500 (H0) and the PD 700 (H2), fit to the dataset is 2.32. The small ∆TS value of 2.32 shows the inability to distinguish between the models corresponding to E cut,p (T eV ) of 500 and 700 TeV. From these values, we can deduce that the limit of CTA lies around 500 TeV.

From the simulations, it is clear that CTA provides a much more accurate flux with a lower uncertainty in the range of 30 GeV to 150 TeV compared to the present instruments. As can be seen in Figure 7.9, models start to differ from each other only at very high energies (> 10 13 eV). Therefore, to truly disentangle between the different cut-off values, flux extending up to ∼ 300 TeV will be necessary to be sensitive to fluxes having different high-energy cut-off values. CHAPTER 7. SIMULATIONS FOR CTA

Effect of heavy elements

As we have discussed previously (Chapter 6), in some SNRs, we observe a flux excess at high energies compared to the theoretical models. In the case of heavy elements, the measured flux suppression in the CR spectrum occurs at higher energies with the increasing value of the charge number (Z) of the CR particle. This led us to suggest that the flux excess at the highest energies could be linked to heavy elements, supporting the paradigm of hadronic emission at high energies from SNRs. The four SNRs (RX J1713.7-3946, W49B, W28, and CTB 37A) from the study, which show such behaviour are presented below in Figure 7 For the preliminary study, RX J1713.7-3946 has been chosen as it not only has excess flux at high energies but also shows high-energy hadronic contribution spread across the multi-TeV domain. In order to account for the heavier elements, the proton particle distribution function (6.4) was slightly modified following the paper by S. Thoudam et al. [START_REF] Thoudam | Cosmic-ray energy spectrum and composition up to the ankle: the case for a second Galactic component[END_REF]:

f p (E) = f × A × A p × ( E E 0 ) α × e -E/Ecop×Z , (7.1)
where f is the amount of energy channeled into CRs by a single supernova event into different CR elements, A is the atomic mass, and Z is the charge number.

Using the equation ( 7.1), we have created different pion-decay models due to the contribution of different elements with the aid of Gammapy. To do so, one basic assumption is that the maximum energy for CR nuclei produced by an SNR is Z times the maximum energy for protons. Three different mass classes were considered for modeling, depending on the mass of the dominant composition:

EFFECT OF HEAVY ELEMENTS

153 proton-like (consisting of a mixture of H and He), nitrogen-like (representing the CNO group), and finally, iron-like.

To generate the different models mentioned above using Gammapy, the subpackage gammapy.modelling was used. For this study, we have used a spectral model that convolves an ExpCutoffPowerLawSpectralModel proton distribution with a pion-decay radiative model. Additionally, a CompoundSpectralModel has been generated, which allows us to combine the pion-decay models for different compositions.

The study consisted of making models using different combinations of the three main mass composition groups. Qualitatively, we tried to determine which combination model of the heavy elements reproduced the observed data best. Pion-decay contributions due to different elements are shown in Figure 7.16. Observed data have been plotted along with the models for comparison. We can see that the pion-decay models for different elements follow the general trend expected, i.e., elements with heavier mass have a higher cut-off. We can also notice that the flux of heavy elements is lower than that of protons. This is due to the value of f in equation (7.1). After testing different combinations, the combined model of pion-decay for protons and nitrogen reproduced the observed data well, qualitatively. Therefore for the simulation, we created a heavy element model (HE-model), which consisted of a combined model of pion-decay for protons and nitrogen. HE-model was chosen as the alternate hypothesis compared to the null hypothesis, which was the pion-decay model accounting for protons only (p-model). The parameters for the models are taken from the Naima fit results as input parameters in Gammapy. The list of parameters for RX J1713.7-3946 can be found in Chapter 6 in Table 6.6. The information regarding the amount of energy channeled into CRs by a single supernova event used for modeling the resulting flux of heavy elements due to pion-decay radiation was taken from the paper [START_REF] Thoudam | Cosmic-ray energy spectrum and composition up to the ankle: the case for a second Galactic component[END_REF].

To simulate the CTA data points, we followed the same procedure described previously. We created a Dataset that contained the observed flux provided by the present instruments combined with the CTA flux simulated using the HE-model containing a mixture of protons and nitrogen. For this study, the flux of RX J1713.7-3946 has been simulated using 200 hrs livetime and the CTA South Prod5 IRF with a zenith angle of 20 • . The on-radius was set as 0.65 • with the offset of 1 • .

The fit results for both models applied to the Dataset are compared in Figure 7.5. EFFECT OF HEAVY ELEMENTS 155 7.18. The p-model is shown by a red curve, and the HE-model is represented by a black curve. The shaded area shows the uncertainties in the fit. The fit has been performed in Gammapy using the optimizer called Minuit. In Figure 7.18, data points are plotted with the observed flux represented by the orange markers and the simulated flux represented by the blue markers. We can see that the simulated data coincides with the observed data quite well in the entire energy range accessible to CTA with much smaller flux uncertainties. Additionally, the simulated points are in agreement with the excess flux in the data observed by the present instruments. One interesting outcome of using a combined model which includes heavy elements for the simulation is the increase of photons extending to energies higher than that found for the case of the proton pion-decay model (see Figure 7.3 in section 7.3.1). Therefore, we deduce that adding heavy elements to the model has a different physical impact on the flux than the effect of increasing the proton cut-off value.

CHAPTER 7. SIMULATIONS FOR CTA

The fit results have been tabulated in Table 7 From the loglikelihood values, we can clearly deduce that the HE-model is preferred as the loglikelihood value for HE-model is smaller compared to the one with the p-model.

As done above, to compute the level of agreement of the two hypotheses models, H0 and H1, to a particular data, one can use the ∆TS-value.

The ∆TS value for the two hypotheses, the p-model(H0) and the HE-model(H1), fit to the Dataset is 27. From the results, we can conclude that the physical model of HE is preferred over a proton pion-decay model.

Therefore, we conclude that if indeed the SNR RX J1713.7-3946 accelerates a mixture of protons and nitrogen, then based on these preliminary results, CTA will be able to distinguish such a case. This work has yielded quite interesting results, and in the future, we plan to create a more detailed 3D analysis (including spatial and temporal characteristics of the source). This will allow us to obtain a more precise flux estimation. Furthermore, we would like to perform the entire analysis using an IRF extended up to higher energies. We can also study the effect of using longer observing time. It would be interesting to repeat this study for the SNRs W 49B, W28, and CTB 37A.

CTA Galactic plane survey

One of CTA's key science projects [START_REF]Science with the Cherenkov Telescope Array[END_REF] is understanding our local neighborhood, the Milky Way. A deep and complete survey ranging from 30 GeV to 300 TeV has been planned for the Galactic Plane (GP). Dedicated observing times are envisioned, ranging from more than 1600 hrs to create an unprecedented dataset, with improved angular resolution and sensitivity, which is important for various studies.

A simulation of the GP has been made by the Galactic group of the CTA collaboration. The full-sky simulation result is shown in Figure 7.19 using events recorded by both the northern and the southern CTA arrays. Sky models for the synthetic population of PWN, SNRs comprising their evolutionary stages and interaction with molecular clouds, and gamma-ray binaries have been accounted for in the GPS simulation. To make the GPS simulation more realistic, observations from gammacat (consisting of catalogues from MAGIC, HESS, VERITAS) and catalogues containing sources detected by Fermi (3FHL) and HAWC (2WHC) have been added to the simulation. Additionally, sky models for interstellar emission have also been considered. For more details, refer to the article by Remy et al. [START_REF] Remy | Survey of the Galactic Plane with the Cherenkov Telescope Array[END_REF]. In this paper, we aimed to estimate the significance of CTA's role in the population studies of two main classes: PWN and SNRs. All the SNRs for which the CTA pipeline was able to correctly identify the spatial information of the reconstructed SNR with respect to the seed SNR lie around the line y = 1. However, we can see that a few points lie around the Reff ratio of 2, which shows poor reconstruction. We see that for SNRs with such a high ratio, the flux is also very small, between 10 -14 to between 10 -13 photons cm -2 s -1 , which could be a major contributing factor to the poor reconstruction. Mostly all other sources have been reconstructed well within the ratio of 0.75 -1.25. For sources with very large flux, i.e.,between 10 -11 photons cm -2 s -1 , the reconstruction is quite good. It can also be seen that most of the large sources lie below 1, signifying that the reconstructed fluxes have been attributed a larger Reff than the input seed fluxes. This may be the effect of the complex shape of the SNRs leading to source confusion. Following the trend above, Figure 7.23 shows a distribution of the flux of SNRs with respect to the age of the SNR. Blue, pink and yellow markers represent synthesized shell-type SNRs, synthesized interacting SNRs, and known SNRs, respectively. The black crosses correspond to those sources which were detected by CTA. From the plot, we can see that CTA promises to discover various new sources, covering a wide age range from 1 to 100 kyr.

The results of the GPS simulation for Galactic SNRs are very promising. It was possible to detect and measure new SNRs even with the rather short exposure used for the survey compared to the current instruments, which require deep > 100 hrs exposures for the detection of the faintest SNRs [START_REF] Remy | Survey of the Galactic Plane with the Cherenkov Telescope Array[END_REF]. According to the findings of the GPS survey, SNRs will be the second most dominant Galactic source detected by CTA, after PWNe. CTA GPS may increase the number of detected SNRs at TeV energies by a factor of 2. More than half of the new detections have an extended geometry, which is valuable for identifying new sources that have no known counterparts in other wavebands. CTA can detect SNRs up to the other side of our Galaxy and provide 5-10 times better flux sensitivity than the current TeV SNR sample.

Conclusion

Chapter 7 has been dedicated to understanding the potential of CTA in searching for PeVatron sources. To do so, we have used the open software of Gammapy (version 0.19). We focused on the four SNRs, RX J1713.7-3946, HESS J1731-347, Cassiopeia A, and HAWC J2227+610, which showed significant hadronic contributions ranging up to 100 TeV. For all these studies, for the four SNRs, CTA fluxes were simulated to estimate CTA's ability to:

• Observe the potential PeVatron sources Through this study (section 7.3), we concluded that CTA could observe the sources in an energy range from 30 GeV to 150 TeV, with much lower flux uncertainties than the present instruments.

• Detect different proton cut-off energy values For this study (section 7.4), we focused on the SNR HAWC J2227+610. CTA could provide flux in the multi-TeV domain, which has much less uncertainty than the present instruments working in that energy range. This can significantly help in constraining the source spectral characteristics. Studies showed that the CTA detection limit is 500 TeV. Flux up to 300 TeV will be required to differentiate between models better, which is not possible with the current IRF and the observation time of 200 hrs used in the simulation.

• Identify the contribution of heavier elements to the high-energy flux This study (section 7.5) provided the most promising results as it showed that if SNR RX J1713.7-3946 indeed accelerates heavy elements at high energy, CTA will be able to differentiate between the flux containing just protons compared to the flux containing contribution from heavier elements. The addition of CTA flux modeled using a combined model containing a mixture of protons and nitrogens reproduces the observed data better than the proton pion-decay model.

To obtain better results, the flux needs to be extended up to higher energies ∼ 300 TeV. This can be made possible by using an IRF extended up to higher energies or by using longer observation times. Additionally, more realistic models can be built using Gammapy in the future to put stricter constraints and thus generate a flux close to what is expected in reality.

Lastly, through the analysis of the data obtained from GPS simulation, we can end our study positively since the findings suggest that SNRs will be the second most dominant Galactic γ-ray source detected by CTA (after PWNe). Using CTA, we will be able to significantly increase our knowledge about SNRs as potential PeVatron sources, as the number of detected SNRs will increase by a factor of 2. Additionally, CTA will provide us with SNRs having extended geometry, covering a large distance of up to 20 kpcs, with flux as low as ∼ 10 -14 photons cm -2 s -1 . This increases the possibility of detecting new sources of SNRs.

The thesis has been motivated by the upcoming observatory for ground-based very-high-energy γ-ray astronomy, the Cherenkov Telescope Array (CTA). This work attempts to understand better the various aspects of the γ-ray astronomy, involving 1) the R&D activity done to design a calibration system to improve the detection of incoming γ-rays, 2) an investigation of the nature of the emission processes from Galactic supernova remnants (SNR) at such high energies and 3) a high-level scientific analysis using Gammapy to explore detection capabilities of CTA in the context of SNRs.

