Simulazioni Della Sensibilità Del Cherenkov Telescope Array Ai Gamma Ray Bursts

Università degli Studi di Napoli “Federico II”

Scuola Politecnica e delle Scienze di Base Area Didattica di Scienze Matematiche Fisiche e Naturali

Dipartimento di Fisica “Ettore Pancini”

Laurea Magistrale in Fisica

Simulazioni della sensibilità del Cherenkov Telescope Array ai Gamma Ray Bursts

Simulations of the sensitivity of the Cherenkov Telescope Array to Gamma Ray Bursts

Relatori: Candidato: Prof. Tristano Di Girolamo Antonio Circiello Dr.ssa Carla Aramo Matricola N94000468

A.A. 2019/2020 Simulations of the sensitivity of the Cherenkov Telescope Array to Gamma Ray Bursts

Antonio Circiello Contents

Abstract 1

1 GRBs 4 1.1 Properties ...... 5 1.1.1 Prompt Emission ...... 5 1.1.2 Classiﬁcation beyond the Short-Long divide ...... 6 1.1.3 Afterglow ...... 7 1.2 Progenitors ...... 7 1.2.1 Short GRB progenitors ...... 8 1.2.2 Long GRB progenitors ...... 9 1.3 Dynamics ...... 10 1.3.1 Relativistic motion ...... 11 1.3.2 Shocks and acceleration ...... 13 1.3.3 Dissipation processes ...... 14 1.4 Beyond gamma rays ...... 16 1.4.1 Particle counterparts ...... 16 1.4.2 Gravitational wave counterpart ...... 19

2 GRB observations and simulations 20 2.1 The Cherenkov Telescope Array ...... 22 2.2 Description of the software utilities ...... 27 2.2.1 GammaLib ...... 28 2.2.2 ctools ...... 31

3 Simulations of the ﬁrst two TeV GRBs 34 3.1 GRB 190114C ...... 35 3.1.1 CTA simulation ...... 36 3.1.2 Horizon of the observation ...... 39 3.2 GRB 180720B ...... 43

Conclusions 46

1 Abstract

Gamma Ray Bursts (GRBs) are the most energetic explosive phenomena currently known in the universe. Since their serendipitous discovery in the late ’60s, the great efforts put through their detection and analysis managed to un- veil many peculiar features of these remarkable events. The extreme energies involved in their evolution, the cosmological origin, and the production of all four messengers from the universe (photons, cosmic rays, neutrinos and gravitational waves) are only some of the properties that qualify GRBs as uniquely interesting among the broad selection of signals reaching the Earth. Still, we do not have a complete understanding of the processes involved in GRB production and evolution. In this work I focused on the electromagnetic signal from GRBs and its observation. Very High Energy (VHE) emission from GRBs has been detected only recently thanks to Imaging Air Cherenkov Telescopes (IACTs), able to detect the flashes of Cherenkov radiation from the Extensive Air Showers produced when an energetic gamma-ray photon collides with the atmosphere. In particular, I was interested in analysing the response to these signals with the Cherenkov Telescope Array (CTA), which represents the next generation of IACTs. CTA will be built in two arrays to observe both the Northern and Southern regions of the sky and will increase the energy range for IACT observations both in their lower and upper values, reaching a total range from 20 GeV to 300 TeV. With this goal, I used the ctools software package, distributed by the CTA collaboration, in order to simulate known GRB sources and test how CTA would carry out their observations. This package was developed to provide the scientific community with a common framework for the gamma-ray data analysis. Currently, all data taken from gamma-ray telescopes are stored using the Flexible Image Transport System (FITS) format, making them easy to share between different collaboration, while each instrument usually has its suite of software packages for the analysis. Thus, the ctools software package is implemented to be highly versatile and easily adaptable to one’s analysis needs, whether the observation is carried out by a ground-based or a satellite telescope. In my master thesis I study two of the three VHE events (GRB 190114C and GRB 180720B) observed so far. GRB 190114C, though being not extremely energetic overall, emitted single high energy photons over 200 GeV during its early afterglow emission, as observed by the MAGIC telescopes. After simulating the CTA response to the same event, I performed several simulations moving the source farther away, analysing how

2 CONTENTS the significance of the observation is affected. GRB 180720B, on the other hand was a high energetic event observed by the H.E.S.S. telescopes during its faint late afterglow emission, over 10 hr after its trigger. In order to reach the lowest energy and detect such a faint signal, only the larger telescope in the H.E.S.S. array was operated. In this case, the aim of the CTA simulation was to test its efficiency at the lowest energies, without using any peculiar detection technique or pre-manipulation of data. When modelling the source to run the simulations, a few crucial steps are needed. First, I had to find the best way to reconstruct the evolution of the spectrum during the observation. This was a subtle process, as I wanted to introduce the minimum amount of assumptions to not bias the simulations. Sec- ond, the Extragalactic Background Light (EBL) absorption effect on gamma-ray propagation must be considered. Indeed, this is critical when simulating an observation carried out by a ground-based telescope, sensitive to energies at which this cosmological absorption effect can be strong, depending on the redshift of the source, as opposed to most satellite observations, which detect lower energies and are almost unhampered by EBL absorption effects. The EBL model I choose is by Dominguez et al., however other models could be preferred when considering high redshift observations. Third, I consider ideal observation conditions. Further development could include the effects of different conditions for night sky background and moon light. Nonetheless, the results drawn from the simulations showed how CTA will give a huge boost to our ability in detecting VHE signals from GRBs, both in the observable horizon and in the sensitivity to less energetic photons with IACTs.

3 Chapter 1

GRBs

Gamma Ray Bursts (GRBs) are short, intense, non-repeating flashes of ≈ 100 keV to ≈ MeV photons. In spite of having a wide range of spectral and temporal properties, GRBs are usually classified by the duration-intensity of their spectrum in a short-hard or a long-soft category, the separation being at 2 seconds. GRBs were first detected by chance in the late 1960s by the Vela mili- tary satellites, which were monitoring the Test Ban Treaty between the United States and the Soviet Union. Over time, the interest about these signals raised as the improvements in observational techniques and procedures showed their cosmological origin, and therefore their incredibly high energy release. Thanks to the launch of the Compton Gamma Ray Observatory (CGRO), equipped with the Burst And Transient Source Explorer (BATSE), in 1991, it became clear that the GRB sky distribution is isotropic, suggesting a possible cosmological origin. The turning point in the study of GRBs came with the launch of the Beppo- SAX satellite, which in 1997 performed the first detection of a GRB afterglow emission, which follows the prompt emission. Information gained studying the afterglows were able to answer many of the questions we had on GRBs. First of all, the hypothesis of a cosmological origin, when combined with the short variability timescale and the large fluence (flux integrated over duration) of these signals, made us figure a plasma-like internal structure for GRBs, expect- ing them to have a typical thermal spectrum. The measured spectra, however, displayed a highly non-thermal shape, in the form of a power law. This ap- parent inconsistency was known as the ’compactness problem’. One can avoid it by considering the GRB plasma to expand with a high bulk Lorentz factor (Γ & 100), but this would in order lead to another problem, namely the ’baryon loading problem’, as the plasma should be loaded with a very small baryon mass to achieve such an ultra-relativistic expansion. Furthermore, while first models for GRBs pictured an isotropic emission, we had no way of performing accurate measurements of their energy or localization. The observation of afterglows allowed us to analyse GRBs via optical spec- troscopy, getting some precious information about these phenomena. First of

4 CHAPTER 1. GRBS all, we were able to perform redshift measurements, directly conﬁrming their cosmological origin. We also got observational evidence on the emission energy and geometry, noticing how GRBs are emitted as jets, with typical opening angles of ∼ 3 − 10◦ [1], rather than as isotropic outﬂows. At present, our knowledge about these signals is far from being complete. Sev- eral models were proposed in the last 50 years to explain their internal dynamics, while the search for their progenitors still goes on.

1.1 Properties

GRBs are indeed uniquely interesting among the broad selection of signals that reach the Earth. To display a brief review of their properties, it is useful to analyse separately the prompt emission, which is the main GRB emission, and its afterglow, which is, instead, the delayed secondary emission from the interaction with the interstellar medium (ISM).

1.1.1 Prompt Emission The GRB itself, namely the γ-rays and any lower-energy emission that occurs simultaneously with them, is usually referred to as the prompt emission, to distinguish it from all the secondary emissions that come from the same phenomenon. Other than γ-rays, lower frequency emissions may also occur as an optical ﬂash.

The prompt emission is operationally defined as the time period when the γ-ray detector sees a signal above background. To properly characterize the prompt emission, one has to describe its spectral and temporal behaviours. The spectrum is highly non-thermal, with a peak energy usually located at a few hundred keV. The spectral shape varies strongly between different GRBs, but an excellent phenomenological function able to describe most of them was introduced in [2] using two power laws joined smoothly at a break energy EBR = ˜ (˜α − β)E0:  α˜ hν ˜ (hν) exp − for hν < (˜α − β)E0  E0 N(ν) = N0 ˜ (˜α−β˜) β˜ ˜ ˜ [(˜α − β)E0] (hν) exp β − α˜ for hν > (˜α − β)E0 (1.1) Behind this spectral shape, there is no assumption of a particular theoretical model. The first property that comes out from this description is that, for a large amount of GRBs, the break energy is in the range 100 keV < EBR < 400 keV, with a clear maximum of the distribution around EBR ∼ 250 keV [1] Concerning the temporal characteristics, the usual parameter to describe the burst duration is T90, which is the time in which from 5% to 95% of the total

5 CHAPTER 1. GRBS

counts are collected. According to T90 the bursts are divided into the short and long categories, with a separation at 2 seconds. The time behaviour of a signal, as seen in a plot counts/second vs time from trigger, displays a sequence of peaks with a total span going from 0.01 s to several hundreds of seconds for diﬀerent GRBs [1]. Most GRBs show a variability time scale δt of the counts on much shorter time than T90, determined by the width of the peaks; however, while the majority of bursts (∼ 80%) shows a substantial temporal substructure in their lightcurves, the remaining fraction displays rather smooth spectra.

1.1.2 Classification beyond the Short-Long divide As previously stated, the main defining feature of GRBs among the wide vari- ety of known astrophysical transients is their dominant, non-periodic and non- repeating prompt γ-ray emission, which displays a wide array of different properties. Within these, the clearest sub-classes are the short-hard and soft-long bursts. Anyway, this rough division results many times in being too simplistic as the two distributions show an overlap, with detections of GRBs lasting . 2s which have characteristics typical of long GRBs and of long GRBs with properties of short events. Cosmological time dilation adds another potential complication, mainly for high- redshift signals, whose observed duration could place them in the long category, while their rest-frame duration lays under the limit of 2s. Such effects could be potentially mitigated adopting a different classification scheme, based on a deeper knowledge of GRBs and their progenitors. An example of such schemes is give in [3], which divides these signals in Type I GRBs (from mergers of compact objects) and Type II GRBs (from massive star progenitors); another viable classification is proposed in [4], which, basing on the physical properties of the progenitor systems, divides γ-ray bursting signals in destructive (Type I) versus non-destructive (Type II) events, with further separation into sub-classes based on the presence or absence of a degenerate object (and whether it is a BH or a NS). Though alternative classification schemes are potentially more powerful than simply relying on the duration-hardness of the spectrum alone, and in the long run may be essential for a complete mapping of GRB progenitors, they carry the risk of biasing the results. For example, in the case of a progenitor-based classification scheme, it is currently unclear either from observation or from theory how different systems manifest in terms of unique observables, particularly in the context of the prompt γ-ray emission for which even the radiation mechanism has not been conclusively identified. In conclusion, since the complete knowledge of the whole set of properties char- acterizing a GRB signal is far from being achieved, it is currently more profitable and natural to stick to the simplest phenomenological classification scheme.