The work on the calibration has been described in Chapter 5. It discusses how we can accurately measure the gain of the photomultiplier tubes (PMTs) of NectarCAM, a proposed camera for the Medium-Sized Telescope (MST) of CTA. We designed and characterized a dedicated calibration system at IJCLab. The final system consists of an octagonal screen coated with varying layers (3-2-1 from the light injection point) of Eljen paint. The screen's geometry and painting pattern aided in the homogenous spreading of light across the calibration screen, enabling measurements at the Single Photoelectron (SPE) level. The calibration screen is mounted on motors to access each PMT on the camera to determine its response to the single incoming photon. Several homogeneity and temperature tests were conducted to ensure the efficiency and prolonged durability of the calibration screen. To reduce the time taken to scan all the PMTs during a calibration run, we wrote an algorithm that provided us with optimized scan positions. Additionally, a python program was written to analyze the calibration data and identify only the pixels that are illuminated by the screen to allow for a quick and precise estimation of the gain of the selected PMTs. With the help of the tools listed above, the calibration data taken at Adlershof for the first MST prototype and at CEA/IRFU for the first MST was analyzed.

One of the key science projects of CTA is to understand the origin of Cosmic Ray (CR) particles, accelerated up to the knee of the CR spectrum. Chapter 6 of 164 CHAPTER 8. CONCLUSIONS the thesis dealt with observations based on present instruments to understand if SNRs can be potential accelerators of Galactic CRs. In this study, a Multiwavelength (MWL) analysis of 9 galactic SNRs was performed using publicly available data from recent experiments. To build the MWL SEDs, we assumed that the observed SED was due to the synchrotron, bremsstrahlung, inverse Compton and pion-decay processes. A lepto-hadronic and pure leptonic scenarios were considered to model the observed spectra. The Naima package was used to fit the observations. The fit results were analyzed using three different methods: likelihood comparison, BIC criterion, and the estimation of the hadronic contribution as a function of energy bins. The Likelihood method used to compare the two scenarios showed more confidence in the lepto-hadronic scenario than in the purely leptonic scenario for most sources. This study found four SNRs, RX J1713, Cassiopeia A, HESS J1731, and HAWC J2227, which showed a hadronic contribution up to the highest energies. These SNRs were identified as potential PeVatron sources. However, a firm conclusion could not be drawn due to limited statistics at high-energy. Additionally, the observations for the SNR RX J1713, CTB 37A, W49B, and W28 showed excess flux than predicted by the model above 10 13 eV when continuing to higher energies making them an interesting study for the possible acceleration of heavy elements.

Finally, the need for finer statistics brings us to Chapter 7 of the thesis -CTA simulations. The driving factor behind this study was to see if CTA can 1) improve the observations of the four potential PeVatron sources previously identified, 2) detect different proton cutoff energy values, and 3) identify the contribution of heavier elements to the high-energy flux. To answer these questions, we simulated spectra as CTA would see, based on physically motivated models generated using Gammapy. Through CTA simulations, we concluded that CTA would provide spectra in the multi-TeV domain, which has much less uncertainty than the present instruments working in that energy range. This can significantly help in constraining the source spectral characteristics. For the study of different proton energy cut-off values, we choose the SNR HAWC J2227 which has recent highenergy data. We simulated CTA data by using proton distribution with different cut-off values. By fitting the CTA simulated data, we found the proton cut-off energy limit for CTA detection to be ∼ 500 TeV. This reflects the limit on the photon counts that can be generated for a given maximum proton energy simulated using the present IRF. This study could be improved if deep observations (greater than 200 hrs) are made, or the present IRFs are extended up to 300 TeV. For the study of heavy elements, we choose the SNR RX J1713. This study showed that if the SNR indeed accelerates heavy elements to high energies, CTA will be able to differentiate between the flux containing just protons versus the contribution from for the electron distribution [?]. The equation for the electron distribution using Naima is given by:

f e (E) = A e × ( E E 0 ) α × exp(-E/E coe ) β , (6.5)
with :

• A p : the amplitude of the proton SED

• A e : the amplitude of the electron SED

• α e : the electron spectral index

• α p : the proton spectral index

• E coe : the electron energy cut-off

• E cop : the proton energy cut-off

• β: the cutoff exponent

The distribution that we have previously used in Chapter 6, corresponds to β = 1. To account for change in the slope after the cutoff energy, we studied the effect of having a fixed value of β = 0.5 and also the effect of leaving the β value as a free parameter (varying between 0 -1), as compared to β = 1. The results of the fits are shown in Table B. [START_REF] Venters | Contribution to the extragalactic gamma-ray background from the cascades of very high energy gamma rays from Blazars[END_REF]. By comparing the MaxLogLikelihood and the BIC value for each SNR, we deduced that for 7 out of 9 SNRs, ECPL with β = 1 gives a lower MaxLogLikelihood and a lower BIC value. For the SNRs, RX J1713 and W 49B, β = 0.5 would give a better fit.

These results show that the general conclusions of our study, pertaining to the contribution of lepto-hadronic emissions at the highest energies, would remain the same. We suspect that our study is not sensitive enough to be affected by different electron distributions due to the lack of observations in the X-ray domain. For this reason and the ones mentioned above, for our study ECPL seems to give accurate description on the underlying electron population.Therefore, we chose to discuss the results obtained for ECPL with β = 1. • A eff (p true , E true )(m 2 ): is the effective collection area of the detector. It is calculated as detector collection area (A geom ) times its detection efficiency (η) at true energy E true and position p true .

A ef f (E true , p true , ξ) ∝ A geom × η(E true , p true , ξ). ( 7.3) where ξ encapsulates the observation conditions such as the zenith angle.

The larger the number of telescopes, the greater the A geom of the array. Hence having several SSTs in the southern site provides a good effective area that opens the opportunity to detect rare high-energy events. For different sets of E true , p true and ξ, the detection efficiency (η) can be calculated by determining the fraction of γ-ray events which passed the hadron separation test.

• P SF (p|p true , E true )(sr -1 ) is the point spread function that measures the error on the reconstructed event direction. The error comes from the optical effects that reduce the quality of the image formed on the camera. Often seen as the blurring of a point source on the FoV, it can either be deduced by using MC simulations or checked by pointing toward a bright isolated known point source. PSF is given by: P SF = P SF (p true |E true , p true , ξ). The ratio E reco /E true is known as the migration (µ) and hence E disp takes the form of an energy migration matrix. For a given E true and p true , there exists a E disp corresponding to a 1-D Gaussian along the E reco axis, having a center (energy bias) and a width (energy resolution). If µ is > 1, the reconstructed event energy is biased towards high values and if µ is < 1, the reconstructed event energy is biased towards low values. The energy resolution is commonly quoted as a containment interval of a Gaussian (eg. 68%) but the Gaussian approximation may not always be correct.

All these functions can be drawn from MC simulations of γ-ray showers by varying observing conditions such as detector configuration, zenith angle, detector state and various event reconstruction and selection schemes.

D.2. γ-RAY STATISTICS 189

For source events, the IRFs are required to follow the conversion of incident γ-ray photon to a measured event. Whereas for background events, no IRF convolution is used. They are modeled as a general mix of interactions resulting from cosmic rays (CRs) with interstellar gas and radiation fields, along with the cumulative emission from ambient sources. It is difficult to differentiate between the source of background events and needs to be inferred statistically based on information on each event's morphology, spatial, spectral, and temporal characteristics.

D.2 γ-ray statistics

D.2.1 Test statistic

In our studies, we need to answer questions such as: Has a particular source been detected or not? Or Which shape best describes the spectrum? To answer such a question, we use Wilk's theorem, or the likelihood ratio test [?]. It helps us to estimate the relative significance using a test statistic:

T S = -2ln L 0 L 1 . ( 7.6)
Where L 0 and L 1 represent the maximum likelihood of the model under a null and alternative hypothesis, respectively. The null hypothesis could signify the absence of a source in the FoV, while the alternative hypothesis could indicate the presence of the source in the FoV.

Wilk's theorem states that if the distribution function of data follows the likelihood function L, then the maximum in the likelihood ratio (eg ( 7.6)) follows a chi-square distribution as the sample size approaches infinity under the null hypothesis. With the aid of this theorem, we can calculate the statistical significance of the alternative hypothesis to the null hypothesis. This is done by simply finding the corresponding right-tail p-value of the chi-square distribution.

If the p-value is small, the probability of obtaining a high TS value, provided the null hypothesis is correct, is very small, making the alternative hypothesis the preferred one. The significance is highly dependent on the tail of the distribution, which is sensitive to systematic uncertainties.

D.2.2 Count statistic

Gammapy makes use of fit statistics to fit models and estimate parameters. When a reliable background model is not present, WStat can be used also known as the ON-OFF statistics. When there is a significant excess of the number of photon counts compared to the hadronic background photon count, it is termed as the

D.3.2 Gammapy Datasets

It is a class that contains reduced γ-ray data to model and fit data of astrophysical sources. It comprises of reduced data, IRF, model, and fit statistics to allow the likelihood fitting of observations. Using Gammapy Datasets, we can compute the predicted counts in each reconstructed energy bin using a model and then compare it to the measured data using the maximum likelihood technique. Different Dataset objects are available depending on whether 1D (e.g., SpectrumDataset), 2D, or 3D (e.g., MapDataset) analysis is required. After data reduction, different Datasets store the different observations with their corresponding IRF. Each Dataset can be kept separate (joint-likelihood analysis) or can be combined into a single Dataset (stacked analysis).

D.3.3 Gammapy Makers

It is a class that consists of Maker objects that help reduce data from DL3 to DL4. Here the event lists can be binned with respect to energy or direction. The IRFs are then interpolated to the chosen bins. At this stage, the hadronic background at each energy and position is computed to ensure that the analysis is contained with safe energy and spatial range. For a stacked analysis the following tasks are performed:

• An empty Dataset is created.

• For each run, observations are binned with the corresponding IRF.

• A safe range is computed.

• Background is computed.

• Observations are stacked.

D.3.4 Gammapy Estimators

Gammapy estimators help in extracting the flux estimate and its uncertainty based on any input model. The class gammapy.estimators.FluxPointsEstimator helps to estimate the flux points for a specific dataset, energy, and spectral model that is given as input. Gammapy does this by fitting the amplitude of a spectral model within the energy range provided as input. The fitting is done separately for the spectral model in different energy bins. tats très intéressants dans leur recherche de candidats PeVatron. Avec l'évolution des détecteurs terrestres de haute énergie, des instruments futuristes tels que le Cherenkov Telescope Array (CTA) promettent de résoudre les mystères de l'astronomie des rayons gamma.

Dans cette thèse, nous nous concentrons sur l'observatoire CTA. Il est réparti entre les hémisphères Nord et Sud (Paranal au Chili et La Palma en Espagne) et permettra une couverture complète du ciel. La combinaison de trois tailles différentes de télescopes permet de couvrir une large gamme d'énergie de 20 GeV à 300 TeV. Un champ de vision plus large associé à une meilleure sensibilité permettra un relevé rapide par rapport à ses prédécesseurs. Enfin, CTA offrira une résolution angulaire et énergétique sans précédent qui garantira l'imagerie détaillée de nombreuses sources de rayons gamma. Pour ces raisons, CTA promet de donner une vue du ciel des hautes énergies jamais égalée auparavant et contribuera à faire des découvertes capitales en physique des astroparticules et dans d'autres domaines connexes.

La première partie de la thèse concerne le développement d'un système d'étalonnage de photoélectrons uniques pour la caméra NectarCAM. La deuxième partie vise à comprendre l'origine des RCs en effectuant une analyse multi-longueurs d'onde (MWL) des données existantes des restes de supernova (SNRs) galactiques. Enfin, la troisième partie étudie le rôle du CTA dans la détection des SNRs à la recherche de PeVatrons en simulant les flux à l'aide de Gammapy.

Chacun des télescopes du CTA a été équipé de sa propre variation de caméra robuste, conçue pour collecter habilement la faible lumière Cherenkov de courte durée. Cette thèse traite de la caméra NectarCAM du télescope de taille moyenne (MST) de CTA. La caméra NectarCAM a un FoV de 9 • , rendu possible par ses 1855 pixels. Chaque pixel est un photodétecteur PMT de 1,5 pouces de long de Hamamatsu (R12992-100), avec 7 dynodes par module, ayant un diamètre angulaire de 0,18 • . Devant chaque PMT, un cône Winston est fixé pour assurer une collecte maximale de la lumière à la photocathode. En utilisant les pixels, nous pouvons récupérer la charge et le temps d'arrivée des photons entrants. L'incertitude systématique lors de la reconstruction du signal provient de l'incertitude du gain de la chaîne de détection, qui comprend des photodétecteurs tels que les PMTs. L'amélioration des IACT actuels ou futurs nécessite un étalonnage précis pour extraire la direction et l'énergie d'arrivée du photon incident. Un système de calibration par photoélectron unique (SPE) a été conçu au IJCLab pour la caméra NectarCAM des télescopes MST. Ce système est intégré dans la caméra Nectar-CAM.

Le système d'étalonnage se compose d'un écran peint en blanc, d'un guide de lumière en queue de poisson et d'un flash. Les flashs imitent le rayonnement Cherenkov et illuminent le plan focal sous l'écran de manière homogène. Ensuite, grâce à la motorisation XY, l'écran est déplacé sur l'ensemble du plan focal de la caméra NectarCAM. Notre objectif était de concevoir un écran d'étalonnage qui produise la lumière la plus homogène possible. Pour ce faire, différentes procédures et géométries de peinture ont été testées. La configuration finale de l'écran d'étalonnage a été peinte avec de la peinture Eljen avec une dilution de 18%, avec une épaisseur de peinture variable. Pour la géométrie finale, un écran plat octogonal d'une surface de 1338 cm 2 , avec un guide de lumière plat en queue de poisson et une rainure coudée (30 • ), ont été sélectionnés. Les résultats montrent que la lumière est répartie de manière satisfaisante sur l'écran à l'intérieur de 10 contours, ce qui permet d'effectuer des mesures au niveau de la SPE. Des tests de température ont également été effectués au IJCLab pour vérifier si les fluctuations de température peuvent affecter le revêtement de la peinture et ainsi affecter l'homogénéité de l'écran de calibration. Nous avons conclu que la température n'a pas d'impact significatif sur l'homogénéité de l'écran du motif de la peinture.

L'écran de calibration étant prêt, nous nous sommes concentrés sur l'optimisation du temps nécessaire à la réalisation des tests de calibration pour déterminer le gain des PMTs. Pour cela, deux algorithmes ont été écrits. Le premier algorithme visait à trouver les positions optimales de l'écran nécessaires pour balayer l'ensemble du plan focal de la caméra afin de garantir la couverture de tous les pixels avec une redondance raisonnable et de minimiser le temps nécessaire à la calibration. De nombreux facteurs ont été pris en compte, et le temps total nécessaire à un balayage complet a été estimé entre 17 et 28 minutes pour un total de 55 positions successives. Lors de la mesure dans le régime SPE, il était difficile de différencier le signal d'un photoélectron unique du bruit de fond. Par conséquent, un deuxième algorithme a été écrit pour trouver uniquement les pixels illuminés par l'écran d'étalonnage. En utilisant cette information, nous pouvons obtenir la charge des seuls pixels illuminés et en déduire leur gain. L'écran d'étalonnage et les algorithmes ont ensuite été testés avec succès à l'aide des données d'étalonnage acquises avec la mini caméra d'Adlershof et la première caméra entièrement fonctionnelle du CEA.

Les SNRs sont des sources candidates prometteuses pour les RCs galactiques. Les RCs chargés peuvent être détectés indirectement par les observations de rayons gamma à travers la production d'un π 0 et la désintégration consécutive en rayons gamma de haute énergie. L'un des principaux projets scientifiques du CTA est de comprendre l'origine des particules des RCs, accélérées jusqu'au genou de leur spectre. La thèse traite des observations basées sur les instruments actuels pour comprendre si les SNRs peuvent être des accélérateurs potentiels de RCs galactiques. Dans cette étude, une analyse multi-longueurs d'onde (MWL) de 9 SNRs galactiques a été réalisée en utilisant des données disponibles publiquement provenant d'expériences récentes. Nous étudions les tendances en faveur des scénarios lepto-hadroniques et recherchons des SNRs qui montrent des signes d'accélération hadronique jusqu'aux plus hautes énergies. L'étude MWL sur les 9 SNRs a été réalisée en utilisant des données provenant de différents instruments. Les données ont été ajustées avec des modèles radiatifs pour évaluer la contribution hadronique. Pour cette étude, nous avons considéré 4 émissions radiatives : Synchrotron, Bremsstrahlung, Compton Inverse et désintégration des Pions. Pour ajuster les modèles théoriques aux spectres observés, nous avons utilisé Naima. Il s'agit d'un paquetage Python composé de modèles radiatifs qui nous permettent de calculer l'émission non-thermique des populations d'électrons et de protons relativistes et d'effectuer un ajustement MCMC (Méthode de Monte-Carlo par chaînes de Markov) aux spectres observés. Les résultats de l'ajustement ont été analysés à l'aide de trois méthodes différentes : la comparaison de vraisemblance, le critère BIC et l'estimation de la contribution hadronique en fonction des tranches d'énergie. Les résultats montrent que tous les SNRs étudiés favorisent le modèle lepto-hadronique par rapport à un modèle purement leptonique. Nous avons identifié 4 SNRs ; RX J1713, Cassiopée A, HESS J1731, et HAWC J2227. Tous ont montré des contributions hadroniques importantes jusqu'à quelques TeV, ce qui en fait des candidats prometteurs pour le PeVatron. De plus, pour certains SNRs, un excès de flux a été observé à des énergies élevées.

La dernière partie de la thèse est consacrée à l'évaluation de la capacité de CTA à détecter les SNRs. Il s'agit de répondre si CTA peut 1) améliorer les obser-vations des sources potentielles de PeVatron précédemment identifiées, 2) détecter différentes valeurs d'énergie de coupure des protons, et 3) identifier la contribution des éléments plus lourds à l'excès de flux à haute énergie observé auparavant. Pour ce faire, les flux de CTA sont simulés par Gammapy à l'aide de modèles physiquement motivés tirés des résultats de l'étude MWL réalisée précédemment.

Pour obtenir des points de données CTA, le logiciel Gammapy a été utilisé. Gammapy est un logiciel d'analyse open-source qui a été développé pour fournir une analyse de haut niveau des données IACT. Gammapy nous permet également de simuler des points de données en utilisant des modèles physiquement motivés. Nous avons utilisé les modèles radiatifs discutés précédemment pour effectuer les simulations pour différents SNRs. Les résultats des simulations ont montré que CTA fournit un flux couvrant une large couverture énergétique et une plus faible incertitude par rapport aux instruments actuels. Ainsi, le remplacement des observations à haute énergie par des points de données CTA uniquement donne une valeur absolue de MaxLogLikelihood inférieure pour toutes les sources. Cela montre que CTA peut mieux contraindre les paramètres par rapport aux données actuelles. Nous avons également effectué des études de coupure pour le SNR HAWC J2227. L'étude a montré la capacité de CTA à démêler différentes valeurs de coupure de l'énergie du proton avec une limite de détection d'environ 500 TeV. Pour la source RX J1713, une contribution des éléments lourds a été introduite. Le résultat a montré qu'en utilisant une combinaison d'éléments de type hydrogène et azote, on obtient un meilleur ajustement par rapport à l'ajustement utilisant uniquement des protons. La sensibilité accrue de CTA à la forme spectrale et sa large couverture énergétique offrent une possibilité très prometteuse de détecter la contribution d'éléments plus lourds. Pour obtenir de meilleurs résultats, le flux doit être étendu jusqu'à des énergies plus élevées ∼ 300 TeV. Cela peut être rendu possible en utilisant un IRF étendu à des énergies plus élevées ou en utilisant des temps d'observation plus longs.

En plus de l'étude de simulation précédente, nous avons également analysé les résultats de l'étude du plan galactique simulée par le groupe galactique du CTA. L'étude a montré que le CTA augmenterait d'un facteur 2, le nombre de SNRs détectés. De plus, les SNRs couvrant une grande distance (jusqu'à 20 kpcs), avec un flux aussi faible que ∼ 10 -14 photons cm -2 s -1 seraient facilement détectés par le CTA.

14 LIST OF FIGURES 3 . 2 49 4. 1

 1432491 Simplified diagram of a hadronic shower[START_REF] Matthews | A Heitler model of extensive air showers[END_REF]. The dashed lines represent neutral pions which decay fast, leading to EM subshowers (not shown). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40 3.3 Pictorial representation of the emitted Cherenkov radiation at an angle θ c from the direction of particle motion. . . . . . . . . . . . .42 3.4 Image shows how an IACT works. The incoming γ-ray induces an electromagnetic shower in which the secondary particles generate Cherenkov radiation. This radiation is captured by the IACT and recorded as a signal by the camera. Credit: Mikael Jacquemont et al.[START_REF] Jacquemont | Deep learning for astrophysics, understanding the impact of attention on variability induced by parameter initialization[END_REF] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.5 The image focuses on the part of the IACT camera plane. The signal of the incident Cherenkov radiation is shown as recorded by the camera. Credit: [6] . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.6 Image of 1.0 TeV gamma shower (left) and 2.6 TeV proton shower (right). The images highlight the difference between a gammainduced and a proton-induced shower image. Credit: K. Bernlohr [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.7 An example of how stereoscopy works. Several images from an event are shown on the left, and their projection into one camera plane is shown on the right. Credit: K. Bernlohr [7] . . . . . . . . . . . . . . 45 3.8 Photo after the completion of Phase 2 of the H.E.S.S. Telescope. Credit: H.E.S.S. Collaboration . . . . . . . . . . . . . . . . . . . . . 46 3.9 The two MAGIC telescopes at La Palma. Credit: MAGIC Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.10 The four VERITAS Telescope at the Whipple Observatory on Mt. Hopkins. Credit: VERITAS Collaboration . . . . . . . . . . . . . . 47 3.11 The H.E.S.S. Galactic Plane Survey. It shows the HGPS superimposed on an all-sky image of Planck CO(1-0) data. HEGRA and VERITAS plane surveys have been overlayed for comparison. The white triangles depict Fermi -LAT 2FHL γ-ray sources, and stars depict γ-ray sources outside the HGPS region. The gray hue represents the part of the sky that H.E.S.S. is blind to. The lower panels show the HGPS γ-ray flux > 1 TeV and observation time with respect to the Galactic coordinates. Credit: H.E.S.S. Collaboration [8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.12 The H.E.S.S. Galactic Plane Survey Catalogue source identification [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The image is an artist's rendition that captures all three types, Large, Medium, and Small-sized telescopes of the Cherenkov Telescope Array in the southern hemisphere. Credit: BY-NC-ND 2.0 . . 52 LIST OF FIGURES 4.2 Potential CTA array in the Northern and the Southern site. Credithttps://www.cta-observatory.org/. . . . . . . . . . . . . . . . . . . . 4.3 Expected "Alpha Configuration" sensitivity curves for CTAO vs other γ-ray instruments. Credit-https://www.cta-observatory.org/. 4.4 Illustration of the MST telescope of CTA with the main components highlighted [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.5 Different components that make up the NectarCAM camera are shown on the left, and the central part is shown on the right [10]. . 4.6 NectarCAM's focal plane instrumentation connected to the FEB [10]. 4.7 NectarCAM front-end board V5 Credit: Jean-Luc Meunier. . . . . . 5.1 Schematic Diagram of a PMT consisting of a photocathode, 8 dynodes, and an anode. The path of the incident photon is shown in blue. Image credit: Wikipedia. . . . . . . . . . . . . . . . . . . . . 5.2 Single photoelectron charge histogram for pixel number 660, the two peaks correspond to 0 and 1 photoelectron. . . . . . . . . . . . . . 5.3 Calibration screen with the fishtail and the groove. . . . . . . . . . 5.4 Calibration screen along with the light box containing LEDs. . . . . 5.5 Front view of the NectarCAM camera. With PMTs modules represented by the yellow, green, blue, and red colours. The target rests on the bottom right corner (parking position) of the camera attached to the XY motors. . . . . . . . . . . . . . . . . . . . . . . 5.6 Zoomed view of the front side of the screen, used for the SPE calibration, with layers of varying thickness. The back side, used for alignment and PSF studies, is coated homogeneously with 3 layers. 5.7 Test-bench set up in the dark room. It consists of motors which moves a PMT attached to a NectarCAM FEB across the screen. The flasher injects light pulses with the aid of the fishtail light guide. 5.8 Dip coating set up at IJCLab for painting the calibration screen. . 5.9 Examples of the contour maps of screens resulting from the data acquisition in the high-intensity regime. The different colours on the screen represent different contours that enclose the regions where the light intensity is within a given percentage of the maximum intensity measured on the screen (see text). . . . . . . . . . . . . . 5.10 List of the tested screens. . . . . . . . . . . . . . . . . . . . . . . . . 5.11 List of the tested screens (continued). . . . . . . . . . . . . . . . . . LIST OF FIGURES 5.12 Figure on the left shows the light intensity contour map. The black lines mark the different regions of the screen which are painted with different layers. The different colours on the screen represent different contours that enclose the regions where the light intensity is within a given percentage of the maximum intensity measured on the screen, along with the cumulative area of the screen enclosed by the contours is shown in Table on the right. . . . . . . . . . . . . . 77 5.13 Scheme of the temperature test of the calibration screen (see text). 78 5.14 Homogeneity test of the calibration screen number 24 showcasing how the light is spread across the screen after undergoing a series of temperature changes. The screen on the top left shows the map before starting temperature measurements. The top right image shows the map after the high-temperature test, and the bottom left and right show the resultant homogeneity map for low temperature and cycle, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.15 Transit time periods. . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.16 Scan positions required to calibrate the entire camera (see text). . . 82 5.17 Illuminated pixels in the first position for the data acquired in Aldershof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.18 Selection of illuminated pixels for the data acquired in Aldershof. . 83 5.19 SPE fit at high-intensity region (Pixel 441). . . . . . . . . . . . . . 84 5.20 SPE fit at low-intensity region (Pixel 564). . . . . . . . . . . . . . . 84 5.21 NectarCAM camera installed at CEA with the calibration screen (white target) and XY motorization. . . . . . . . . . . . . . . . . . 85 5.22 Illuminated pixels in the first position for data acquired at CEA. . . 86 5.23 Selection of illuminated pixels for data acquired at CEA. . . . . . . 86 5.24 SPE fit at high-intensity region. . . . . . . . . . . . . . . . . . . . . 86 5.25 SPE fit at low-intensity region. . . . . . . . . . . . . . . . . . . . . 86 6.1 Illustration of the SED of a source is shown. Various theoretical models such as pion-decay (PI), synchrotron (Sync), inverse Compton (IC), and bremsstrahlung (BRE) together with the sum are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6.2 Example of Naima MCMC output for the parameter N H for the