6 CHAPTER 1. GRBS

1.1.3 Afterglow The afterglow is produced when the jet is slowed down by the surrounding matter. It can be a delayed emission (as for most short GRBs) or it could overlap with the prompt emission (as for some long GRBs). The afterglow covers a wider range of the electromagnetic spectrum than the prompt emission, though being fainter, and lasts longer, up to several days. During the first hours, the dissipation processes discussed in §1.3.3 become more relevant, starting a radiative phase where the emitted energy strongly relies on the bulk Lorentz factor of the burst. Later on, since this Lorentz factor lowers and these processes become less efficient, the afterglow undergoes an adiabatic evolution, during which there are lower radiation losses. A good description for the typical observed afterglow flux is in the form of a series of power law segments in time and frequency:

−α −β Fν ∝ t ν (1.2) where the power law breaks as the exponents change at some relevant frequencies, namely the typical synchrotron frequency νm, the cooling frequency νc, and the synchrotron self-absorption frequency νsa. The discussion in the next sections should give a better understanding on why these parameters are important for the lightcurve. A more detailed description of the model can be found in [5].

1.2 Progenitors

The high resolution imaging performed by the Hubble Space Telescope showed that long GRBs follow the radial distribution expected for star formation in disk galaxies, and are spatially correlated with bright star-forming regions in their hosts. Other studies displayed how long GRBs are associated with Type Ic Supernovae (SNe), based on both photometric and spectroscopic observations [6],[7],[8]. At this point it became clear how long GRBs arise somehow from the death of massive stars, leading to the ”collapsar model” as the most accounted theory for long GRBs production at present. While our understanding of long GRBs improved fast, the study of short ones resulted much more challenging, mostly due to observational subtleties. First of all, it is almost impossible to lock a telescope on a short GRB prompt emission, if not by chance, because of their much shorter duration; this meaning that only survey telescopes come in help for the shearching. Moreover, as pointed out in [9], lower energy scale, and potentially lower circumburst densities, result in dimmer afterglows compared with long GRBs, by at least an order of magnitude. In spite of all the observational problems, compact object binary mergers remain an attractive progenitor model for short GRBs. In fact, basing on compact object binary population synthesis models [10], one can see how, due to kicks, such mergers will tend to occur in lower density environments than long GRBs,

7 CHAPTER 1. GRBS hence, if they are actually able of producing short GRBs, those would lead to fainter afterglows. Again, the observational turning point in the study of these phenomena came with the detection of the ﬁrst afterglows in May-July 2005, following bursts observed with Swift and HETE-2 satellites (which will be presented in §2).

1.2.1 Short GRB progenitors The bimodality of GRB durations suggests the existence of two dominant progenitor populations. The different variability timescales of the two GRB classes is probably due to the different timescales of the physical processes involved in their production. The most popular progenitor model for short GRBs, proposed way before the actual discovery of the binary division for the duration, is the merger of compact object binaries, namely of two neutron stars or a neutron star and a black hole (NS-NS/BH-NS). This model was initially so attractive because it provided a known source population with roughly the correct event rate, an enough rapid release of large energies and a clean environment to achieve a sufficiently low baryon loading. After the first observations on the short-long divide, if possible, this model became even more accounted, because the merger processes happen on a dynamical timescale of milliseconds, and such is the variability timescale for short GRB prompt emission. Such systems are characterized by angular momentum and energy losses by gravitational wave radiation, that cause the merging process to happen. In the binary NS case, the expected remnant from the merging is a black hole sur- rounded by an hyper-accreting disk of debris. The NS-BH merger can lead to the same configuration if the NS is tidally disrupted outside of the BH horizon. From this configuration, a high enough accretion, coupled with a rapid rotation of the system can lead to energy extraction via neutrino-antineutrino annihilation or magnetohydrodynamic processes, which in turn drive to a collimated relativistic outflow. Observational confirmation on the validity of the model can be obtained thanks to several testable predictions made from it. Some examples are: • The delay time between the binary formation and eventual merger depends on the initial separation and constituent masses, covering a wide range, that lead to the short bursts happening both in early- and late-type galaxies.

• Natal kicks from SNe which give rise to BH or NS in binary systems, coupled with the wide range of merger timescales, should lead to some mergers at large oﬀsets from their birth sites. • Mergers will be accompanied by a strong Gravitational Wave emission, detectable by LIGO/Virgo interferometers if the production site is within about 100 Mpc [11]. • The mergers will produce neutron-rich ejecta, that will in turn lead to

8 CHAPTER 1. GRBS

r-process nucleosynthesis, which radioactive results may be detectable at optical/near-IR wavelengths. • The mergers will not be accompanied by SN explosions. These properties can also be helpful to distinguish between NS-NS and BH-NS mergers. However, no BH-NS binaries have been identified at all; it is therefore not clear wether their contribution to the short GRB population is negligible, or the differencies from the NS-NS model are not significant enough. These questions might be answered by joint gravitational wave and GRB detections.

1.2.2 Long GRB progenitors Also for long GRBs the first hypotheses on their progenitor model were proposed before observational clues were available. As pointed out in [12], the cosmological origin hypothesis for GRBs implies that their energy release is comparable to that of a typical Supernova (SN) explosion. Considered as more than just a coincidence, this property was largely tested, leading to the formulation of the collapsar model [13], which still holds as the most accounted progenitor for long GRBs. According to the most recent ver- sions of this model, the core collapse of a fast rotating massive star (M > 30M ) leads to the formation of a black hole and a disk with M ∼ 0.1M around it. The accretion of this disk of debris onto the central BH feeds the GRB, as the energy extracted via neutrino annihilation or Bladford-Znajek mechanism is leaked out producing jets with opening angles < 10◦, preferably along the rotation axis. If such jets are powerful enough, they will penetrate the stellar envelope and be ejected as long GRBs. A list of observational evidences supporting the long GRB-SN association can be found in [8]. To date, this connection appears unequivocal. Still, it is unclear what sets a GRB/SN progenitor apart from SN progenitors which do not produce GRBs. Demographic studies have shown how only a small fraction (∼ 1%) of core collapse events producing type Ic SNe also produce a detectable GRB. This could just be a viewing angle effect, since GRBs are ejected along jets in the rotation axis direction of the central engine, while SNe are roughly isotropic. However, this notion is statistically disfavored because no evidence for highly energetic and off-axis component was found in radio observations of type Ic SNe. Further understanding on this matter could be provided studying the distribution of the available energy in various channels (neutrinos, GWs, γ-rays, kinetic energy of the relativistic outflow and kinetic energy of the non relativistic SN outflow) when the core collapse happens. However, performing this analysis by only using SN and GRB detections could lead to the introduction of strong correlations due to observational biases. A few examples are that GRB events with lower energies are more readily detected at low redshifts, improving the SN detection probability; also, when the kinetic energy of the relativistic outflow is low, fainter afterglows are produced, resulting again in increased odds for the SN observation.

9 CHAPTER 1. GRBS

In this sense, a multimessenger approach could come in hand, as GW and neutrino coincidences with GRB/SN observations could give us a more complete picture of the energy partition when these events occur in the local universe. In conclusion, one could consider the SN association as a good criterion for a better classiﬁcation of long/short GRBs. This, however, could be misleading as a few nearby long GRBs lacking a SN were observed, which opened up the possibility that some GRBs either are not associated to a SN at all or are associated to a very faint SNe, or that no radioactive material is formed or ejected. This class of SN-less long GRBs could be representative of the original collapsar model, which was based on failed Type Ib rather than Ic SNe. Anyway, the fraction of SN-less long GRBs remains unknown. Here the multimessenger approach could fail too, as even in the most optimistic guesses, GW and neutrino signatures would only be detectable for the nearest events, which are quite rare.

1.3 Dynamics

Over time, several models were proposed to explain the detected GRB spectra. Despite these models involving many different processes, all of them usually follow the same scheme, i.e. the formation of a black hole with a fast rotating disk of debris, whose accretion causes the ejection of a jet with relativistic motion, in which dissipation processes are considered to explain the high radiation efficiency. All current GRB models involve a relativistic motion with a bulk Lorentz factor Γ > 100, which is needed to overcome the compactness problem. While this property was at first only based on theoretical arguments, it was proven by direct observation of the afterglows. In fact, it is now generally accepted that both the radio scintillation and the synchrotron self-absorption provide independent estimates of the size of the afterglow several days after the prompt emission [1]. The large value observed for this size implies that the afterglow has indeed expanded relativistically, even though different models provide different values for the actual Lorentz factor. Considering such an ultra-relativistic motion leads most of its initial energy to be dissipated in the form of kinetic energy of the expansion. To correct this issue, dissipation processes are usually taken into account to provide the radiation efficiency needed for the GRB and the subsequent afterglow. The dissipation is due to shocks occurring inside the jet itself (internal), when a faster shell takes over a slower one, or when this collides with the ISM (external), by means of synchrotron emission from relativistic electrons accelerated within the shocks, as well as synchrotron self-Compton or Inverse Compton (IC) scattering of external light, the latter requiring a reasonably bright ISM. Picking the right model for the description of GRBs is based on deriving the above effects whether from the presence of baryons or from magnetic fields in the jet. Usually, hybrid models containing both of them are considered, each

10 CHAPTER 1. GRBS with a different balance. However, in spite of the different nature of the dominant physics, all of these models rely on a similar mathematical description and lead to the physical effects stated above, the only difference being in their intensities. I will therefore focus on a brief description of these effects, without referring to a specific model.