7 . 10

 710 The high-energy part of the SED of HAWC J2227+610 along with the CTA simulated data points (blue) generated by the pion-decay model with E cut,p = 300 TeV (see text). . . . . . . . . . . . . . . . . 7.11 The high-energy part of the SED of HAWC J2227+610 along with the CTA simulated data points (blue) generated by the pion-decay model with E cut,p = 500 TeV (see text). . . . . . . . . . . . . . . . . 7.12 The high-energy part of the SED of HAWC J2227+610 along with the CTA simulated data points (blue) generated by the pion-decay model with E cut,p = 700 TeV (see text). . . . . . . . . . . . . . . . . 7.13 The fit results of the different proton energy cut-off models and the simulated data for HAWC J2227+610 generated using proton energy cut-off value = 300 TeV. . . . . . . . . . . . . . . . . . . . . 7.14 The fit results of the different proton energy cut-off models and the simulated data for HAWC J2227+610 generated using proton energy cut-off value = 500 TeV. . . . . . . . . . . . . . . . . . . . . 7.15 The excess flux deviating from the theoretical models for SNRs CTB 37A, W49B, RX J1713.7-3946, and W28 (indicated by circles). . . 7.16 The combined heavy-element model (green) for RX J1713.7-3946 consisting of the pion-decay model for different elements: protons (blue), helium (orange), nitrogen (green), and iron (red). For comparison, the observed data for RX J1713.7-3946 are also shown. . . 7.17 Combined heavy-element model (green) of the SNR RX J1713.7-3946 consisting of the pion-decay model for proton-like elements (blue) and N-like elements (orange). For comparison, the observed data for RX J1713.7-3946 are also shown . . . . . . . . . . . . . . . 7.18 The fit result of the observed (orange) and simulated (blue) data in the Dataset for RX J1713.7-3946 with the p-model (red) and HE-model (black). . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.19 Simulation of the entire Galactic Plane observed by CTA. It shows the excess counts compared to the instrumental background model in the energy range of 0.07-200 TeV. Credit: Remy et al. [12] . . . . 7.20 The spatial distribution of all the simulated SNRs (represented by blue dots) in our Galaxy, along with the detected shell-type SNRs (represented by orange dots) and the detected ISNRs (represented by pink diamonds). . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2 . 1 :

 21 Figure 2.1:The energy (energy-per-nucleus) spectrum of all particles from various air shower instruments. Credit Particle Data Group[START_REF] Workman | Review of Particle Physics[END_REF]

Figure 2 . 2 :

 22 Figure 2.2: Hillas plot showing the size and magnetic field strength of various astrophysical sources which could be potential accelerators [2].

Figure 2 . 3 :

 23 Figure 2.3: TeV Galactic gamma-ray sources with PWN/TeV Halo shown by green dots, starburst shown in dark blue, GRBs AGNs and Blazar shown in light blue, SNRs shown in pink dots, DARK and unid objects represented by black dots and finally, binaries, XRB and Nova given by purple dots. Credit: TeVCat online source catalogue

Figure 2 . 4 :

 24 Figure 2.4: The graph shows the pair production mean free path of VHE γ photons propagating through soft photon background as a function of energy corresponding to different background models. The solid black line represents the contribution from cosmic microwave background radiation. Different EBL models have been represented by dashed and dotted lines. Credits:Tonia M. Venters[START_REF] Venters | Contribution to the extragalactic gamma-ray background from the cascades of very high energy gamma rays from Blazars[END_REF]

Figure 2 . 5 :

 25 Figure 2.5: Illustration of a supernova remnant producing relativistic protons which interact with surrounding molecular clouds to produce gamma rays. Unlike charged protons, gamma rays travel in a straight trajectory toward the Earth. The colourful blob on the top left represents a supernova remnant. The yellow cloud lying between the SNR and the Earth represents a molecular cloud. The orange curved path indicates the path of the charged proton, gamma rays are represented by the blue straight lines. Direct detection of gamma rays is done using the satellite shown in grey and finally, the interaction of protons and gamma rays is indicated by the shower in orange and blue, respectively.

Figure 3 . 1 :

 31 Figure 3.1: Simplified diagram of an electromagnetic cascade [4]. The squiggly lines represent photons, and solid lines represent electrons/positrons.

Figure 3 . 2 :

 32 Figure 3.2: Simplified diagram of a hadronic shower [4]. The dashed lines represent neutral pions which decay fast, leading to EM subshowers (not shown).

Figure 3 . 3 :

 33 Figure 3.3: Pictorial representation of the emitted Cherenkov radiation at an angle θ c from the direction of particle motion.

Figure 3 . 4 :

 34 Figure 3.4: Image shows how an IACT works. The incoming γ-ray induces an electromagneticshower in which the secondary particles generate Cherenkov radiation. This radiation is captured by the IACT and recorded as a signal by the camera. Credit: Mikael Jacquemont et al.[START_REF] Jacquemont | Deep learning for astrophysics, understanding the impact of attention on variability induced by parameter initialization[END_REF]

Figure 3 . 5 :

 35 Figure 3.5:The image focuses on the part of the IACT camera plane. The signal of the incident Cherenkov radiation is shown as recorded by the camera. Credit:[START_REF] Fernandez | Gamma-Ray Telescopes[END_REF]

Figure 3 .

 3 Figure 3.6 shows the image on a focal plane of a camera of a hadronic shower (right) which is broader and irregular, and of an electromagnetic shower (left), which takes the form of a thin ellipse. The colours change from dark blue to brighter shades, with red being the brightest, and represent the number of incident photoelectrons on each pixel. This provides us with an observational tool to separate the signal from the background.

Figure 3 . 6 :

 36 Figure 3.6: Image of 1.0 TeV gamma shower (left) and 2.6 TeV proton shower (right).The images highlight the difference between a gamma-induced and a proton-induced shower image. Credit: K. Bernlohr[START_REF] Völk | Imaging very high energy gamma-ray telescopes[END_REF]

Figure 3 . 7 :

 37 Figure 3.7: An example of how stereoscopy works. Several images from an event are shown on the left, and their projection into one camera plane is shown on the right. Credit: K. Bernlohr [7]

Figure 3 . 8 :

 38 Figure 3.8: Photo after the completion of Phase 2 of the H.E.S.S. Telescope. Credit: H.E.S.S. Collaboration

Figure 3 . 9 :

 39 Figure 3.9: The two MAGIC telescopes at La Palma. Credit: MAGIC Collaboration

Figure 3 . 10 :

 310 Figure 3.10: The four VERITAS Telescope at the Whipple Observatory on Mt. Hopkins. Credit: VERITAS Collaboration

Figure 3 . 11 :

 311 Figure 3.11: The H.E.S.S. Galactic Plane Survey. It shows the HGPS superimposed on an allsky image of Planck CO(1-0) data. HEGRA and VERITAS plane surveys have been overlayed for comparison. The white triangles depict Fermi -LAT 2FHL γ-ray sources, and stars depict γ-ray sources outside the HGPS region. The gray hue represents the part of the sky that H.E.S.S. is blind to. The lower panels show the HGPS γ-ray flux > 1 TeV and observation time with respect to the Galactic coordinates. Credit: H.E.S.S. Collaboration[START_REF] Abdalla | Galactic plane survey[END_REF]

52 CHAPTER 4 .

 524 Medium-Sized Telescope (MST): Known as the work-horse of CTA, MSTs have GAMMA RAY OBSERVATION BY CTA an effective area of ∼ 90 m 2 and are sensitive to γ-rays in the core energy range. In this energy range, the flux of incoming γ-rays has slightly decreased. Hence more telescopes are required.

Figure 4 . 1 :

 41 Figure 4.1: The image is an artist's rendition that captures all three types, Large, Medium, and Small-sized telescopes of the Cherenkov Telescope Array in the southern hemisphere. Credit: BY-NC-ND 2.0

Figure 4 . 2 :

 42 Figure 4.2: Potential CTA array in the Northern and the Southern site.Credithttps://www.cta-observatory.org/.

Figure 4 .

 4 Figure 4.3 shows the plot of the differential sensitivity, which is the minimum flux required to detect a point source with the confidence level of 5σ. The plot has been made using non-overlapping logarithmic energy bins (5 bins per 10 yrs). The sensitivity curve is dependent on the observation time. We can clearly see from the figure that CTA's sensitivity curve is an order of magnitude better and also covers a much wider energy range than the present IACTs.

Figure 4 . 3 :

 43 Figure 4.3: Expected "Alpha Configuration" sensitivity curves for CTAO vs other γ-ray instruments. Credit-https://www.cta-observatory.org/.

Figure 4 . 4 :

 44 Figure 4.4: Illustration of the MST telescope of CTA with the main components highlighted [9].

Figure 4 . 5 :

 45 Figure 4.5: Different components that make up the NectarCAM camera are shown on the left, and the central part is shown on the right [10].

CHAPTER 4 .

 4 GAMMA RAY OBSERVATION BY CTA The basic working principle of NectarCAM is: • The Focal Plane Instrumentation (FPI) is used to detect light and convert photons into an electrical signal with the aid of PMTs. Together the high voltage and preamplification board (HVPA) and a phototube form a 'Detector Unit'(DU). An HVPA is required to amplify the signal of the PMT. The front-end board (FEB) contains a second amplification stage (ACTA) to amplify the incoming signal from faint sources further. Seven DUs of the NECTar module are controlled by a single Interface Board.

Figure 4 . 6 :

 46 Figure 4.6: NectarCAM's focal plane instrumentation connected to the FEB [10].

Figure 4 . 7 :

 47 Figure 4.7: NectarCAM front-end board V5 Credit: Jean-Luc Meunier.

Figure 5 . 1 :

 51 Figure 5.1: Schematic Diagram of a PMT consisting of a photocathode, 8 dynodes, and an anode. The path of the incident photon is shown in blue. Image credit: Wikipedia.

Figure 5 . 2 :

 52 Figure 5.2: Single photoelectron charge histogram for pixel number 660, the two peaks correspond to 0 and 1 photoelectron.

. 3 •

 3 Light box: It contains 12 LEDs at 390 nm imitating Cherenkov light. The light box is attached at the beginning of the screen as shown in Figure 5.4 (transparent box). It is used to inject light into the screen. The light box was developed by Laboratoire Univers et Particules de Montpellier (LUPM).

Figure 5 . 3 :

 53 Figure 5.3: Calibration screen with the fishtail and the groove.

Figure 5 . 4 :

 54 Figure 5.4: Calibration screen along with the light box containing LEDs.

Figure 5 . 5 :

 55 Figure 5.5: Front view of the NectarCAM camera. With PMTs modules represented by the yellow, green, blue, and red colours. The target rests on the bottom right corner (parking position) of the camera attached to the XY motors.

Figure 5 . 6 :

 56 Figure 5.6: Zoomed view of the front side of the screen, used for the SPE calibration, with layers of varying thickness. The back side, used for alignment and PSF studies, is coated homogeneously with 3 layers.

Figure 5 . 7 :

 57 Figure 5.7: Test-bench set up in the dark room. It consists of motors which moves a PMT attached to a NectarCAM FEB across the screen. The flasher injects light pulses with the aid of the fishtail light guide.

Figure 5 . 8 :

 58 Figure 5.8: Dip coating set up at IJCLab for painting the calibration screen.

Figure 5 . 9 :

 59 Figure 5.9: Examples of the contour maps of screens resulting from the data acquisition in the high-intensity regime. The different colours on the screen represent different contours that enclose the regions where the light intensity is within a given percentage of the maximum intensity measured on the screen (see text).

Figure 5 . 10 :

 510 Figure 5.10: List of the tested screens.

77 Figure 5 . 11 :

 77511 Figure 5.11: List of the tested screens (continued).

Figure 5 . 12 :

 512 Figure 5.12: Figure on the left shows the light intensity contour map. The black lines mark the different regions of the screen which are painted with different layers. The different colours on the screen represent different contours that enclose the regions where the light intensity is within a given percentage of the maximum intensity measured on the screen, along with the cumulative area of the screen enclosed by the contours is shown in Table on the right.

•

  Low-temperature model: Covers a temperature change from room temperature, 22 • C to -15 • C for a duration of 24 hrs. • High-temperature model: Covers a temperature change from room temperature, 22 • C to 35 • C for a duration of 24 hrs. • Temperature cycle: Covers a temperature fluctuation from -15 • C to room temperature, slowly rising to a high temperature of 35 • C. This temperature cycle was repeated six times after maintaining a particular temperature for 30 mins.

Figure 5 . 13 :

 513 Figure 5.13: Scheme of the temperature test of the calibration screen (see text).

Figure 5 . 14 :

 514 Figure 5.14: Homogeneity test of the calibration screen number 24 showcasing how the light is spread across the screen after undergoing a series of temperature changes. The screen on the top left shows the map before starting temperature measurements. The top right image shows the map after the high-temperature test, and the bottom left and right show the resultant homogeneity map for low temperature and cycle, respectively.

Figure 5 . 15 :

 515 Figure 5.15: Transit time periods.

CHAPTER 5 .Figure 5 . 16 :

 5516 Figure 5.16: Scan positions required to calibrate the entire camera (see text).

4

  Karl Kosack et al.cta-observatory/ctapipe: v0.11.0. Version v0.11.0. May 2021.

Figure 5 . 17 :

 517 Figure 5.17: Illuminated pixels in the first position for the data acquired in Aldershof.

Figure 5 . 18 :

 518 Figure 5.18: Selection of illuminated pixels for the data acquired in Aldershof.

  gain = 58.13 +/-0.79 ADC/pe data

Figure 5 . 19 :

 519 Figure 5.19: SPE fit at high-intensity region (Pixel 441).

Figure 5 . 20 :

 520 Figure 5.20: SPE fit at low-intensity region (Pixel 564).

5. 10 .

 10 CALIBRATION TESTS AT CEA 85 5.10 Calibration tests at CEA The calibration system described above has been assembled in CEA, where currently final checks are undergoing before moving the camera to La Palma for commissioning. The front view of the NectarCAM camera assembled at CEA is given in Figure 5.21. It shows the calibration screen in the middle of the camera attached to grey rails.

Figure 5 . 21 :

 521 Figure 5.21: NectarCAM camera installed at CEA with the calibration screen (white target) and XY motorization.

Figure 5 . 22 :

 522 Figure 5.22: Illuminated pixels in the first position for data acquired at CEA.

Figure 5 . 23 :Figure 5 . 24 :Figure 5 . 25 :

 523524525 Figure 5.23: Selection of illuminated pixels for data acquired at CEA.

Figure 6 . 1 :

 61 Figure 6.1: Illustration of the SED of a source is shown. Various theoretical models such as pion-decay (PI), synchrotron (Sync), inverse Compton (IC), and bremsstrahlung (BRE) together with the sum are shown.

Figure 6 . 2 :

 62 Figure 6.2: Example of Naima MCMC output for the parameter N H for the SNR HAWC J2227+610 modelled using the lepto-hadronic scenario.

Figure 6 . 3 :

 63 Figure 6.3: Naima MCMC output of a corner plot for the SNR RX J1713.7-3946 modeled using the hadronic scenario.

Figure 6 . 4 :

 64 Figure 6.4: MWL SED of the SNR RX J0852.0-4622 modeled by using the hadronic scenario (left) and the leptonic scenario (right).

Figure 6 . 5 :

 65 Figure 6.5: MWL SED of the SNR RX J1713.7-3946 modeled by using the hadronic scenario (left) and the leptonic scenario (right).

6. 7 . RESULTS 109 Figure 6 . 6 :

 710966 Figure 6.6: MWL SED of the SNR Cassiopeia A modeled by using the hadronic scenario (left) and the leptonic scenario (right).

110 CHAPTER 6 Figure 6 . 7 :

 110667 Figure 6.7: MWL SED of the SNR CTB 37A modeled by using the hadronic scenario (left) and the leptonic scenario (right).

6. 7 . RESULTS 111 Figure 6 . 8 :

 711168 Figure 6.8: MWL SED of the SNR HAWC J2227+610 modeled by using the hadronic scenario (left) and the leptonic scenario (right).

Figure 6 . 9 :

 69 Figure 6.9: MWL SED of the SNR HESS J1731-347 modeled by using the hadronic scenario (left) and the leptonic scenario (right).

Figure 6 . 10 :

 610 Figure 6.10: MWL SED of the SNR IC 443 modeled by using the hadronic scenario (left) and the leptonic scenario (right).

Figure 6 . 11 :

 611 Figure 6.11: MWL SED of the SNR W28 modeled by using the hadronic scenario (left) and the leptonic scenario (right).

Figure 6 . 14 :

 614 Figure 6.14: The magnetic field as a function of the electron energy cut-off value obtained from the fit. The age and the magnetic field of the SNRs have been taken from Table 6.3, and the references therein. The old SNRs are indicated by blue circles, while the young SNRs are represented by orange circles.

Figure 6 . 15 :

 615 Figure 6.15: The magnetic field as a function of the cut-off energy of protons obtained from the fit. The age of the SNRs has been taken from Table 1, and references therein. The old SNRs are indicated by blue circles, while the young SNRs are represented by orange circles.

Figure 6 . 16 :

 616 Figure 6.16: The magnetic field as a function of the cut-off energy of protons obtained from the fit. The interacting SNRs are indicated by blue circles, while the shell-type SNRs are represented by orange circles.

Figure 6 . 17 :

 617 Figure6.17: The magnetic field as a function of the cut-off energy of protons obtained from the fit. The age of the SNRs has been taken from Table1, and references therein. The old SNRs are indicated by blue circles, while the young SNRs are represented by orange circles.

Figure 6 . 19 :

 619 Figure 6.19: Integration method. Different radiative models are shown similarly to the figures above. The light peach bars represent small energy intervals over which integration has been made to obtain the contribution of radiative processes at different energy intervals.

Figure 6 . 20 :

 620 Figure 6.20: Flux integrated over one order of magnitude energy bins. The number depicts the percentage of the hadronic component in each energy bin.

Figure 6 . 21 :

 621 Figure 6.21: Sensitivity for CTA North (grey points) and South (black points) for a point source. The flux of four SNRs, RX J1713.7-3946 (red), HESS J1731-347 (orange), HAWC J2227+610 (green), and Cassiopeia A (blue) are compared to the CTA flux sensitivity.

Figure 7 . 1 :

 71 Figure 7.1: Modular scheme of how data flows from its collection to its scientific analysis. Credit: Jürgen Knödlseder et al. [11].

Figure 7 .

 7 Figure 7.1 shows the overall workflow of CTA data. At first, raw data is captured from the cameras of the telescope arrays and injected into a pipeline for initial processing. This involves calibration of data, reconstruction of events, and performing analysis for selecting gamma-ray-like events. The last step also includes providing the Instrument Response Functions (IRFs), a mathematical function, or a set of lookup tables that relates the measured event to the incoming

Figure 7 . 2 :

 72 Figure 7.2: Flow chart of the high-level γ-ray data analysis from level DL3 to DL5 as followed in Gammapy. Credit: https://docs.gammapy.org/0.20.1/user-guide/package.html.

Figure 7 . 3 :

 73 Figure 7.3: The Naima fit result for SNR RX J1713.7-3946 of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at high-energy generated using the PD model (see text).

Figure 7 . 4 :

 74 Figure 7.4: The Naima fit result for SNR RX J1713.7-3946 of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at high-energy generated using the IC+PD model (see text).

Figure 7 . 7 :

 77 Figure 7.7: The Naima fit result for SNR HESS J1731-347 of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at high-energy generated using the PD model (see text).

Figure 7 . 8 :

 78 Figure 7.8: The Naima fit result for SNR HAWC J2227+610 of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at highenergy generated using the PD model (see text).

Figure 7 . 9 :

 79 Figure 7.9: Different pion-decay models with varying maximum proton energy. The pion-decay model with E cut,p = 300, 400, 500, 600, 700 eV are represented by blue, orange, green, red, and violet curves, respectively. The observed data measurements for the source are also shown (see text).

Figure 7 . 10 :

 710 Figure 7.10: The high-energy part of the SED of HAWC J2227+610 along with the CTA simulated data points (blue) generated by the pion-decay model with E cut,p = 300 TeV (see text).

Figure 7 .

 7 Figure 7.10 shows the zoomed-in Naima fit for a maximum proton energy cutoff value of 300 TeV. The flux in the energy range provided for the simulation shows low uncertainty compared to the present instruments. However, the statistics are very limited at the energy where the cut-off begins, and the simulated data points fluctuate around the line depicting the pion-decay contribution. The resulting best-fit parameters of the Naima fit have been tabulated in Table7.8.

Figure 7 . 11 :

 711 Figure 7.11: The high-energy part of the SED of HAWC J2227+610 along with the CTA simulated data points (blue) generated by the pion-decay model with E cut,p = 500 TeV (see text).

Figure 7 . 12 :

 712 Figure 7.12: The high-energy part of the SED of HAWC J2227+610 along with the CTA simulated data points (blue) generated by the pion-decay model with E cut,p = 700 TeV (see text).

Figure 7 . 13 :

 713 Figure 7.13: The fit results of the different proton energy cut-off models and the simulated data for HAWC J2227+610 generated using proton energy cut-off value = 300 TeV.

Figure 7 . 14 :

 714 Figure 7.14: The fit results of the different proton energy cut-off models and the simulated data for HAWC J2227+610 generated using proton energy cut-off value = 500 TeV.

  .15. Only the zoomed-in version of the high-energy component of the SEDs for each SNR is shown. The encircled region is the focus of this study.

Figure 7 . 15 :

 715 Figure 7.15: The excess flux deviating from the theoretical models for SNRs CTB 37A, W49B, RX J1713.7-3946, and W28 (indicated by circles).

Figure 7 . 16 :

 716 Figure 7.16: The combined heavy-element model (green) for RX J1713.7-3946 consisting of the pion-decay model for different elements: protons (blue), helium (orange), nitrogen (green), and iron (red). For comparison, the observed data for RX J1713.7-3946 are also shown.

Figure 7 . 17 :

 717 Figure 7.17: Combined heavy-element model (green) of the SNR RX J1713.7-3946 consisting of the pion-decay model for proton-like elements (blue) and N-like elements (orange). For comparison, the observed data for RX J1713.7-3946 are also shown

Figure 7 . 18 :

 718 Figure 7.18: The fit result of the observed (orange) and simulated (blue) data in the Dataset for RX J1713.7-3946 with the p-model (red) and HE-model (black).

Figure 7 . 19 :

 719 Figure 7.19: Simulation of the entire Galactic Plane observed by CTA. It shows the excess counts compared to the instrumental background model in the energy range of 0.07-200 TeV.Credit: Remy et al.[START_REF] Remy | Survey of the Galactic Plane with the Cherenkov Telescope Array[END_REF]

Figure 7 .

 7 [START_REF] Kawai | Telescope Array Experiment[END_REF] shows in blue the distribution of all the synthetic SNRs in our Galaxy. The right-handed galactic coordinate system has been used. The dots in orange are the shell-type SNRs, and the pink diamonds show interacting SNRs (ISNRs). The plot only shows the SNRs detected with a significance of TS > 25.The Sun has been represented by the yellow dot.

Figure 7 . 20 :

 720 Figure 7.20: The spatial distribution of all the simulated SNRs (represented by blue dots) in our Galaxy, along with the detected shell-type SNRs (represented by orange dots) and the detected ISNRs (represented by pink diamonds).

Figure 7 .

 7 Figure 7.21 shows the ratio of the effective radius of the input simulated and reconstructed simulated SNRs (Reff ratio) as a function of the seed flux. Effective radius depends on the spatial model used to simulate the source. The varying size of the markers corresponds to the size of the reconstructed sources. Using this plot, we try to deduce CTA's capability to reconstruct the flux with different spatial geometry. All the SNRs for which the CTA pipeline was able to correctly identify the spatial information of the reconstructed SNR with respect to the seed SNR lie around the line y = 1. However, we can see that a few points lie around the Reff ratio of 2, which shows poor reconstruction. We see that for SNRs with such a high ratio, the flux is also very small, between 10 -14 to between 10 -13 photons cm -2 s -1 , which could be a major contributing factor to the poor reconstruction. Mostly all other sources have been reconstructed well within the ratio of 0.75 -1.25. For sources with very large flux, i.e.,between 10 -11 photons cm -2 s -1 , the

Figure 7 . 21 :

 721 Figure 7.21: Ratio of the effective radius of the seed and the observed radius as a function of the seed flux for detected shell-type SNRs (blue dots) and ISNRs (orange diamonds).