1.3.1 Relativistic motion Way before having direct means to confirm the relativistic expansion occurring in GRBs, the strongest theoretical clues of this effect arose from the compactness problem, which comes from the observation that the typical GRB spectrum shows a non-thermal shape, while a rough calculation implies that the source should be optically thick. In fact, supposing to have a lightcurve with a variability timescale δt, the size of the source can be at most cδt. Given its flux F and duration T over a distance d, we can compute the energy E emitted at source. For a typical photon energy Eγ , this yields a photon number density:

4πd2F nγ = 3 2 (1.3) Eγ c δt Two colliding photons whose energy in the Centre of Mass (CM) frame is higher 2 + − than 2mec can produce an e e pair. The optical depth for this process can be written as: 2 fe± σT 4πd F τγγ ∼ 2 (1.4) Eγ c δt where fe± is a numerical factor denoting the average probability that a photon will collide with another photon having enough energy to cause pair production. Using typical values and cosmological distances leads to an extremely large 15 optical depth of τγγ ≈ 10 , which is clearly inconsistent with the observed non-thermal spectra. Anyway, when considering the emitting matter moving relativistically towards the observer, we can see how the photon energy in the CM frame is corrected and the optical thickness for the pair production process lowers. Given a bulk Lorentz factor Γ for the motion, the two following correctionto the above computation have to be indeed taken into account: • the implied size of the source becomes Γ2cδt;

• the photons are blue-shifted and their energy in the source frame is lowered by a factor of Γ. The increased size of the source lowers the photon number density by a factor −4 −2 Γ , reducing the optical depth as Γ , while the blue-shift eﬀect modiﬁes fe± by a factor Γ−2α, where α is the photon index of the observed spectrum. This means that we can lower the optical thickness of the source by increasing the Lorentz factor of its motion. Therefore, considering a typical photon index

11 CHAPTER 1. GRBS

α ∼ 2 and requesting the source to be optically thin (τ < 1) we can compute a lower limit for its relativistic expansion, obtaining a Lorentz factor Γ > 100. Further details can be found in [14]. To press on, once the need for a relativistic motion is understood, a few additional GRB properties can be inferred from it. First of all, the value of the Lorentz factor is important when evaluating radial and angular timescales for the photon detection from a GRB. For instance, when considering a source moving relativistically with a constant velocity towards the observer and two photons emitted at r1 and r2, the observer detects them with a timescale r − r δt = 2 1 (1.5) 2cΓ2 This time interval should be modiﬁed when the source velocity is not constant, but it would only be aﬀected by a numerical factor. On the other hand, when considering a relativistically expanding spherical (at least locally) shell as source, emission from parts of the shell moving at an angle θ relative to the line of sight of the observer will be delayed by a time:

rθ2 T = (1.6) θ 2c which reduces to (1.5) as the radiation from a relativistic source is beamed with a typical angle 1/Γ. This beaming for the radiation implies that if the source is expanding relativistically, the observer can only detect it from an angular region within Γ−1 from its line of sight. Therefore, when considering an extended source with radius RS, the observer will detect radiation from a region of size RS/Γ. Since a high Lorentz factor is needed in order to explain the non-thermal spectra of GRBs, radiation is observed only from a small fraction of the emitting shell, which could behave differently from the true average conditions across the whole shell. On top of that, when considering the contribution from different shells according to the internal shock model (described in §1.3.2), the inhomo- geneity of individual shells could be wiped out (if the fluctuations are randomly distributed above them) or accentuated (if all the fluctuations are in the same position in all shells). Concerning shocks, while the internal ones only dissipate the relative motion within the flow, leaving the bulk Lorentz factor unchanged and producing the actual GRB, during the afterglow the jet is slowed down through the external ones. These shocks reduce the bulk Lorentz factor with time, allowing the observer to detect an increasingly large fraction of the emitting region. The direct implication of this difference between internal and external shocks is that if the initial relativistic flow is inhomogeneous on a small angular scale different observers looking at it at early times might see different regions of the source, detecting different lightcurves that will merge later on as the Lorentz bulk factor decreases and they start to observe the same region. Therefore, assuming that the GRB population follows some given distribution, we expect

12 CHAPTER 1. GRBS that the ﬂuctuations between diﬀerent observed bursts will be higher at early times than during the afterglow.

1.3.2 Shocks and acceleration The observed prompt emission is produced by dissipation processes affecting the charged particles in the jet, which have been accelerated to sufficiently high energies. Like for cosmic rays, this is performed via first order Fermi acceleration. In brief, charged particles are accelerated by repeatedly crossing a shock front. Magnetic field irregularities generated by the shock keep scattering the particles back, across the same shock. The competition between the energy gain in an acceleration loop and the escape probability per cycle leads to a power law spectrum. While a formal description of the process can be found in [15], it is interesting here to see how the picture changes when referring to GRBs. Indeed, in these sources shocks are relativistic and a few different considerations have to be done. 2 In a relativistic shock the energy gain in the first crossing is of the order of Γsh, where Γsh is the shell Lorentz factor, while subsequent crossings are way less efficient, leading to an energy gain that is of order unity. Repeated cycles of back and forth crossing lead to a power law particle spectrum dN/dE ∝ E−p with index p ∼ 2.2−2.3, independently of specific assumptions on the scattering process (see, for example, [16]). This spectrum agrees nicely with data from observed GRBs, though it is often required to take into account absorption effects from the ISM. However, the acceleration process has to compete with radiation losses of the accelerated particles, mainly synchrotron losses, but IC scattering is also possible. Comparing the energy loss rate with the energy gain, one can obtain the maximum energy reachable by charged particles in the jet. Internal shocks can only dissipate a fraction of the kinetic energy and require the presence of external shocks which follow and dissipate the remaining energy. In the same way, external shocks alone could not explain the observed GRB spectral shape, and they are unable to produce variable bursts. Thus, both kinds of shocks are required. When considering a locally spherical relativistic emitting shell with thickness R in a jet with opening angle θ > Γ−1, where Γ is the Lorentz factor of the shell, the important timescales determining the hardness of the observed spectrum are tR, that is, the time interval between the observations of a photon emitted at the shell front and one emitted at the shell back, and tang, that is, the time interval between the observations of a photon emitted towards the observer and −1 one emitted from matter moving at an angle Γ . While tR gives the overall duration of the observation, the effect of tang is to smooth the spectral shape. Therefore, the condition tR > tang has to be fulfilled in order to get a variable spectrum. This condition rules out the possibility of having only external shocks, as one can find tR ∼ tang ∼ R/cΓ for them [17, 18].

13 CHAPTER 1. GRBS

In internal shocks the condition is fulﬁlled, but their presence alone does not suﬃce to dissipate the whole kinetic energy of the burst, hence, the most accounted picture is that the GRB prompt emission is produced by internal shocks, whereas external shocks subsequently produce the afterglow as a smooth long lasting emission.

1.3.3 Dissipation processes The observation of polarized light from GRBs supports the idea that synchrotron emission is indeed taking place. At higher energies, even IC scattering is possible, as it produces polarized emission too. Here, I give a brief description of the relevant features of these processes and their role in GRBs. Focusing ﬁrst on synchrotron emission, considering an emitting material moving with a Lorentz factor Γ, the energy in the observer’s frame of a photon emitted by a relativistic electron with Lorentz factor γe moving in a magnetic ﬁeld B is:

~qeB 2 (hνsyn)OBS = γe Γ (1.7) mec In the local frame, a single electron emits synchrotron radiation with a power: 4 P = σ cU γ2 (1.8) syn 3 T B e

2 where UB = B /8π = Bqe is the magnetic energy density and σT is the Thom- son cross section. The cooling time of the electron in the ﬂuid frame is then 2 γemec /Psyn and is shortened by a factor Γ in the observer frame:

3mec tsyn(γe) = (1.9) 4σT UBγeΓ Combining equations (1.7) and (1.9), the cooling timescale as a function of the observed photon energy results:

r 1 3 2πcmeqe − 2 tsyn = 2 νsyn (1.10) σT B Γ

This formula shows how at a given observed frequency tsyn is independent of the electron energy distribution within the shock, provided that electrons with − 1 the required γe are present. The characteristic scaling t ∝ ν 2 is similar to the time-energy autocorrelation evaluated in [19]. This is a hint that, in the asymmetric spikes typical of GRB intensity variations, the fast rise is probably due to the rapid acceleration of electrons via shocks, while synchrotron cooling, as well as cooling from IC scattering set the lower limit for their decaying side. Synchrotron Self-Absorption (SSA) takes place at radio frequencies, leading to a steep cut-oﬀ on the low edge of the spectrum, as a power law that is either ∝ ν2 or ν5/2. The computation of the self-absorption frequency has some subtleties, because it requires the knowledge of the Lorentz factor and the position

14 CHAPTER 1. GRBS over time of the emitting matter, as well as of the optical depth along the line of sight. The spectrum below the SSA frequency depends on the synchrotron frequency of the electrons emitting the self-absorbed radiation. If it is in the self-absorption range, the spectrum varies as ν5/2, while it varies as ν2 if the radiation within the self-absorption frequency range is due to the low energy tail of the electrons which are radiating effectively at higher energies. SSA is almost always irrelevant during the prompt GRB emission but in extreme conditions, while it gains relevance during the afterglow when it is usually observed as a radio emission. IC scattering could modify the spectrum even though Compton scattering is not significant. Photons below the Klein-Nishina limit can be upscattered by the relativistic electrons in the jet, populating the high energy tail of the spectrum. As the energy gain is quite robust, most of these photons are unlikely to be scattered more than once, and, in some cases, even the first scattering might suffer a low probability. IC depends on the Comptonization parameter Y = γτe, which for fast cooling results:

Y = Ue/UB if Ue UB p (1.11) Y = Ue/UB if Ue UB where Ue and UB are the energy densities of electrons and magnetic field, re- spectively. When Y < 1, IC scattering is negligible and does not affect the spectrum. On the other hand, with Y > 1, that is Ue > UB, a large fraction of the low energy Synchrotron Radiation (SR) will be upscattered through IC producing a strong outflow of Synchrotron Self-Compton (SSC) radiation. This would introduce a higher energy component in the spectrum, as SSC pho- 2 ton energies are indeed higher than SR ones by γe , the typical Lorentz factor of electrons in the jet. From the internal shocks, where electrons are usually 3 accelerated to γe ≈ 10 , we would get a SSC radiation at a few hundred GeV. We would get an even higher component from the forward external shocks, up to TeV energies. Other mechanisms could explain the detection of such high energy components in GRB spectra, e.g., SR from extremely accelerated protons, though this is unlikely because of their low radiative efficiency. Whatever process is involved in producing this spectral component it is out of the detectable energy range for most space telescopes. Thus they could only confirm its presence relying on its influence at lower energies, as it will shorten the cooling time and decrease the amount of observed events in this range. Because of these observational difficulties, the theoretically predicted SSC radiation from GRBs remained undetected for a long time. However, Imaging Atmospheric Cherenkov Telescopes (IACTs) could be able to observe the high energy tail from IC scattering directly, as they can detect photons at the energies of interest. In this case, the observational difficulty is the necessary fast repointing to the source localization region, together with their

15 CHAPTER 1. GRBS small field of view. Another complication in the observation of VHE radiation comes from the Extragalactic Background Light (EBL), which consists of the sum of the starlight emitted by galaxies through the history of the Universe, and it could also have and important contribution from the first stars formed. The issue is that VHE photons travelling from remote sources interact with the EBL undegoing pair production. This absorption effect reduces the amount of photons arriving to the observer. It is more robust over the high energy components of the spectrum, above a few GeV, and the total amount of absorbed radiation depends on the redshift of the source. The EBL absorption steeply reduces the spectrum of the source, with the effect of an exponential factor depending on energy and redshift. Due to all these difficulties, the first observation of TeV emission was only recently carried out by MAGIC, which has an average repointing time of 40 seconds, and was able to detect GRB 190114C during its early afterglow and directly confirm the presence of the IC scattering among the radiation production processes [20].

1.4 Beyond gamma rays

In the last few decades, the improving technology in detectors made us recon- sider our approach to astrophysics. More than one of the four main messenger signals coming as probes from the far universe, i.e. electromagnetic radiation, neutrinos (νs), cosmic rays (CRs), and gravitational waves (GWs), can be produced within the same astrophysical event. Therefore, we can get deeper insights on a phenomenon by ”looking” at it using different probes. This is referred to as the multimessenger approach to astrophysics, and has rapidly become a new way of investigating the universe around us. Moving back to GRBs, again they prove to be unique and surprising phenomena. From them we expect the whole collection of messenger signals to be produced, which is quite rare among astrophysical sources. Obviously, different signals carry different observational difficulties, hence some messengers still remain expected while not detected. In this section, I am going through a brief discussion about the multi-messenger observation of a GRB, focusing on each signal separately.