Figure 7 .

 7 Figure 7.22 shows the distribution of the flux of simulated and known SNRs with respect to the distance. The shell-type SNRs are represented by the blue dots, and ISNRs are represented by the pink dots. Out of all the simulated SNRs, the ones reconstructed by the pipeline have been shown by a cross symbol. Yellow squares represent the known SNRs.Comparing the simulated SNRs with the known SNRs, we can see that CTA promises to detect more SNRs at larger distances with a range covering 3 to 20 kpc. Additionally, SNRs with flux as low as ∼ 10 -14 photons cm -2 s -1 can be detected by CTA.

Figure 7 . 22 :

 722 Figure 7.22: Distribution of shell-type SNRs (blue dots) and ISNRs (pink dots) in the fluxdistance parameter space.

Figure 7 . 23 :

 723 Figure 7.23: Distribution of shell-type SNRs (blue dots) and ISNRs (pink dots) in the flux-age parameter space.

( 7. 4 )•

 4 E disp (E|p true , E true )(T eV -1 ) is the energy dispersion. It gives the probability to reconstruct the photon at energy E when the true energy is E true and the true position is p true . E disp E disp = E disp (E reco |E true , p true , ξ).( 7.5)

Table 1 ,

 1 and references therein. The old SNRs are indicated by blue circles, while the young SNRs are represented by orange circles. . .6.18 Statistical comparison between leptonic and lepto-hadronic models using likelihood method. . . . . . . . . . . . . . . . . . . . . . . . . Integration method. Different radiative models are shown similarly to the figures above. The light peach bars represent small energy intervals over which integration has been made to obtain the contribution of radiative processes at different energy intervals. . . . . 123 6.20 Flux integrated over one order of magnitude energy bins. The number depicts the percentage of the hadronic component in each energy bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 6.21 Sensitivity for CTA North (grey points) and South (black points) for a point source. The flux of four SNRs, RX J1713.7-3946 (red), HESS J1731-347 (orange), HAWC J2227+610 (green), and Cassiopeia A (blue) are compared to the CTA flux sensitivity. . . . . . . . . . . 126 7.1 Modular scheme of how data flows from its collection to its scientific analysis. Credit: Jürgen Knödlseder et al. [11]. . . . . . . . . . . . 130 7.2 Flow chart of the high-level γ-ray data analysis from level DL3 to DL5 as followed in Gammapy. The Naima fit result for SNR HESS J1731-347 of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at high-energy generated using the PD model (see text). . . . . . . . . . . . . . . . . . . . . . . . . 140 7.8 The Naima fit result for SNR HAWC J2227+610 of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at high-energy generated using the PD model (see text). . . . . . . . . . . . . . . . . . . . . . . . . 141 7.9 Different pion-decay models with varying maximum proton energy. The pion-decay model with E cut,p = 300, 400, 500, 600, 700 eV are represented by blue, orange, green, red, and violet curves, respectively. The observed data measurements for the source are also shown (see text). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	LIST OF FIGURES

Credit: https://docs.gammapy.org/0.20.1/userguide/package.html. . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 7.3 The Naima fit result for SNR RX J1713.7-3946 of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at high-energy generated using the PD model (see text). . . . . . . . . . . . . . . . . . . . . . . . . 135 7.4 The Naima fit result for SNR RX J1713.7-3946 of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at high-energy generated using the IC+PD model (see text). . . . . . . . . . . . . . . . . . . . . . . 136 7.5 The Naima fit result for SNR RX J1713.7-3946 of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at high-energy generated using the BR+IC+PD model (see text). . . . . . . . . . . . . . . . . . . . 137 7.6 The Naima fit result for SNR Cassiopeia A of the combined observations of the real data (black points) at low-energy and the simulated CTA data (blue points) at high-energy generated using the PD model (see text). . . . . . . . . . . . . . . . . . . . . . . . . 139 7.7

Table 5 .

 5 2 is tabulated below:

	Parameter	Minimum Typical	Maximum
	QE (300 nm -450 nm)	25 %	-	-
	Peak QE (385 nm)	32%	35%	-
	Nominal voltage (for gain 4 x 10 4 )	900 V	-	1600 V
	Pulse width (FWHM)	2.5 ns	-	3.0 ns
	Rise time (10-90%)	2.5 ns	-	-
	Transit time spread		-	2.0 ns
	Afterpulse percentage	-	0.02	-

1: Specifications for PMT R12992-100 manufactured by Hamamatsu C.1.

  Table on the right-hand side of the figure.

	Light intensity	Cumulative percentage
	(as a fraction of the maximum)	of covered area
	> 50.0%	10 %
	33.3% > I > 50.0%	22 %
	25.0% > I > 33.3%	52 %
	20.0% > I > 25.0%	> 90 %
	16.7% > I > 20.0%	> 90 %
	14.3% > I > 16.7%	> 90 %
	12.5% > I > 14.3%	> 99 %
	11.1% > I > 12.5%	> 99 %
	< 10.0%	> 99 %

Table 6 . 1 :

 61 .2. For more information, see Appendix A. Information on the SNRs

	Source	Type RA(hh mm	DEC(dd		Gal	Gal Lat	Distance	Spectral	Silver	Golden
			ss)	mm ss)		Long	(deg)	(kpc)	Index	Data	Data
						(deg)
	RX J1713.7-3946	Shell 17 13 33.6	-39 45 36		347.34	-0.47	1	2.2	Y	Y
	HESS J1731-347	Shell 17 32 03	-34 45 18		353.54	-0.67	3.2	2.32	Y	Y
	Tycho	Shell 00 25 21.6	+64 07 48	120.09	1.4	3.5	1.95	Y	N
	RX J0852.0-4622	Shell 08 52 00	-46 22 00		266.28	-1.24	0.2	1.81	Y	Y
	IC 443	Shell 06 16 51	+22 30 11	189.07	2.92	1.5	3	Y	Y
	RCW 86	Shell 14 43 02.16	-62 26 56		315.44	-2.32	2.5	2.54	Y	N
	SN 1006 SW	Shell 15 02 03.2	-41 07 05		327.86	15.35	2.2	2.29	N	N
	SN 1006	Shell 15 02 50	-41 56 30		327.57	14.56	2.18		Y	N
	SN 1006 NE	Shell 15 04 03.4	-41 48 11		327.84	14.56	2.2	2.35	N	N
	HESS J1534-571	Shell 15 34 00	-57 06 00		323.65	-0.92		2.51	N	N
	HESS J1614-518	Shell 16 14 19.2	-51 49 12		331.52	-0.58	1.5	2.46	N	N
	CTB 37B	Shell 17 13 57.6	-38 12 00		348.65	0.38	13.2	2.65	Y	Y
	HESS J1912+101	Shell 19 12 49	+10 09 06	44.39	-0.07		2.7	Y	N
	0FGL	Shell 19 54 27.47	+28 38 54.6	65.3	0.38	9.2		N	N
	J1954.4+2838
	SNR G106.3+02.7	Shell 22 27 59	+60 52 37	106.35	2.71	0.8	2.29	Y	Y
	SNR G106.3+02.7	Shell 22 27 59	+ 60 52 37	106.35	2.71	0.8	2.29	Y	N
	Cassiopeia A	Shell 23 23 13.8	+58 48 26	111.71	-2.13	3.4	2.3	Y	Y
	LMC N132D	MC	05 25 02.20	-69 38 39.0	280.31	-32.78	50	2.4	Y	N
	SNR G318.2+00.1	MC	14 57 46	-59 28 00		318.36	-0.43	3.5	2.52	N	N
	CTB 37A	MC	17 14 15	-38 31 27		348.42	0.14	7.9	2.3	Y	Y
	W 28	MC	18 01 42.2	-23 20 06.0	6.66	-0.27	2	2.66	Y	Y
	W 49B	MC	19 11 07.3	+09 09 37.0	43.32	-0.16	11.3	3.14	Y	Y
	SNR G349.7+00.2	MC	17 17 57.8	-37 26 39.6	349.72	0.17	11.5	2.8	Y	N
	HESS J1745-303	MC	17 45 02.10	-30	22	358.71	-0.64		1.82	Y	N
				14.00
	HESS J1800-240A	MC	18 01 57.8	-23 57 43.2	6.14	-0.63	2	2.55	N	N
	HESS J1800-240B	MC	18 00 26.4	-24 02 20.4	5.9	-0.37	2	2.5	Y	N
	HESS J1800-240C	MC	17 58 51.6	-24 03 07.2	5.71	-0.06	2	2.31	N	N
	W 51	MC	19 22 55.2	+ 14 11	49.12	-0.36	5.4		N	N
				27.6

Table 6 . 4 :

 64 Parameter range used as input prior information.

	Lower limit	Upper limit

Table 6 . 5

 65

	+0.02
	-0.02

: Parameters obtained from the fit for RX J0852.0-4622. using Naima.

Table 6 . 6 :

 66 Parameters obtained from the fit for RX J1713.7-3946 using Naima.

	+0.01 -0.02	X

Table 6 . 7 :

 67 Parameters obtained from the fit for Cassiopeia A using Naima.

	+0.002
	-0.003

Table 6 . 8 :

 68 Parameters obtained from the fit for CTB 37A using Naima.

	+0.04 -0.05	50.04 +0.18 -0.17

Table 6 .

 6

	+0.02
	-0.03

10: Parameters obtained from the fit for HESS J1731-347 using Naima.

Table 6 .

 6

	+0.03 -0.03	49.01 +0.1 -0.1

11: Parameters obtained from the fit for IC 443 using Naima.

Table 6 .

 6

	+0.02 -0.02	49.10 +0.19 -0.12

[START_REF] Sharma | A single photoelectron calibration system for the NectarCAM camera of the Cherenkov Telescope Array Medium-Sized Telescopes[END_REF]

: Parameters obtained from the fit for W49B using Naima.

Table 6 .

 6 14: Range of fit parameters obtained for all studied SNRs using Naima for different radiative scenarios.

	Parameter	Lepto-hadronic	Leptonic
	α e	1.61 -2.80	1.34 -2.66
	α p	1.64 -2.49	Nil
	E cut,e (T eV )	0.69 -14.80	0.17 -630.96
	E cut,p (T eV )	0.02 -446.68	Nil
	B(µG)	14.12 -960.61	0.29-86.08
	K ep	0.00160 -0.024	Nil
	N H (cm -3 )	1.70 -163.21	0.07 -205.86
	SNR	E coe (TeV)	E cop (TeV)
	HAWC J2227+610 Cassiopea A CTB 37A IC 443 RX J1713.7-3946 HESS J1731-347 RX J0852.0-4622 W28 W 49B	0.69 +0.004 -0.004 8.32 +0.004 -0.004 4.50 +0.02 -0.02 1.46 +0.04 -0.03 14.80 +0.04 -0.03 7.41 +0.04 -0.03 10.80 +0.02 -0.02 2.02 +0.01 -0.01 3.10 +0.01 -0.02	446.68 +0.07 -0.07 23.40 +0.01 -0.01 0.08 +0.05 -0.05 0.80 +0.04 -0.06 74.10 +0.04 -0.05 20.40 +0.04 -0.06 0.02 +0.08 -0.05 0.35 +0.01 -0.02 1.60 +0.00 -0.01

Table 6 .

 6

15:

Electron (E coe ) and proton (E cop ) distribution cut-off energies obtained from the fit of the studied sources.

Table 6 .

 6

	Source	Leptonic Lepto-hadronic ∆ BIC
	Cassiopea A	6851	2956	3895
	CTB 37A	194	47	147
	HAWC J2227+610	118	82	36
	HESS J1731-347	52	41	11
	IC 443	235	219	16
	RX J1713.7-3946	112	106	6
	RX J0852.0-4622	5088	4994	94
	W28	207	172	35
	W49B	1158	285	873

[START_REF] Hummel | The first stars: formation under cosmic ray feedback[END_REF]

: BIC values for considered sources. ∆BIC is defined by BIC(Leptonic) -BIC(Leptohadronic).