1.4.1 Particle counterparts There are several ways in which νs could be produced during the evolution of a typical GRB. The first process we should mention is inverse beta decay taking place during the accretion of the disk of debris into the central black hole, both for merger and collapsar models. Anyway, even though a large amount of ∼ MeV neutrinos are produced in this phase, their energy is similar to those produced in SNe, which are ejected with a higher rate. For this reason it is difficult to detect this kind of outflow from GRBs, as it would be completely overwhelmed by that from SNe. Continuing along the GRB evolution, we see how internal shocks are a possible

16 CHAPTER 1. GRBS site for ν production at high energies. Here, collisions between protons and neutrons can lead to the creation of charged pions, whose decay chain gives the neutrino outﬂow:

± ± ± π → µ + νµ(¯νµ) → e + νe(¯νe) + νµ(¯νµ) (1.12)

Neutrinos are produced with an average energy Eν ∼ 0.05Ep, where Ep is the average energy of colliding protons, so that the spectrum of neutrinos closely follows the one of charged particles accelerated within the shocks. Because of the low mass and cross section of νs, they are able to reach the observer almost unhampered. This, combined to the statement above, means that they would provide a source of pristine information over the acceleration processes taking place in GRBs, allowing us to get further insights about their internal dynamics. This is also true in external shocks, where the main decay chain involved is again (1.12). Another contribution to the ν outflow comes from kaon production and decay. However, kaons provide a much lower contribution with respect to the main pion component, and they are usually treated as effective πs for the computation of the resulting ν spectrum. The key point here seems to be pion production in GRBs, which happens in different ways within internal or external shocks. Focussing first on internal shocks, as stated above, the main source for pion production are the collisions between neutrons and protons. Anyway, longitudinal and transverse collisions need to be considered separately as they are caused by different effects, the former coming from the evolution of the GRB bulk Lorentz factor, whereas the latter is caused by transverse thermal drifts of nucleons in the jet. The bulk Lorentz factor of a GRB evolves as a power law in terms of the distance from the central engine, until a certain saturation value: ( rµ for r < r 1 Γ ∝ SAT with µ ∈ ; 1 (1.13) η for r ≥ rSAT 3 where different models are discerned by different values for µ, which tends to 1/3 for extreme magnetic models, or to 1 for extreme baryonic ones. For further details on this matter, see [21]. When nucleons are initially injected in the GRB plasma, they are coupled and gain the same Lorentz factor. Due to the expansion, they eventually decouple at a certain distance rD. From this moment on, neutrons coast with their decoupling Lorentz factor. On the other hand, if rD < rSAT , protons will still be accelerated by the magnetic fields inside the GRB and their Lorentz factor will still follow (1.13). Thus, if this is achieved early enough, the relative Γ between neutrons and protons can reach the threshold for inelastic collisions to take place, and the pion production starts. This is basically how longitudinal collisions contribute to the pion production. A few corrections should be included in this explanation, as I clearly avoided to consider the thermal motion that nucleons could undergo.

17 CHAPTER 1. GRBS

Thermal motion is instead the main cause for transverse collisions leading to pion production, which is also the main contribution to the neutrino flux from internal shocks. This effect depends on the structure of a realistic GRB model. The bulk Lorentz factor shown above, in fact, is unlikely to be constant over the jet transverse section. If we consider a realistic jet to have a core with bulk Lorentz factor given by (1.13) and an external sheath with a constant Γsh, once again we have a relative Lorentz factor between core protons and sheath neutrons, which will eventually overcome the pion production threshold. The collisions happen when neutrons from the sheath drift through the core by thermal motion. Again, [21] shows numerical methods to compute the flux of pions produced through these channels, assuming different models for the GRB internal dynamics. While neutrinos from internal shocks reach energies up to TeV, when considering external shocks the energy range extends to PeV. Here, once again the pion decay chain (1.12) is involved, the difference being in how pions are produced. While neutron-proton collisions are still possible, the main contribution to pion production in external shocks comes from proton-photon interactions. Depending on the photon energy Eγ in the proton rest frame, the differential cross section for p-γ interactions is dominated either by the resonances (mainly + the ∆[1232] resonance) at energies 0.2 GeV < Eγ < 1 GeV or multi-pion production at energies Eγ > 1 GeV . When discussing neutrino production in GRBs, we can not avoid considering that most models take into account dissipative processes to explain the high radiative efficiency of the burst. Radiative cooling adds up as a competing process to neutrino production, as it lowers the energy of charged particles involved in pion production and decay. As a result of such processes, the neutrino flux from a single GRB decreases by a few orders of magnitude, thus the most interesting observational quantity is the diffuse neutrino flux from the whole sky, rather than that from a single jet. To date, however, we have no direct detection of a GRB-ν coincidence. Never- theless, the non-detection of neutrinos from GRBs, allowed constraints on GRB models, as we obviously expect different outflows from differently structured GRBs [22]. GRBs are potential sources for Ultra High Energy Cosmic Rays (UHECRs) too, 18 which are cosmic rays at E & 10 eV . They indeed show most of the properties we expect from such sources. Moreover, in the Hillas plot, GRBs are located across the top line, meaning that, based on their inner magnetic energy density and their size, they are able to accelerate charged particles up to 1021eV . Considering UHECRs only as accelerated protons, the production process is the first order Fermi acceleration described in §1.3.2. Direct observation of the said protons is challenging as they are deflected by magnetic fields during their propagation. However, as explained before, such protons are involved in the production of νs within the jet, via internal and external shocks. Thus, we rely on neutrino detection to confirm or reject the connection with UHECRs. Neutrino and cosmic ray fluxes from GRBs will depend on the same factors,

18 CHAPTER 1. GRBS such as the baryon loading, which is constrained to low values to achieve the high bulk Lorentz factors needed in GRBs. A detailed description of the energy budget for the connection with neutrinos, CRs and GRBs can be found in [23].

1.4.2 Gravitational wave counterpart In the framework of the multimessenger study of GRBs, another important question is whether or not they can be associated to GW signals. In theory, two kinds of GW outflows are expected to be produced in coincidence with a GRB. One of them is a pulse generated during the acceleration of charged particles of the jet. This signal, however, carries two main issues; first, it should propagate perpendicularly to the prompt emission, thus it cannot be observed with it [1]. However, the interesting GW signal associated to a GRB is not produced within the jet itself. Indeed, when considering GRB progenitor models, it is clear how they are also candidate sources for the production of GWs. Therefore, we expect GRB sources to produce GW counterparts as well, which can be detected on Earth. Presently, this detection can only be performed for the closest events (∼ 200 Mpc), as the amplitude of a GW decreases moving away from its source. An interesting question is what do we expect to learn by observing both the electromagnetic signal and its GW counterpart. On one side, we get important constraints on fundamental physics. For example, gravitational waves and gamma-ray photons are expected to travel at the same speed, and by measuring the time delay between the detection of both signals, we obtain information about the discrepancy between their speeds. However, this analysis carries some subtleties, as we do not expect the two signals to be produced at the same time. We can therefore estimate an upper limit on this violation by considering GWs and γ-rays to be generated together, and a lower limit by introducing a lag time between their ejections. Moreover, it is important to point out that prob- ing gravitational potentials to affect in the same way both electromagnetic and gravitational waves means to directly test the validity of the Equivalence Prin- ciple. This is done by evaluating the Shapiro time delay on both signals [24],[1]. While a full computation would need the exact characterization of the gravitational potential along the whole wave path, a lower bound can be obtained by only introducing the effects of the Milky way. On the other side, the multimessenger observation of GRBs and GWs can provide insightful information about their progenitors. A clear example comes from the observations of both GW170817 and GRB 170817A. To date, this is the only coincident detection of a GRB and GW. Given their spatial and temporal coincidence, there is a negligible probability for these events not to be correlated. This association confirms that mergers of compact binary objects are the sources of at least some short GRBs. Further observations could give us more details about the mechanisms involved in GRB production, as well as about their internal dynamics. For a more detailed discussion about the GRB 170817A/GW170817 association and its direct implications, see [11]

19 Chapter 2

GRB observations and simulations

The history of GRB observations began with the serendipitous detection by the Vela satellites on July 2, 1967. Soon the common idea was that in order to investigate their sources it was necessary to look for their emission at multiple wavelengths. This required far more accuracy in reconstructing GRB position than the Vela satellites could provide, thus the probes had to be spaced farther apart, not just orbiting around the Earth. With this purpose, the In- terPlanetary Network (IPN) was established in 1978. It included 5 different probes: Prognoz 7 orbiting around Earth, Helios 2 around the Sun, Pioneer Venus Orbiter, Venera 11 and Venera 12 all orbiting around Venus. Even with the IPN active, little progress was made, at least until the launch of the Comp- ton Gamma Ray Observatory (CGRO) in 1990, equipped with the Burst And Transient Source Explorer (BATSE), which provided a lot of information about GRBs. The launch of the Beppo-SAX satellite on April 30, 1996, started the afterglow hunt, allowing X-rays measurements on the delayed emissions from GRBs. In the same year the first GRB dedicated mission was launched, i.e. the High Energy Transient Explorer (HETE). Its launch, however, was unsuccessful, and all radio contacts were lost within a day. Nevertheless, its direct successor, HETE-2 was successfully launched on October 9, 2000, and observed its first GRB on February 13, 2001. At present, several satellites are actively looking for GRBs: • Konus, consisting in two γ-ray spectrometers on opposite sides of the Wind spacecraft, launched in 1994; • INTEGRAL, launched on October 17, 2002, by the European Space Agency, which can simultaneously observe objects at multiple wavelengths; • Swift, launched on November 20, 2004, by NASA, which combines a rather sensitive γ-ray detector with the ability to point on-board X-ray and op-

20 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS

tical telescopes towards the direction of a new GRB within a few minutes from its detection;

• Fermi Gamma-ray Space Telescope, originally named GLAST (Gamma- ray Large Area Space Telescope), launched by NASA as well on June 11, 2008; • AGILE, an italian satellite by ASI, launched on April 23, 2007.

Though they have a wide field of view, the main issue with space telescopes lies in their small collection areas, which imply a low sensitivity coupled with small ranges of detectable energies. In the last few decades a handful of ground-based telescopes capable of detecting GRBs were built too, mainly in the form of Imaging Atmospheric Cherenkov Telescopes (IACTs). This kind of telescope uses the atmosphere itself as a calorimeter, implying a much wider collection area than satellites. The effect on which the detection is based is pretty simple. Basically, a very high energy γ-ray striking the atmosphere has a fair probability of producing a cascade of charged particles, i.e. an Extensive Air Shower (EAS). This process usually starts at ∼ 10 − 20 km of altitude, where the energetic gamma-ray photons undergo pair production. Electrons in EAS, due to Bremsstrahlung, produce secondary photons which are still energetic enough to make e± pairs, generating secondary cascades. The charged particles, both in primary and secondary cascades, move faster than light in the atmosphere, emitting flashes of Cherenkov radiation lasting 5 − 10 ns. This way, several hundreds of square meters are illuminated at the ground, increasing the effective area of IACTs. These telescopes usually comprise a large segmented mirror which reflects the Cherenkov radiation onto an array of photosensors, which are coupled to fast electronics, in order to amplify, digitize and record signals from the showers. The standard setup for IACTs consists in using more than a single telescope, allowing stereoscopic observation of the detected signal. Furthermore, having multiple telescopes helps eliminating local signals from cosmic ray showers, effectively reducing the energy threshold for the detection. The shower reconstruction and background rejection obtained with an array of telescopes increase the sensitivity by an order of magnitude as compared with a single telescope, and improve both its angular and energy resolution. There are four IACT systems currently active: the High Energy Stereoscopic System (HESS), the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) Telescopes, the First G-APD Cherenkov Telescope (FACT), and the Very En- ergetic Radiation Imaging Telescope Array System (VERITAS). Two more are under construction, namely the Major Atmospheric Cherenkov Experiment (MACE) telescope and the Cherenkov Telescope Array (CTA).

21 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS

2.1 The Cherenkov Telescope Array

In this work I will mainly focus on analysing the sensitivity of CTA1 to GRBs, by simulating observations of known sources. The importance of this telescope array for the observation of GRBs is undoubted as it will increase the current IACT energy range of sensitivity both in its upper and lower edges. CTA will consist of two extended arrays, a Southern one near Paranal, Chile, located at about 10 km southeast of the Very Large Telescope (VLT), and a Northern one in La Palma (Canary Islands), Spain, at the Observatorio del Roque de los Muchachos. To build the arrays, three kinds of telescopes will be used. The Large-Sized Telescopes (LSTs), with a diameter of 23 m, will detect low energy γ-rays, in the 20−200 GeV range [25]. To detect the faint Cherenkov light in this energy range, large mirrors are required. Despite being 42 m tall, the entire structure will be able to re-position within 20 seconds (Fig. 2.1). The wide segmented mirror will have a reflective surface of 400 m2, focussing light into the camera, which is designed for maximum compactness and a low weight of less than two tonnes, with a field of view of about 4.3 degrees. In the camera, a total number of 1855 channels are divided into 265 photomultiplier tubes (PMT) modules, with a peak quantum efficiency of 42 %, each equipped with an optical light concetrator, optimized for the field of view and geometry of the photosensor. The camera trigger strategy is based on the signal topology and temporal evolution, and dedicated algorithms are used to look for short and compact light flashes. Furthermore, all LST cameras are kept in communication and use coincidences to suppress the accidental triggers by up to a factor of 100 [26].

1More information about the consortium and the observatory can be found at: https://www.cta-observatory.org/

22 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS

Figure 2.1: LST schematic with the main assemblies. The whole structure is 42 m tall, with a reﬂective surface of 400 m2 over the segmented mirror and a less than two tonnes weighting camera, though it is able to re-position within 20 seconds. The telescope will cover a ﬁeld of view of about 4.3 degrees and detect radiation in the [20 - 200] GeV range.

The Medium-Sized Telescopes (MSTs) will be sensitive to the energy flux of γ-rays in the 100 GeV - 10 TeV range. With a 12 m diameter, they will have a large field of view of 7−8 degrees, enabling CTA to carry out rapid surveys of the γ-ray sky (Fig. 2.2). MST mirrors will have up to 90 hexagonal-shaped sections aligned with an active mirror control assembly to create a uniform reflector [27]. There are two camera concepts in development for the MST, NectarCAM and FlashCAM. NectarCAM is composed of 265 individual and easily removable

23 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS modules, each composed of 7 PMTs with their associated electronics. Each PMT is associated with an individual high voltage and preampliﬁed board. The power supply for each PMT is controlled remotely. FlashCAM is designed to have and horizontal architecture, with the photon detector plane (PDP), the readout electronics and the data acquisition system as key building blocks. The PDP is divided in hexagonal modules, each containing 12 PMTs. The signals are then transmitted through cables to the readout electronics designed to digitize the signal continuously with a sampling frequency of 250 MS/s.

Figure 2.2: MST will be sensitive to the 100 GeV - 10 TeV, with a ﬁeld of view of about 8◦.

Schwarzschild-Couder Telescopes (SCTs) were proposed as an alternative to MSTs. They are designed with a 9.7 m diameter primary and a 5.4 m diameter secondary segmented mirrors, which allow to better focus the light for greater imaging detail and improved detection of faint sources (Fig. 2.3). SCTs have a reduced Point Spread Function (PSF), leading to a better angular resolution over a ﬁeld of view of approximately 8 degrees. The camera uses SiPMs mounted in focal plane modules instead of PMTs [28],[29].

24 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS

Figure 2.3: SCTs are an alternative to MSTs, with similar energy sensitivity and ﬁeld of view, but an improved angular resolution due to the dual mirror conﬁguration.

At last, the Small-Sized Telescopes (SSTs) will be sensitive to the highest energy γ-rays (∼ 5 − 300 TeV) coming from our Galaxy2. They will be located only in the Southern array and will outnumber all other telescopes. Among the three different designs that were initially proposed for SSTs, the CTA consortium decide in June 2019 that they will be based on the ASTRI/CECH design (Fig. 2.4), as a dual-mirror Schwarzschild-Couder aplanatic configuration using a novel compact camera based on SiPM sensors. The primary mirror is 4.3 m in diameter with hexagonal segmentation, while the 1.8 m diameter secondary mirror is not. The dual mirror configuration allows to mantain the same high angular resolution and collecting area across the wide field of view of 9 degrees of the camera [26].

2It is unlikely to detect extragalactic sources in this energy range due to the amount of the EBL absorption

25 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS

Figure 2.4: The ﬁnal design of SSTs will follow the one of SCTs, though they will be smaller and detect higher energies over a slightly larger ﬁeld of view.

In Fig. 2.5, all the diﬀerent sized telescopes are compared to scale. Note that the image is still displaying the three possible designs of the SSTs, which were harmonized in the ASTRI/CCH design.

Figure 2.5: The diﬀerent sized CTA telescopes compared to scale.

The CTA baseline array layout (Fig. 2.6) will include a total of 118 telescopes, 99 in the Southern array (4 LSTs, 25 MSTs, and 70 SSTs) and 19 in the Northern one (4 LSTs, 15 MSTs) [30].

26 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS

Figure 2.6: Layout of the Northern and Southern arrays for CTA.

Many telescopes involved in GRB observations communicate via the GCN/TAN3 (GRB Coordinates Network/Transient Astronomy Network). Every time a burst is detected, the GCN/TAN distributes two kind of notiﬁcations: • the GCN Notice, which is a token distributed automatically to every telescope in the network, without any human intervention; • the GCN Circular, which is a prose-style email message sent to the whole GRB community, which reports on the observation results.

Figure 2.7: Phyisical GCN/TAN scheme.

2.2 Description of the software utilities

All data taken with gamma-ray telescopes are then saved using the Flexible Image Transport System (FITS) format, thus making them shareable between diﬀerent collaborations. However, when it comes to data analysis, no standard

3A complete explanation on how the GCN/TAN works can be found at: https://gcn.gsfc.nasa.gov/about.html

27 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS workflow or software is used. Indeed, each instrument usually has its suite of software packages for the analysis, which often requires expensive maintenance and development, and forces astronomers to learn how to use many of them for scientific research. To overcome this issue, the CTA consortium developed the GammaLib software package, to provide the scientific community with a common framework for gamma-ray analysis. On top of the GammaLib, the CTA consortium developed the ctools software package, a suite of tools and scripts which can be used to build flexible workflows for data analysis. All the simulations and analysis I am going to show in this work have been performed using the GammaLib/ctools packages. Therefore, in the remaining part of this chapter, I will explain the base structure and classes of GammaLib, and the tools involved in my work, as it will make easier to understand he next chapter. Here I will stick on the actual tools which were useful for my work, while the distribution website 4 and the paper [31] give more information.

2.2.1 GammaLib In GammaLib are included all the classes and methods needed for the γ-ray data analysis. The library was built to be almost independent of external tools. This allows an easy installation procedure and lowers the maintenance costs, while keeping the package as user friendly as it can be. The classes in Gam- maLib are organised in three software layers (Fig. 2.8), each with a diﬀerent purpose: the high-level analysis, the core services and the interfaces. These layers are completely independent from the particular telescope considered for data acquisition, as all the instrument information is kept in separate modules.

High-level analysis modules The high-level analysis layer contains all the classes needed to handle observations, models and skymaps. In the observation handling module, an observation is defined as a period of time in which an instrument was taking data in a stable configuration, meaning that a fixed Instrument Response Function (IRF) could be considered. In an observation, data are stored as event lists (when unbinned) or counts cubes (when binned). There is almost no difference in how binned or unbinned data are handled, as both the single event in a list or the single bin in a counts cube are characterized by three fundamental features, which are the instrument direction p0, the measured energy E0, and the trigger time t0. These are measured quantities, which are related to the intrinsic properties of the detected photon by the IRF R(p0,E0, t0|p, E, t) associated to the observation. Another fundamental function associated to each observation is the Likelihood function L(M), which quantifies the probability that data are drawn from a given source model. The actual formulae used to compute L(M) depend on

4http://cta.irap.omp.eu/ctools/index.html

28 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS

Figure 2.8: GammaLib structure

29 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS whether data are binned or not, and on the statistical law assumed to draw data from models. For unbinned data, the negative log-likelihood is computed using the Poisson formula: X 0 0 0 − ln Li(M) = ei(M) − ln Pi(pk,Ek, tk|M) (2.1) k where the index i characterizes the observation; ei(M) is the total number of 0 0 0 events that are predicted to occur during the observation i, and Pi(p ,E , t |M) is the probability density to draw an event (p0,E0, t0), given the model M; the sum is taken over all events k in the list. For binned analysis, the formula becomes: X − ln Li(M) = ek,i(M) − nk,i ln ek,i(M) (2.2) k where k is now the bin index and nk,i is the number of events in the bin k of the observation i. GammaLib enables the handling of multi-instrument and multi-wavelength data by allowing the stack of observations in an observation container class, which is the main object that is manipulated during the analysis. Source models are needed to describe data in a parametrised way, and are stored in the model modules, which include methods to compute the probability density 0 0 0 Pi(p ,E , t |Mj). Here j is the model index, as more than one source model can be stacked together in a single model container, and the cumulative probability will be computed summing over models:

0 0 0 X 0 0 0 Pi(p ,E , t |M) = Pi(p ,E , t |Mj) (2.3) j

There are two ways to express a model, using diﬀerent classes: • GModelSky implements a factorised representation of the spatial, spectral and temporal components of a source in terms of true quantities; for this one the probability density is obtained by convolving those components with the IRF of the observation: Z 0 0 0 0 0 0 S Pi(p ,E , t |Mj) = Ri(p ,E , t |p, E, t) × Mj (p, E, t)dpdEdt (2.4)

• GModelData implements the description of events from a speciﬁc instrument and is generally used to deﬁne backgrounds; here the event probability is given by the model itself, which depends on measured quantities:

0 0 0 D 0 0 0 Pi(p ,E , t |Mj) = Mj,i(p ,E , t ) (2.5)

The last two modules of the high-level analysis layer are the skymap module, which is used to handle sky maps and sky regions, and the application module,

30 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS which provides classes useful for the actual process of analysing data, estabil- ishing the direct link to the ctools software package.

Core services This layer is ﬁlled with modules and classes needed for numerical computation and matrix operations. The optimization module contains classes needed for function minimization; the standard optimizer is based on the Levenberg- Marquardt algorithm, which performs an iterative interpolation between the gradient descent and Gauss-Newton methods. Additional services include classes to perform linear or bilinear interpolation, random number generation, ASCII (American Standard Code for Information Interchange) or CSV (Comma-Separated Values) data handling, and ﬁlename handling.