Table 7 . 1 :

 71

	+0.001 -0.001 2.13 +0.03 -0.04 1.73 +0.01 -0.02 electron energy cut-off (TeV) 14.80 +0.03 Electron spectral index Proton spectral index -0.02 proton energy cut-off (TeV) 74.10 +0.03 -0.03 B (µG) 90.34 +3.72 -4.35 K ep 0.0075 +0.0003 -0.0004 N H (cm -3 ) 39.89 +0.83 -0.96	47.0591 +0.0007 -0.0007 2.14 +0.02 -0.02 1.76 +0.01 -0.01 14.66 +0.01 -0.01 81.28 +0.01 -0.01 92.39 +2.34 -1.50 0.0075 +0.0001 -0.0001 39.06 +0.40 -0.29
	MaxLogLikelihood	-37.69	-18.29

Table 7 . 2 :

 72

	+0.001 -0.001 2.13 +0.03 -0.04 1.73 +0.01 -0.02 electron energy cut-off (TeV) 14.80 +0.03 Electron spectral index Proton spectral index -0.02 proton energy cut-off (TeV) 74.10 +0.03 -0.03 B (µG) 90.34 +3.72 -4.35 K ep 0.0075 +0.0003 -0.0004 N H (cm -3 ) 39.89 +0.83 -0.96	47.0600 +0.0006 -0.0006 2.17 +0.02 -0.02 1.75 +0.01 -0.01 14.89 +0.01 -0.01 77.27 +0.01 -0.01 94.80 +0.73 -0.87 0.0077 +0.0001 -0.0001 41.12 +0.38 -0.42
	MaxLogLikelihood	-37.69	-26.26

Table 7 . 4 :

 74 Fit results of different physical models for RX J1713.7-3946 compared to the fit with original data.

		MaxLogLikelihood
	Original Data	-37.69
	CTA PD	-18.29
	CTA IC+PD	-26.26
	CTA BR+IC+PD	-27.23

Table 7 . 6 :

 76

	+0.007 -0.009 2.02 +0.02 -0.03 1.62 +0.02 -0.02 electron energy cut-off (TeV) 7.41 +0.04 Electron spectral index Proton spectral index -0.03 proton energy cut-off (TeV) 20.40 +0.04 -0.06 B (µG) 91.98 +3.63 -4.37 K ep 0.0117 +0.0005 -0.005 N H (cm -3 ) 45.16 +2.04 -2.16	47.28 +0.01 -0.01 2.08 +0.05 -0.03 1.62 +0.02 -0.02 7.41 +0.02 -0.02 18.54 +0.02 -0.02 100.65 +3.52 -2.31 0.0114 +0.0004 -0.0004 43.83 +0.89 -1.09
	MaxLogLikelihood	-7.01	-13.78

Table 7 . 7 :

 77

	+0.02 -0.03 1.76 +0.02 -0.03 electron energy cut-off (TeV) 0.69 +0.004 Proton spectral index -0.004 proton energy cut-off (TeV) 446.68 +0.07 -0.07 B (µG) 596.94 +12.97 -13.12 K ep 0.0047 +0.0002 -0.0004 N H (cm -3 ) 1.70 +0.09 -0.10	1.69 +0.02 -0.02 1.75 +0.01 -0.01 0.68 +0.01 -0.01 346.73 +0.04 -0.04 613.26 +12.43 -12.29 0.0047 +0.0002 -0.0001 1.70 +0.04 -0.05
	MaxLogLikelihood	-27.45	-8.95

Table 7 .

 7 8.

	Parameter	Lepto-hadronic
	log10(Amplitude) Proton spectral index proton energy cut-off (TeV) K ep N H (cm -3 )	47.021 +0.002 -0.002 1.72 +0.01 -0.02 239.88 +0.02 -0.05 0.0053 +0.0004 -0.0004 1.57 +0.05 -0.05
	MaxLogLikelihood	-22.31

Table 7 . 8 :

 78 Parameters obtained from the fit of HAWC J2227+610 using Naima.

Table 7 .

 7 10: Parameters obtained from the fit for HAWC J2227+610 using Naima.

	+0.02
	-0.01

Table 7 .

 7 11: Fit results of the simulated pion-decay models with different proton cut-off values for the SNR HAWC J2227+610.

Table 7 .

 7 12. .

	Optimizer	Method	Model	Loglikelihood Convergence
	Minuit	Migrad PD 300 (H0)	48.71	True
	Minuit	Migrad PD 500 (H1)	85.47	True
	Minuit	Migrad PD 700 (H2)	124.

Table 7 .

 7 .13. . 13:

	Optimizer	Method	Model	Loglikelihood Convergence
	Minuit	Migrad PD 500 (H0)	34.27	True
	Minuit	Migrad PD 300 (H1)	59.87	True
	Minuit	Migrad PD 700 (H2)	36.59	True

Table 7 .

 7 .14. . 14: The fit results for different models for the SNR RX J1712 using Dataset containing the observed data and the simulated data consisting of a mixture of protons and nitrogen.

	Optimizer	Method	Model	Loglikelihood Convergence
	Minuit	Migrad	p-model (H0)	107.99	True
	Minuit	Migrad HE-model (H1)	81.29	True

Table B . 3 :

 B3 Fit results for SNRs using different slopes of the electron cut-off energy. The beta value for which the MaxLogLikelihood and the BIC values are the lowest for each SNR have been highlighted using bold letters and numbers.

	Source	β-value	MaxLogLikelihood	BIC
	Vela Jr.	1 (ECPL)	-2484.37
		0.5	-2567.50
		Free	-2531.65
	HESS J1731	1 (ECPL)	-7.01
		0.5	-67.18
		Free	-6.63
	W28	1 (ECPL)	-73.51
		0.5	-82.78
		Free	-72.06
	RX J1713	1 (ECPL)	-37.69
		0.5	-36.50
		Free	-36.22
	W49B	1 (ECPL)	-128.36
		0.5	-122.59
		Free	-125.31
	CTB 37A	1 (ECPL)	-12.59
		0.5	-13.57
		Free	-12.22
	HAWC J2227	1 (ECPL)	-27.45
		0.5	-27.52
		Free	-28.30
	IC 443	1 (ECPL)	-97.10
		0.5	-246.55
		Free	-50.29
	Cass A	1 (ECPL)	-1461.56
		0.5	-1740.52
		Free	-1513.68

The gyroradius (also known as the radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. Credit: Wikipedia

TeVCat online source catalog. Home page. http://tevcat.uchicago.edu.

The Rayleigh-Taylor instability is an instability of an interface between two fluids of different densities, which occurs when the lighter fluid is pushing, the heavier fluid. Credit: Wikipedia

https://fermi.gsfc.nasa.gov/

https://heasarc.gsfc.nasa.gov/docs/cgro/cgro.html

https://veritas.sao.arizona.edu/

https://www.mpi-hd.mpg.de/hfm/HESS/

https://astro.desy.de/gamma_astronomy/magic/index_eng.html

https://www.hawc-observatory.org/

https://directory.eoportal.org/web/eoportal/satellite-missions/l/lhaaso

https://www.cta-observatory.org/about/

Field Programmable Gate Array, which is a semiconductor device that can be programmed by the user.

www.hamamatsu.com

https://www.vertex-icbuy.com/uploads/soft/20220107/5-22010G10450G0.pdf

In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed Credit Wikipedia

https://sci.esa.int/web/planck

https://chandra.harvard.edu/

https://www.swift.ac.uk/

https://sci.esa.int/web/integral

https://www.cosmos.esa.int/web/xmm-newton

https://www.icrr.u-tokyo.ac.jp/em/index.html

The Klein-Nishina formula shows that the total cross section and expected deflection angle decrease with increasing photon energy.

It is all the accumulated radiation in the universe due to star formation processes. This radiation covers almost all wavelengths of the electromagnetic spectrum except the microwave.

https://tools.ssdc.asi.it/SED/

https://hea-www.harvard.edu/ChandraSNR/snrcat_gal.html

Covariance measures how a particular random variable varies with respect to another variable.

For the latest publicly available IRF please visit -https://www.ctaobservatory.org/science/cta-performance/

It can also deal with any kind of X-ray data analysis from NASA mission, see https://heasarc.gsfc.nasa.gov/ftools/.

https://www.cta-observatory.org/ctao-adopts-the-gammapy-software-package-for-scienceanalysis/.

3 https://www.mpi-hd.mpg.de/hfm/HESS/pages/newsarchive/.

The distance between the source position and telescope pointing in the sky.

Size of the ON region where you assume your source lies.

Acknowledgements

heavier elements. This study could be extended to other interesting candidates such as W 49B, W28, and CTB 37A.

In the end, we analyzed the detected SNRs found in the Galactic Plane Survey simulated by the Galactic group of CTA. In this study, we found that SNRs will be the second most dominant γ-ray source detected by CTA (after PWNe) and that CTA would increase the number of detected SNRs by a factor of 2. Additionally, SNRs covering a large distance (up to 20 kpcs), with flux as low as ∼ 10 -14 photons cm -2 s -1 would be easily detected by CTA. All these findings bring us closer to the possibility of unraveling the origin of Galactic CRs.

with a particular source type. Figure 3.12 shows a pie chart depicting the types of sources identified by the HGPS.

Figure 3.12: The H.E.S.S. Galactic Plane Survey Catalogue source identification [START_REF] Abdalla | Galactic plane survey[END_REF].

Research on performing a blind search of γ-rays detected by H.E.S.S. above 20 TeV [START_REF] Giunti | The Galaxy beyond TeV energies with H.E.S.S. and CTA[END_REF] has been done, which serves a valuable legacy for future IACT such as CTA.

A review article by A.M.W. Mitchell [START_REF] Mitchell | Status of Ground-based and Galactic Gamma-ray Astronomy[END_REF] encapsulates all the recent status on the ground-based and Galactic γ-ray astronomy.

Comparing the two scenarios also shows more confidence in the lepto-hadronic scenario than in the purely leptonic scenario for each source since the ratio r Lepto-hadronic is greater than 0.5 for all sources. The most uncertain ones are Vela-Junior and IC 443. RX J1713.7-3946 shows only a slight tendency towards the leptohadronic scenario. However, unlike the previously discussed qualitative analysis, this method allows us to conclude that for W 49B, HESS J1731-347, CTB 37A, HAWC J2227+610, and Cassiopeia A, the lepto-hadronic model is favoured. Figure 6.18: Statistical comparison between leptonic and lepto-hadronic models using likelihood method.

BIC criterion

From the BIC value of the leptonic and lepto-hadronic scenarios obtained for each source, we can compute the ∆BIC value and apply the previously introduced In Figure 7.5, the CTA flux has been simulated by using a combined spectral model of bremsstrahlung, inverse Compton, and pion-decay. Table 7.3, lists the output parameters of the fits. It can be observed that the parameters only slightly vary from the previous fit results.

Parameter

Real Observations Combined Observations log10(Amplitude) 47.060 The Naima fit parameters obtained from the fit for the lepto-hadronic model of RX J1713.7-3946 with the real observations, and combined data of the observed data at low-energy and the CTA simulated data points at high-energy generated using the BR+IC+PD model.

Cassiopeia A

The flux for Cassiopeia A has been simulated using 200 hrs livetime and the CTA North Prod5 IRF with a zenith angle of 20 • . The on-radius has been set as 0.1 • with the offset of 0.4 • . In Figure 7.6, the CTA flux has been simulated by using the spectral model of pion-decay radiation only. Table 7.5 lists the output parameters of the fit. Table 7.5: The Naima fit parameters obtained from the fit for the lepto-hadronic model of Cassiopeia A with the real observations, and combined data of the observed data at low-energy and the CTA simulated data points at high-energy using the PD model.

Appendix A Data Origin

All the sources and their references are tabulated in It is the Chandra Catalog of Galactic Supernova Remnants. For each SNR in the catalogue, care has been taken to choose hard X-rays to consider only non-thermal emissions (2.1 -10.0 keV). Few sources were well reproduced with an absorbed power-law model however, for some sources, the information about the model chosen is not available. For some sources only the central region was used and for others full SNR was used.

Green

Catalogue [START_REF] Green | A revised catalogue of 294 Galactic supernova remnants[END_REF] In this radio catalogue, the flux density is not a measured value, but is instead derived from the observed radio spectrum of the source. For several SNRs a simple power law is not adequate to describe their radio spectra, either because there is evidence that the integrated spectrum is curved or the spectral index varies across the face of the remnant. In these cases the spectral index is given as 'varies' In some cases where the remnant is highly confused with thermal emission, the spectral index is given as '?' since no value can be deduced with any confidence. The selection effects for the SNR catalogue are therefore dominated by those that apply at radio wavelengths. Current catalogue contains SNRs having surface brightness above 10-20 W m -2

Hz -1 sr -1

.

gamma-cat[70]

The gamma-cat has been used to obtain high-energy gamma-ray points for various sources. It provides data taken by instruments such as HESS, MAGIC, VERITAS and more. For each source, the catalogue provides the high-energy observations along with the source reference.