Interfaces This layer is used to handle Input/Output files and information. Data are exchanged mainly as FITS files, made by a list of Header Data Units (HDUs); each containing a binary table or image and a list of keywords (the header) to interpret it. Sky models, instead, are stored in XML (eXtended Markup Language) files, where the components are saved as separate tags.

Instrument modules All the layers are instrument-independent, and can handle data obtained by any γ-ray telescope. Information about speciﬁc instruments is stored in diﬀerent instrument modules. Within these, the one I used was the CTA module, which characterizes all existing IACTs. IRFs are stored in this module and assumed to factorise into:

0 0 0 0 0 R(p ,E , t |p, E, t) = Aeff (p, E, t) × PSF (p |p, E, t) × Edisp(E |p, E, t) (2.6)

2 0 where Aeff (p, E, t) is the eﬀective area in units of cm , PSF (p |p, E, t) is 0 the point spread function and Edisp(E |p, E, t) is the energy dispersion. Both 0 0 Edisp(E |p, E, t) and PSF (p |p, E, t) are normalized to the unit. There is also a 0 0 0 0 0 0 fourth component for R(p ,E , t |p, E, t), i.e. the background rate Brate(p ,E , t ), given as an input with the source model.

2.2.2 ctools On top of the GammaLib library, the CTA consortium developed the ctools software package, which includes a set of pre-constructed routines for data analysis. Each tool performs a single task needed for the analysis, allowing ﬂexible workﬂows to be built combining them to match the user’s needs. There are two actual kinds of tools in the package, the ctools, which are C++ compiled executables implementing the base building blocks of the package, and

31 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS the cscripts, which are Python scripts used for high-level tasks, eventually performed calling several ctools. All tools can be called from the command line, but they are also implemented as Python classes in the ctools and cscripts modules, both for Python 2 or Python 3. Performing the analysis via Python allows the user to pass observation con- tainers from one tool to another, avoiding to store intermediate results on disk. This enables pure in-memory workflow construction, taking advantage of the growing memories of modern computers, so does the possibility to parallelize most of the tools performing heavy computational duties. ctobssim This tool simulates IACT event lists based on an input model and the specified IRF. The simulation includes photon events from all sources in the model, drawn using the random number generator provided by GammaLib. Giving as input an observation definition file, it is possible to perform multiple simulations in a single run. In this case, the simulation process can be parallelized spreading the observations over all available cores. Each observation will be saved in a FITS file comprising the event list and their Good Time Intervals (GTI). ctskymap This tool generates a skymap from either a single event list or an observation definition file. It will loop over all events filling the specified number of spatial bins. The skymap is useful to have a visual response of the source distribution or data clustering over the considered sky region. Optionally ctskymap can apply a background subtraction algorithm to the input event list. ctlike Although I did not use the ctlike tool directly, it is the main fitting engine of the package, called by so many other tools that it is worth an explanation. The purpose of this tool is to fit event lists to determine any requested parameter of a source model. As it is based on the Levenberg-Marquardt algorithm, an input guess for the model is required,and ctlike will adjust the parameters flagged by the attribute free=”1” in the XML file. Moreover, it is possible to flag model components j with the attribute tscalc=”1”, instructing ctlike to compute the Test Statistics (TS) value for that source, defined by:

TS = 2 ln L(M) − 2lnL(M−j) (2.7) where L(M) is the maximum likelihood value for the full model and L(M−j) is that for a model from which the j component was subtracted. Assuming that 2 the model M ﬁts the data properly, the TS follows a χp distribution, where the number of degrees of freedom p is given by the number of free parameters in the model component j.

32 CHAPTER 2. GRB OBSERVATIONS AND SIMULATIONS

The tool creates an output XML model file with the best fitting parameters, adding an error attribute to each of them which contains the statistical uncer- tainty in the estimate, and a ts attribute to each component j for which it was requested. It is possible to use multiple observations as input for ctlike, allowing it to perform a joint analysis, where each observation is kept separately and associated with its IRF, or a stacked analysis, where an average IRF is used. ctbutterfly This tool calculates a butterfly diagram for the spectral component of a specified source model. Two computation methods are available. The one I used in this work, namely the ’ENVELOPE’ method, is specific for power law spectral models, as it computes the envelope of all power law models which are com- patible with the data within a given confidence limit (the standard confidence level of 68% was used), by evaluating for each energy bin the maximum and minimum intensity of all models which fall within the ellipse of the prefactor and index parameters. The ellipse is calculated from the covariance matrix of a maximum likelihood fit performed in each energy bin via ctlike. cslightcurve This script computes the lightcurve for a specified source in a given observation, calling ctlike to perform a maximum likelihood fit in a series of time bins, which can be either fixed by the script itself with linear or logarithmic spacing, or given as input. The output is saved in a FITS file as a binary table in which each row represents a different time bin and contains its central value, the fitted model parameters and their statistical errors, the statistical significance of the specified source, expressed by the TS value, and the energy flux upper limit.

33 Chapter 3

Simulations of the ﬁrst two TeV GRBs

In this chapter I am going through the simulations of the first two VHE GRBs observed so far, i.e. GRB 190114C and GRB 180720B. Observing the high energy spectra of these events is useful to fully characterize the dissipation processes involved in the emission of GRBs. For example, the detection of TeV photons from the early afterglow emission of GRB 190114C confirmed the presence of a spectral component produced via IC scattering, which was theorized but not directly observed despite many years of search. This was possible only thanks to the fast slewing performed by the MAGIC telescopes, which managed to point the source in less than a minute. Indeed, the slewing time is usually longer, and this is the reason why it is difficult to catch VHE emission from a GRB at the start of its evolution. On the other hand, the observation of GRB 180720B, which started in its late afterglow, is interesting for the opposite reason, that is the sensitivity of CTA near its low energy threshold, since observing signals down to a few tens of GeV is an issue for currently operating IACTs. Before diving into the analysis it is worth to explain how the source modeling and analysis are carried out. As explained in §2.2, the input for a simulation should contain both the source and the background models. Since I considered ideal observation conditions, without including a high night sky luminosity or moon light effects, the background is implemented as a diffuse source with a flat spectrum dN/dE = 10−3 MeV−1sr−1s−1 for both simulations. The source models are a bit more elaborated. The spatial characterization is implemented considering a point-like source located at the centre of the field of view, while the spectral component is a power law

E −γ dN/dEINT = f0,INT (3.1) E0,INT

34 CHAPTER 3. SIMULATIONS OF THE FIRST TWO TEV GRBS representing the intrinsic source which is multiplied by the exponential EBL absorption factor1 e−τ(z,E), becoming

−γ E −τ(z,E) dN/dEINT = f0,INT e (3.2) E0,INT where f0,INT is the prefactor of the intrinsic source spectrum, E0,INT its pivot energy, and τ(z, E) is the absorption factor drawn from the EBL model at the redshift and energy of the emitted photon. After several tests, the most stable method to simulate the temporal behaviour of the source resulted to be achieved by splitting the total livetime into smaller time bins and simulating a constant spectrum in each of them, and then stacking them into a single observation. This was done by computing the spectrum in each interval from the time resolved data for the energy flux of GRB 190114C or by rescaling the time-averaged spectrum for GRB 180720B. After modeling the intrinsic source for both GRBs, the EBL absorption effect was taken into account using the absorption factors by [32]. Among the methods tested to include the EBL absorption, the best one seems to be considering it within the spectral component in the XML file through the ’Multiplicative’ tag, and storing the needed values of the absorption parameter τ in an external file. In order to simulate and analyse the sources, I wrote a Python script which created the EBL external file for the source based on its redshift, simulated the source in each time bin and created an XML definition file of the stacked observation. The same script carried out the analysis on these simulated data, computing and then plotting the skymap, the lightcurve, the test statistics evolution, and the spectrum of the source. The script was structured to be easily adaptable and versatile, and it can be also automated to simulate and analyse a large amount of GRB sources at once.

3.1 GRB 190114C

In this section I will describe the analyses of GRB 190114C simulations. This GRB triggered the Burst Alert Telescope (BAT) on board Swift and Gamma- ray Burst Monitor (GBM) on board Fermi on January 14, 2019, at 20:57:02 UT (trigger time T0)[20]. The duration T90 of the burst was measured to be 116 s with Fermi-GBM, which is sensitive to energies from 8 keV up to 40 MeV, while 362 s with Swift-BAT, which detects energies from 15 to 150 keV. A long lasting emission was detected and analysed, which allowed the measurement of the source redshift z = 0.4245 ± 0.0005. After the GCN/TAN notice the MAGIC telescopes slewed to the source location 57 s after T0, though operation stability was reached at T0 +62 s, as during the ﬁrst few seconds the telescope underwent natural oscillation. The isotropic energy of GRB 190114C was comparable with previous events, being fairly but not extremely energetic. Nonetheless, γ-rays above 0.2 TeV were detected with high signiﬁcance (51.4 standard deviations)

1Note that to take into account the EBL absorption the source redshift is required.

35 CHAPTER 3. SIMULATIONS OF THE FIRST TWO TEV GRBS since the beginning of the observation. Therefore, this GRB is a perfect candidate to study the CTA sensitivity. In the next section I will display the observational results obtained by MAGIC and the results of the CTA simulation. For the other simulations, the source was moved farther away, increasing its redshift to determine the horizon of CTA observations for such a source.

3.1.1 CTA simulation In order to check the consistency of the simulation and analysis routines, I first performed a simulation within the same energy range in which the MAGIC telescopes observed GRB 190114C, that is [0.3 − 1.0] TeV. This would show how the introduction of the CTA IRF affected the data, allowing a comparison with [20] and a test of the source modeling. As explained at the beginning of this chapter, in order to simulate the temporal behaviour of the source, rather than introducing a temporal component in the model, I used a time-averaged spectrum in each time bin with different prefactors and spectral indexes, inferring these from the energy flux values given in [20]. The input values for each time bin are reported in Table 3.1. Computing the spectral parameters directly from the time-resolved data rather than from the fitted temporal behaviour, helped in not introducing further uncertainties in the simulation.

Time bin [s] Prefactor [ph/cm2/MeV/s] Index 62-100 4.59 × 10−3 1.86 100-140 1.24 × 10−1 2.15 140-210 5.86 × 10−1 2.31 210-361.5 4.23 2.53 361.5-800 3.58 × 10−1 2.41 800-2454 0.45 × 102 3.1

Table 3.1: Parameters for the spectral components of the source model in each time bin. For each model, the same pivot energy E0 = 1 MeV is considered.

No EBL absorption was taken into account for this consistency check, in order to allow direct comparison with the intrinsic source data presented in [20]. While this simulation is not giving a picture of how CTA would observe the GRB, it shows the effects of the IRF on the data and it is a check that the routine is not introducing biases of any kind. This first simulation and the subsequent analysis match very well with the results reported in [20] for the first 800 s, as shown in Table 3.2.

36 CHAPTER 3. SIMULATIONS OF THE FIRST TWO TEV GRBS

time bin MAGIC energy ﬂux simulated energy ﬂux [s] [erg/cm2/s] [erg/cm2/s] 62-100 [5.64 ± 0.90] × 10−8 5.77 × 10−8 100-140 [3.31 ± 0.67] × 10−8 3.42 × 10−8 140-210 [1.89 ± 0.36] × 10−8 1.93 × 10−8 210-361.5 [7.54 ± 1.60] × 10−9 7.81 × 10−9 361.5-800 [3.10 ± 0.70] × 10−9 3.16 × 10−9 800-2454 [4.54 ± 2.04] × 10−10 4.75 × 10−11

Table 3.2: Measured and simulated energy ﬂux in each time bin of MAGIC observation. No EBL absorption is considered in this test.