[72]

The paper provides observational data for Cass A. The Differential Spectral Flux Points with Statistical Errors from VERITAS Data have been explicitly provided in the energy range 0.2-12.6 TeV for an observation of 21 hrs. To derive the energy spectrum using VERITAS, a power-law distribution has been assumed. Additionally, 10.8 yr of Pass 8 R3 LAT data has also been provided explicitly in the energy range of 100

MeV to 500 GeV. For Fermi, the spectral shape of the emission from Cass A was assumed to be a smoothly broken power law.

[73]

The paper provides observational data for Vela Jr. With Suzaku. X-rays with the energy up to 22 keV are detected from the northwest region of Vela Jr. The spectra in the hard X-ray band are reproduced with a power-law model.

[74]

The paper provides observational data for RX J1713 in the GeV and TeV band using five years worth of Fermi -LAT data. Flux in the energy range from 500 MeV to 300 GeV has been derived by optimizing a spectral model of the form of a power-law.

[66]

This paper provides non-thermal observations from RX J1713 with Suzaku. Hard X-rays have been detected up to 40 keV and are described by a power law. Table A.2: Origin of the data points for the selected SNRs.

Appendix B Electron Distribution

Different functional forms are available to choose from when deciding upon the form of parent electron and proton particle distributions. In the literature we found majorly two functional forms, exponential cutoff power law and broken power law (BPL). ECPL is a functional form which takes into account a cutoff in the spectrum due to the maximum energy reached by the accelerated particle. A BPL takes into account the fact that particles suffer from radiative losses. It has an additional break which is defined by equating the energy loss time to the age of the system. In particular electrons are suspected to suffer more radiative losses than protons.

In Table B.1 we present the electron and proton particle distributions assumed in various papers. Most papers have used ECPL while some have used BPL. Table B.1: Information about the electron and proton particle distributions used for MWL SED fitting along with the references.

Only a few papers give complete information about the parameters derived from the fit. We could obtain the BPL parameters for the SNRs RX J1713 [START_REF] Abdalla | observations of RX J1713.7-3946 with improved angular and spectral resolution: Evidence for gamma-ray emission extending beyond the Xray emitting shell[END_REF], IC 443 [START_REF] Ackermann | Detection of the Characteristic Pion-Decay Signature in Supernova Remnants[END_REF], and W 49B [START_REF] Abdalla | The supernova remnant W49B as seen with H.E.S.S. and Fermi-LAT[END_REF]. We used these parameters to refit the SEDs to see APPENDIX B. ELECTRON DISTRIBUTION the impact on our conclusions. We made use of the BPL equation in Naima: '

with :

• A: the amplitude of the electron SED

• E 0 : the reference energy

• E break : the break energy

• α 1 : power law index before the break energy • α 2 : power law index after the break energy From Table B.2, we can see that compared to ECPL, the BPL is slightly preferred for RX J1713 and W49B however, for IC443 ECPL is slightly preferred. The difference between the BIC values of the ECPL and BPL models for the SNRs RX J1713 and W49B is very small and does not change enough to affect the final results. Figure B.1 shows as an example, the obtained fit results for the SED for RX J1713 using different model parameters. We can see that changing the electron distribution has no significant qualitative impact on the overall SED.

Hence, we conclude that using ECPL for electron and proton distributions, although simplistic, is a valid approximation. Additionally, we also studied the effect on the fit by using a more general form

Procedures

Detailed procedure for conducting high-intensity measurements using the test bench setup at IJCLab is given below:

Procedure for conducting high-intensity homogeneity test N.B. 2. The names of the file saved are very important and ensure the same format is followed for all the runs. Keep checking if the data is being saved properly or not.

Different scan positions on the screen are provided below:

Detailed procedure for painting the screen using the dip-coating setup at IJ-CLab is given below:

The dip-coating procedure of the calibration screen of NectarCam :

Day 1:

• Mix the two cans of Eljen paint well (already diluted with 12% water), for 1-2 hrs before starting with the dip-coating process. • Before starting with the dip-coating process, it is important to clean the inside of the paint tank with alcohol. • Assemble the dip-coating machine by fixing the paint tank to support using screws and washers. (To screw properly follow the process: use the turntable, then the big screw, and finally the small screw. • Clean the screen with alcohol and place the screen on a table covered with clean cloths.

• Put the large mask ( 23 cm) first on the part of the screen, opposite to the light injection, using scotch tape. Ensure that the mask is placed exactly on the screen and is not protruding out.

• Attach the screen to the mechanical structure with the help of brackets to position it in line with the paint tank (make sure that the brackets are shorter than the metal piece that holds the screen). • Check the alignment of the screen and the tank, if necessary unscrew the large screws to reposition the plate used to attach the tank to the structure. • Fill the tank with water to check for leaks and empty it after the check and leave it to dry. • Try lowering the screen into the empty tank to ensure that the dip-coating process works smoothly. • Connect with the PC to be able to move the motors:

Login : $Admin Pwd: AdminPC1863

• To start the motor, click on the " TLE94112EL_" icon on the desktop. Using this interface you can set the motor speed etc. • Switch on (POWER) the low voltage module and set the voltage value as 20V. Then switch on the voltage (ON/OFF), and you will see the light of the button turn green and the value of the current will appear. • On the PC click on the motor management program to check the speed value. Click on Tools Serial Monitor, and a pop-up window will open. The speed is preset to v max = 30.

Use the motor interface to turn on the motor and to vary the insertion speed of the screen. • Carefully control the lowering of the screen and stop the motor when the screen has sufficiently submerged into the tank (before it reaches too close to the motor), otherwise, there is a risk of breaking the transmission chain. • Insert the paint into the tank up to the fourth screw at the top.

• Insert the screen in the tank filled with paint at v max = 30 (= 1.68 mm/s).

• Once the screen is completely inserted into the tank, wait at least 5 seconds.

• Using the motor control, carefully lift the screen back up.

• Unplug the screen from the metal dip-coating holder and lay it flat on a table covered with clean cloths, and leave it to dry for ~23 hrs. • Switch off the low voltage module and put the PC on standby • Seal the tank with thick tape to prevent the paint from drying in the tank.

Day 2:

• Put the small metal mask (13 cm) on the screen, opposite the light injection, using scotch tape. It is preferable to remove the tape while keeping it parallel to the screen, this way there will be fewer traces of glue.

• Clean the traces of glue left by the tape due to the previous mask with alcohol.

• Remove the tape covering the tank opening and use the stirrer to mix the paint well to avoid a density gradient in the paint. • Hang the screen on the structure, with the same careers described above.

• Switch on the low voltage module, and check the speed value on the program (must be v max = 30). • Insert the screen in the tank filled with paint at v max = 30 (= 1.68 mm/s) using the motor software. Be careful to stop the motor before the screen touches the bottom surface of the tank. • Once the screen is inside the tank, wait for 5 seconds.

• Carefully lift the screen from the tank and leave detach it from the mechanical support.

• Leave it to dry for ~ 23 hrs.

• Turn off the low voltage module and put the PC on standby.

• Seal the tank with thick tape to prevent the paint from drying in the tank.

Day 3:

• Clean the traces of glue left by the tape with alcohol.

• If necessary, add more diluted paint.

• Attach the screen to the support as mentioned previously.

• Use the same method as described before to coat the screen.

Day 4:

• Now we move towards painting the fishtail of the screen.

• Prepare a small tank (dimension: 70 mm * 200 mm *200 mm) to paint the fishtail.

• Remove the large tank from the mechanical support, and transfer the remaining paint into the small tank. • Cover the circular surface of the fishtail to allow for light injection.

• Position the small tank under the screen.

• Place the screen with the fishtail pointed directly above the container.

• Fill the small tank with paint, mix it and wait until the foam that forms on the surface disappears. • Start the motor and insert thefishtail into the tank filled with paint at v max = 30 (= 1.68 mm/s). • Once the fishtail is inside the tank wait 5 seconds and then carefully lift it up from the tank. • Leave the screen attached to the motorization for 3 hours to dry the first coat of paint on the fishtail. • Repeat the stepsmentioned above to coat the fishtail with 3 layers of paint.

• Transfer the paint from the small tank to the can.

• Remove the screen from the motorization once the paint on the fishtail has dried (3h after the last coat).

• To avoid losing light, we wrap the fishtail with black tape. To do so, draw an imaginary line 394 mm away from the end of the screen opposite to the light injection, then cover the triangular part and the cylindrical part of the fishtail with black tape (except the circular surface of the light injection). • To further avoid the light from escaping, we wrap the perimeter of the screen with a black tape. Cut the black tape to a suitable width (between 18 mm and 22 mm), apply this tape in such a way that an equal width of about 4 to 6 mm folds over both sides of the screen. Instrument Response Function (IRF) holds information about the performance of the instrument along with the error associated with the reconstruction of the signal using the MC technique or using dedicated observations. In order to model the expected number of events detected from an incident γ-ray shower, an IRF must be used. It provides the probability of an instrument to detect a photon coming from a true position p true on the sky having a true energy E true at a reconstructed position p and energy E. The expected number of detected events is given by: ( 7.1) where:

APPENDIX C. PROCEDURES

• R(p, E|p true , E true )(m 2 TeV -1 ) : is the instrument response;

• Φ(p true , E true )(m -2 s -1 TeV -1 sr -1 ) : is the sky flux model;

• t obs (s) : is the observation time.

The IRF of CTA has been simplified and is a convolution of three independent functions: the effective area A ef f , the PSF, and the energy dispersion E disp . The response of the instrument is given by the formula ( 7.2): R(p, E|p true , E true ) = A eff (p true , E true ) × P SF (p|p true , E true ) × E disp (E|p true , E true ).

( 7.2) where:

ON region. The background is often calculated by measuring a controlled region slightly away from the ON region and is termed as the OFF region. The ON region signal is given by the formulation [?]:

Where α is a factor that accounts for the differences in the observations of the ON and OFF regions, such as the livetime and solid angles. Smaller α reduces the background fluctuations and hence leads to the higher statistical significance of the γ-ray signal.

The OFF region only contains the background and the ON region consists of both the signal and background. Then we can define a likelihood function that can be marginalised over the mean background counts to obtain the mean signal counts. The WStat can be defined as:

where n of f and n on are the Poisson distributed number of counts for OFF and ON regions respectively and µ sig and µ bkg are the mean of the background and signal count respectively.

When the background model is known, then CASH statistics can be used.

D.3 Components of Gammapy

There are various building blocks in Gammapy that allow for high-level scientific analysis. It has been designed so that it is possible to do all the standard analyses with just a basic knowledge of Python and physics involved for a particular analysis.

D.3.1 Gammapy Models

It combines the spatial, temporal, and spectral model templates, which can aid in fitting and simulating the fluxes of γ-ray sources. Spectral models such as the power-law with exponential cutoff describe the number of counts per true energy bin (differential flux) or the spectral shape of a source. To obtain 3D models, a spectral model can be multiplied by spatial models such as 2D Gaussian models, which store morphological information about a source, and temporal models, such as the exponential decay model, which store information about how the source flux varies with time. The SkyModel is an object that linearly combines the model's spectral and spatial components to give a predicted number of expected events from a source at the true energy, position, and time. '

D.3. COMPONENTS OF GAMMAPY

Appendix E

Résumé détaillé

Les rayons cosmiques (RCs), qui bombardent continuellement la Terre, ont été observés par divers instruments. Observés depuis la Terre, les RCs entrants forment un spectre d'énergie raide avec quelques caractéristiques intéressantes surtout au niveau du genou ("knee"), autour de 10 15 eV, qui est le point central de cette étude.

Les sources qui peuvent accélérer les particules jusqu'aux énergies PeV sont connues sous le nom de PeVatrons. La théorie suggère que le spectre jusqu'au genou peut être attribué à des sources astrophysiques galactiques telles que les restes de supernova (SNRs). Les RCs étant des particules chargées, nous ne pouvons pas retracer les trajectoires jusqu'à la source astrophysique d'origine en raison de la déviation par les champs magnétiques galactiques. Cependant, ces RCs, en se propageant, interagissent avec leur environnement et produisent des radiations gamma qui agissent comme un messager de l'Univers relativiste. En 1989, lorsque le télescope Whipple a détecté les premiers rayons gamma de TeV en provenance de la nébuleuse du Crabe, les physiciens ont commencé à s'intéresser à ces rayons et ont trouvé un nouveau moyen de détecter indirectement les RCs. Les rayons gamma de haute énergie codent des informations physiques essentielles sur l'Univers non-thermique. L'étude de ces conditions extrêmes nous aide à comprendre la physique qui sous-tend l'accélération des particules jusqu'à des énergies aussi élevées.

Après des tentatives rigoureuses, des instruments spatiaux tels que Fermi-LAT et des télescopes atmosphériques imageurs Cherenkov (IACT) au sol tels que H.E.S.S., MAGIC et VERITAS ont conduit à des découvertes passionnantes. Des instruments tels que HAWC et LHAASO ont récemment fourni des résul-193