The next step was to perform the actual simulation of a CTA observation of the GRB 190114C. Thus, I set the energy range to [0.11-1.00] TeV, and introduced the EBL absorption effect for a redshift of z = 0.4245 using the absorption factors from [32]. Notice that I am not using the full energy range at which CTA will be sensitive. The cut at 1 TeV was introduced after verifying that the source radiation at higher energies is negligible. Thus, to include events over that limit would only asdd more background events, effectively reducing the significance of the signal. The low energy threshold of 110 GeV depends on the IRF used for the simulation. Only when observing a source located at a low Zenith Angle (ZA), energies down to 20 GeV can be detected. The energy threshold of the observation increases with the ZA of the source. Within the CTA consortium the adopted thresholds for the simulations are 20 GeV when ◦ ◦ ◦ ◦ ZA . 30 , 40 GeV when 30 . ZA . 50 , and 110 GeV when ZA & 60 . Including the EBL absorption, the source radiation is simulated as follows:

−α −τ(E) E MS(E) = f0e (3.3) E0

The EBL model used for all the simulations I performed is that by [32], from which the absorption factors for the source redshift were automatically extracted by the script and stored in the external file needed by the ’Multiplicative’ spectrum. The power law parameters are still referring to the intrinsic source, as presented in Table 3.1, while the EBL effect is included in the exponential factor. After stacking all the simulations in a single observation, the analysis routine can start. The first step was to compute a skymap, to have a visual response on how data were spatially distributed over the field of view (fig. 3.1). Here, I used the intrinsic background subtraction method implemented in ctskymap, to cut out the background from the image, and applied a gaussian smoothing to the plot. The source appears as a bright region in the centre of the image, and its defined contour means that the skymap computing tool managed to separate it from the background.

37 CHAPTER 3. SIMULATIONS OF THE FIRST TWO TEV GRBS

Figure 3.1: Skymap for the CTA observation of GRB 190114C. This plot drops the temporal information, but its useful the give an immediate idea of the source shape and brightness. It was obtained via ctskymap, applying a background subtraction method and a gassian smoothing. Notice that all time information is dropped in this plot.

From the same observation definition file, I computed the observed spectral density and the lightcurve, shown in fig. 3.2.

(a) (b)

Figure 3.2: (a) Spectral density for GRB 190114C, the green curve is the spectrum of the intrinsic source, without considering the EBL absorption eﬀect, while the blue one shows the spectrum as it would be observed with CTA. The plot was obtained combining the results from ctbutterﬂy and csspectrum. (b) Lighcurve for the GRB 190114C, as it would be observed by CTA.

38 CHAPTER 3. SIMULATIONS OF THE FIRST TWO TEV GRBS

To have a quantitative measure of the confidence level at which CTA would observe the source, I used the test statistics (TS) value for each point of the lightcurve to compute the significance in each time bin, which gives the number of standard deviations that separate the source from the background. A source is considered statistically significant if this number is above 5 σ. Thus, as shown by fig. 3.3b, the source is easily detectable, standing well above the background at least for the first 800 s after when its significance falls steeply. This is not surprising, as from the previous test the source model was failing to reproduce GRB 190114C in the last time bin. When comparing this curve with the significance computed for the intrinsic source from the previous simulation, we can see how the effect of the EBL absoption, which lowers the flux of higher energy photons that are better distinguished from the background, is to lower the significance to about a third of its original value. This is obviously just indicative, as the first simulation has an higher bottom edge for the detected energy, which also reduces the significance of the source, cutting out data.

(a) (b)

Figure 3.3: Temporal behaviour of the significance for the test simulation (a) and the CTA observation simulation. It was calculated by taking the square root of the TS value divided for the degrees of freedom, that are the number of fitted parameters in the source model. The significance gives the number of standard deviations which separate the source from the background. The model is well fitted to the data when its significance is above the 5 σ level.

3.1.2 Horizon of the observation After having simulated the CTA observation for GRB 190114C, the next interesting question was from how far away a source with these features could be detected by CTA. To date, all the observations of gamma-ray signals with energies reaching the TeV level led to measured redshifts z ≤ 1, as reported from the TeVcat2. As CTA has an increased sensitivity when compared to other IACTs

2the TeVcat is an on line catalog for TeV gamma astronomy, which lists the relevant features for all observed gamma sources. It can be explored at: http://tevcat.uchicago.edu/

39 telescopes, both at greater and lower energies, it should push this limit farther away, allowing us to detect energetic sources with redshifts above the unit. To test this statement, I repeated the simulation of GRB 190114C, increasing its redshift3 and analysing how this affected the significance of the observation. Here I will only display a few redshift values, i.e. z = {1.0, 1.5, 2.0, 2.25, 2.5}, which I think to be enough to get the sense of what is happening. As the source is pushed farther away, it becomes harder and harder to be discerned in the skymap, losing its well defined contour and taking the shape of a cluster of events in the centre of the image, until it eventually gets swamped by the background. The significance lowers as a power law in each time bin when the redshift increases, nearly halving for each 0.5 rise of z (Fig 3.9a). This analysis shows how the maximum distance at which this source could be observed is more than doubled compared to the present limit, going up to z = 2.25. This limit could be pushed farther away when using coincidence methods for the observation, working with more than a gamma detector, or observing the source through other messenger signals, as it should increase the statistical significance. However, this is only a preliminary result as, again, I am considering ideal observation conditions.

(a) (b)

Figure 3.4: Simulation results for z = 1.0. This is the actual detection limit for TeV gamma ray source, according to TeVcat. As you can see from the skymap (a), the source is still easily separated from the background, with a well-deﬁned contour. The signiﬁcance(b) is still high, though halved compared to the original simulation.

3The increased redshift value changes the relevant column of the EBL table considered for the simulation, eﬀectively bolstering the absorption eﬀect, thus a fainter signal reaches the telescopes. (a) (b)

Figure 3.5: Simulation results for z = 1.5. In the skymap (a), the source lost its well-deﬁned contour, but a cluster of events is still visible well above background in the centre of the image. The signiﬁcance (b) halved again, still it lays around 10 σ.

(a) (b)

Figure 3.6: Simulation results for z = 2.0. Here it is quite difficult to discerne the source in the skymap (a), though a small cluster of events can still be seen. When inspecting the significance (b), the signal is still detectable for the first 300 s of the observation, after which it drops below the 5 σ threshold.

(a) (b)

Figure 3.8: Simulation results for z = 2.5. From the skymap (a), the data seem to be distributed randomly, without any particular cluster or pattern, meaning that the background subtraction algorithm is failing to isolate the source. The signiﬁcance (b) has dropped below the detection threshold for all the time bins. (a) (b)

Figure 3.7: Simulation results for z = 2.25. The source has completely lost any contour in the skymap (a), leaving but a very faint cluster of events. The signiﬁcance (b) ﬂoats around the detection threshold, meaning this to be the farthest distance at which the source could be observed.

From this set of simulations, the key result is that there probably is a well deﬁned analytic relationship between the redshift of the source and the signiﬁcance of the observation, as long as the source can be detected at all. I plant to carry out further tests on this result, repeating this process over other VHE source and evaluating the index of the power law connecting these two quantities, the behaviour of which is clear when looking at Fig. 3.9b.

(a) (b)

Figure 3.9: The simulations carried out setting different redshift values for GRB 190114C showed that an analytic relationship between the significance and the redshift of the source can be found. In (a) each curve refers to a fixed redshift, showing how the evolution of the significance halves everytime the redshift is increased by 0.5. In (b) each curve refers to a fixed time bin and shows the the evolution of the significance as the redshift is heghtened. The plot suggests a power law relationships between the significance and the redshift, until it goes under the 5σ threshold.

42 3.2 GRB 180720B

The simulation of GRB 190114C investigated the response of CTA to signals up to the TeV energies. Indeed, this was the first time that GRB photons reaching these energies were observed. It is likewise interesting to analyse how CTA would carry out the observation of less energetic GRB events, down to the detectable energy threshold of 20 GeV. With this aim, I simulated the observation of GRB 180720B, an extremely energetic GRB which triggered the Fermi-GBM on July 20, 2018, at 14:21:39 UT (T0), ranking seventh in prompt emission brightness among the over 2.5 thousand GRBs observed by the satellite. Though being so energetic, this GRB was observed by H.E.S.S. during its late afterglow emission, at T0 +10.1 h, when its energy flux was way fainter. The H.E.S.S. array includes 4 telescopes (CT1-4) with a diameter of 12 m, arranged 120 m apart from each other in a square and a fifth telescope (CT5) of 28 m in diameter placed in the centre. The 12 m telescopes, that were the original H.E.S.S. array, are sensitive to energies from 100 GeV up to 100 TeV, while the CT5, added to the array in 2012, is able to detect lower energies, down to 20 GeV4. To reach the minimum detectable energy threshold, only the CT5 was operated among the H.E.S.S. array, which can observe photons down to 20 GeV when operating alone. However, using a single telescope means to include in the observation photons from CR induced showers, which are cut out when operating the full array due to their higher collimation. This leads to an heightening in the noise on the data, and a reduced sensitivity of the telescope. Thus, data have to be pre-processed before the analysis, through ma- chine learning algorithms or other methods able to cut out the majority of the background from the event sample. With this few expedients H.E.S.S. managed to observe GRB 180720B at late times, from T0 + 10.1 h to T0 + 12.1 h, in the energy range [20 - 440] GeV [33]. Using the redshift measured by the European Southern Observatory Very Large Telescope to be z = 0.653, and correcting the observed flux through the EBL model in [34], the anal- −γ −τ(E,z) ysis of the source spectrum dN/dE = f0(E/E0) e resulted in f0 = +4.53 −10 −1 −2 −1 (7.52±2.03(statistical)−3.84(systematic))×10 T eV cm s at E0 = 0.154 TeV, with a spectral index of γ = 1.6 ± 1.2(statistical) ± 0.4(systematic). These values refer to the whole livetime of the H.E.S.S. observation, thus representing a time average of the time interval T0 + [10.1 − 12.1] h. To simulate the evolution of the signal, the time average operation on the spectrum had to be re-scaled into smaller time bins, using the analytic temporal behaviour F (t) ∝ tα. As suggested in [33], I assumed α = −1.2, relying on the average temporal behaviour observed by the Swift-XRT for the X-ray component of the majority of the GRB afterglows. Indeed, the VHE photons of the GRB are produced through IC scattering off synchrotron radiation at X-ray energies. This means that the temporal behaviour of the VHE component of the spectrum is strictly connected to the one in the X-rays, validating the assumption. These

4For further information, see the website of the collaboration: https://www.mpi- hd.mpg.de/hfm/HESS/

43 re-scaling operation led to the normalization factor of the source for each time bin reported in Table 3.3. The same spectral index γ = 1.6 was used for each model and the EBL model considered is again the one from Dominguez et al. [32].

time bin prefactor [h] [MeV −1cm−2s−1] 10.1-10.5 8.20 × 10−16 10.5-10.9 7.83 × 10−16 10.9-11.3 7.49 × 10−16 11.3-11.7 7.18 × 10−16 11.7-12.1 6.89 × 10−16

Table 3.3: The H.E.S.S. collaboration analysis led to a prefactor of 7.52 × 10−16 MeV −1cm−2s−1; this value is time averaged over the whole observation. To reconstruct the temporal behaviour of GRB 180720B, this value was re- scaled into shorter time bins, assuming the spectrum to follow a power law F (t) ∝ t−1.2. These values refer to the intrinsic source, therefore the simulation is performed by including the EBL eﬀects separately, through a Multiplicative spectral model for the source.

Once the source has been simulated separately in each time bin, the output event lists are stacked together in a single observation for the analysis. The ﬁrst step was to draw a skymap of the observed events (Fig. 3.10).

Figure 3.10: Skymap from the simulation of GRB 180720B. The source is only slightly recognizable over the background as a cluster of counts in the centre of the image, as we are observing it over 10 h after the trigger time.

In this image, the source is distinguishable over the background as cluster of data in the central area, without a well-deﬁned contour. This is because the

44 observation is carried out in during the afterglow, where the flux is much lower than the one observed from GRB 190114C. Nonetheless, it is possible to fit the lightcurve of the source with a significance well above the 5σ threshold (Fig. 3.11). This shows how CTA will improve the current sensitivity to less energetic VHE photons, following their evolution farther in time and simplifying the analysis, as the need to pre-process data will be reduced to even lower energies or worse condition.

(a) (b)

Figure 3.11: The lightcurve (a) of GRB 180720B, where the evolution was reproduced using the average temporal behaviour of the X-ray counterpart of the spectrum. Despite the observation taking place in the late afterglow, where the source is near the detectable energy threshold of 20 GeV, the signiﬁcance (b) is still above the 5σ threshold.

45 Conclusions

The simulations concerning the first two TeV GRBs, i.e. GRB 190114C and GRB 180720B, carried out through this work are a preliminary analysis, as this is the first attempt within the CTA consortium to analyse the CTA sensitivity to VHE GRBs already observed. The subject should be further investigated, for example, testing how the results can be affected by different conditions of the night sky background. Nonetheless, from this analysis a few interesting clues were drawn. From the simulation with ctools of GRB 190114C at its measured redshift, it is possible to see how this source is modeled and analysed leading to similar results as those obtained with observations by the MAGIC telescopes, though with an increased significance. The VHE radiation from this GRB was observed thanks to the fast slewing performed by MAGIC, thus CTA is expected to detect more events at these energies since it will also take a shorter time to point at transient sources with respect to all the currently operating IACTs. Moving the source farther away, i.e. increasing its redshift, and repeating the simulations, I obtained that the signal would still be detected with a significance over the 5σ threshold up to redshifts z ' 2. This is utterly interesting, as the current limit at which TeV sources have been observed lies at z ' 1. Furthermore, the significance of the observation seems to be connected to the distance of the source following a power law. The same behaviour was obtained in all time bins, as long as the source remained detectable. Further investigation on this result could lead to the development of methods and algorithms able to increase the sensitivity of observations. The simulation of GRB 180720B showed that CTA will also have an increased sensitivity to signals at a few tens of GeV, without requiring any particular technique or pre-processing of data. This energy range is expected to be particularly interesting for VHE emission in GRB late afterglows. Indeed, the simulations showed thanks to its sensitivity both at low and high VHE energies, CTA should be able to follow-up transient sources through most of their evolution, allowing a better understanding of GRB properties. In order to perform the simulations and analyses, I wrote a Python script which used ctools as base blocks of an extended routine, achieved after testing several procedures. This script ensures high versatility and can be adapted to different observations by changing only a few settings. Moreover, it can be automated to simulate and analyse a large number of sources at once.

46 Concerning future development of this work, the connection of TeV GRBs with other cosmic messengers has to be further investigated. While GRBs are expected to produce all four messengers, the detection of these counterparts is difficult. Thus, the main focus should be on their connection with GWs, as it is the only one observed until now (GRB 170817A/GW170817) and the most promis- ing to be observed again in the next few years. A joint analysis of GWs and GRBs would give insights on their progenitors as well as important constraints on fundamental physics. Information about progenitors would be especially precious when considering short GRBs, which are the most difficult to observe at early times due to their short duration. Currently, the most accounted progenitor model for these events is the merger of compact object binaries, thus the connection with GWs. The coincident detection of GW170817 and GRB 170817A confirmed such a connection. Moreover, this analysis could set important constraints on fundamental physics, measuring the discrepancy between the speed of GWs and GRBs or the effects of the gravitational potential on both signals. On the other hand, the connection between GRBs and neutrinos or CRs could be harder to observe, for different reasons. To date, strong constraints have been set on the neutrino flux from GRBs, combining simulations with the stacked analysis of data from neutrino telescopes. Anyway, observing neutrinos from GRBs could still be useful to draw information on the internal dynamics of the jet. Due to their nature of charged particles, the coincidence with CRs is probably the hardest to observe. Nonetheless, according to the Hillas criterion, GRBs are a suitable source for ultra-high energy CRs, near the top edge or their spectrum.

47 Bibliography

[1] Tsvi Piran. “The Physics of Gamma-Ray Bursts”. In: Reviews of Modern Physics 76 (2005), pp. 1143–1210. [2] D. Band et al. “BATSE observations of gamma-ray burst spectra. I. Spec- tral density”. In: The Astrophysical Journal 413 (1993), pp. 281–292. [3] Zhang et al. “A new classiﬁcation method for gamma-ray bursts”. In: The astrophysical journal 725 (2010), pp. 1965–1970. [4] J. S. Bloom, N. R. Butler, and D. A. Perley. “Gamma-ray bursts, classiﬁed physically”. In: AIP Conference Proceedings 1000 (2008), pp. 11–15. [5] R. Sari, T. Piran, and R. Narayan. “Spectra and Light Curves of Gamma- Ray Burst Afterglows”. In: The Astrophysical Journal Letters 497 (1998). [6] J. Hjorth et al. “A very energetic supernova associated with the gamma- ray burst of 29 March 2003”. In: Nature (2003), pp. 847–850. [7] S. E. Woosley and J. S. Bloom. “The Supernova – Gamma-Ray Burst Con- nection”. In: Annual Reviews of Astronomy and Astrophysics 44 (2006), pp. 507–556. [8] J. Hjorth and J. S. Bloom. “The GRB-Supernova connection”. In: Cam- bridge Astrophysics Series 51 (2011), pp. 169–190. [9] A. Panaitescu, P. Kumar, and R. Narayan. “Observational Prospects for Afterglows of Short-Duration Gamma-Ray Bursts”. In: The Astrophysical Journal Letters 561 (2001), pp. L171–L174. [10] R. Perna and K. Belczynski. “Short Gamma-Ray Bursts and Mergers of Compact Objects: Observational Constraints”. In: The Astrophysical Journal 570 (2002), pp. 252–263. [11] B. P. Abbot et al. “Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A”. In: The Astrophys- ical Journal Letters 848 (2017), pp. L13–L30. [12] B. Paczynski. “Gamma-ray bursters at cosmological distances”. In: The Astrophysical Journal Letters 308 (1986), pp. L43–L46. [13] S. E. Woosley. “Gamma-Ray Bursts from Stellar Mass Accretion Disks around Black Holes”. In: The Astrophysical Journal 405 (1993), pp. 273– 277.

48 [14] Y. Lithwick and R. Sari. “Lower limits on Lorentz factors in gamma-ray bursts”. In: The Astrophysical Journal 555 (2001), pp. 540–545. [15] A. R. Bell. “The acceleration of cosmic rays in shock fronts - I”. In: Monthly Notices of the Royal Astronomical Society 182 (1978), pp. 147– 156. [16] M. Vietri. “The Acceleration of Ultra–High-Energy Cosmic Rays in Gamma- Ray Bursts”. In: The Astrophysical Journal 453 (1995), p. 883. [17] E. E. Fenimore, C. D. Madras, and S. Nayakshin. “Expanding Relativistic Shells and Gamma-Ray Burst Temporal Structure”. In: The Astrophysical Journal 473 (1996), pp. 998–1012. [18] R. Sari and T. Piran. “Variability in Gamma-Ray Bursts: A Clue”. In: The Astrophysical Journal 485 (1997), pp. 998–1012. [19] E. E. Fenimore et al. “Gamma-Ray Burst Peak Duration as a Function of Energy”. In: Astrophysical Journal Letters 448 (1995), p. L101. [20] V. A. Acciari et al. “Teraelectronvolt emission from the gamma-ray burst GRB190114C”. In: Nature 575 (2019), pp. 455–458. [21] S. Gao. “High energy neutrinos from gamma-ray bursts: recent observations and models”. PhD thesis. The Pennsylvania State University, 2014. [22] M. G. Aartsen et al. “Extending the search for muon neutrinos coincident with gamma-ray bursts in IceCube data”. In: The Astrophysical Journal 843 (2017), pp. 112–125. [23] P. Baerwald, M. Bustamante, and W. Winter. “Are gamma-ray bursts the sources of ultra-high energy cosmic rays?” In: Astroparticle Physics 62 (2015), pp. 66–91. [24] Irwin I. Shapiro. “Fourth Test of General Relativity”. In: Physical Review Letters 13 (26 1964), pp. 789–791. [25] T. Di Girolamo et al. “Prospects for detecting Gamma-Ray Bursts with the Cherenkov Telescope Array”. In: Nuclear and Particle Physics Pro- ceedings 291-293 (2017), pp. 44–47. [26] G. Pareschi. “The ASTRI program in the context of the Cherenkov Tele- scope Array Observatory”. In: Proceedings of the 36th International Cos- mic Ray Conference PoS 758 (2019). [27] V. Barbosa Martins et al. “A Condition Monitoring Concept Studied at the MST Prototype for the Cherenkov Telescope Array”. In: Proceedings of the 36th International Cosmic Ray Conference PoS 358 (2019). [28] Q. Feng et al. “Prototype Schwarzschild-Couder Telescope for the Cherenkov Telescope Array: Commissioning Status of the Optical System”. In: Pro- ceedings of the 36th International Cosmic Ray Conference PoS 672 (2019). [29] L. Taylor et al. “Camera design and performance of the prototype Schwarzschild- Couder Telescope for the Cherenkov Telescope Array”. In: Proceedings of the 36th International Cosmic Ray Conference PoS 807 (2019).

49 [30] D. Mazien. “The Cherenkov Telescope Array”. In: Proceedings of the 36th International Cosmic Ray Conference PoS 741 (2019). [31] J. Knodlseder et al. “GammaLib and ctools: A software framework for the analysis of astronomical gamma-ray data”. In: Astronomy and Astro- physics 593 (2016), A1. [32] A. Dominguez et al. “Extragalactic Background Light Inferred from AEGIS Galaxy SED-type Fractions”. In: Monthly Notices of the Royal Astronom- ical Society 410 (2011), pp. 2556–2578. [33] H. Abdalla et al. “A very-high-energy component deep in the gamma ray burst afterglow”. In: Nature 575 (2019), pp. 464–467. [34] A. Franceschini, G. Rodighiero, and M. Vaccari. “Extragalactic optical- infrared background radiation, its time evolution and the cosmic photon- photon opacity”. In: Astronomy and Astrophysics 487 (2008), pp. 837– 852.