Investigation on Gamma-Electron Air Shower Separation for CTA

Taras Shevchenko National University of Kyiv The Faculty of Physics Astronomy and Space Physics Department

Investigation on gamma-electron air shower separation for CTA

Field of study: 0701 – physics Speciality: 8.04020601 – astronomy Specialisation: astrophysics

Master’s thesis the second year master student Iryna Lypova

Supervisor: Dr. Gernot Maier leader of Helmholtz-University Young Investigator Group at DESY and Humboldt University (Berlin)

Kyiv, 2013 Contents

Introduction 2

1 Extensive air showers 3 1.1 Electromagnetic showers ...... 3 1.2 Hadronic showers ...... 7 1.3 Cherenkov radiation ...... 11

2 Cherenkov technique 13 2.1 Cherenkov telescopes ...... 13 2.2 Cherenkov Telescope Array ...... 18 2.3 Air shower reconstruction ...... 24

3 γ-electron separation with telescope arrays 31 3.1 Hybrid array ...... 31 3.2 The Cherenkov Telescope Array ...... 39

Summary 42

Reference 44

Appendix A 47

Appendix B 50 Introduction

Very high energy (VHE) ground-based γ-ray astrophysics is a quite young science. The earth atmosphere absorbs gamma-rays and direct detection is possible only with satellite or balloon experiments. The flux of gamma rays falls rapidly with increasing energy and satellite detectors become not effective anymore due to the limited collection area. Another possibility for gamma- ray detection is usage of Imaging Atmospheric Cherenkov telescopes. The primary γ-ray creates a cascade of the secondary particles which move through the atmosphere. The charged component of the cascade which moves with velocities faster the light in the air, emits Cherenkov light which can be detected by the ground based optical detectors. The ground based gamma astronomy was pioneered by the 10 m single Cherenkov telescope WHIPPLE (1968) [1] in Arizona. It observed in the energy range between 300 GeV and 10 TeV. It was the first ground-based telescope which detected galactic (the Crab Nebula in 1989 [2]) and extragalactic (Mrk 421 in 1992 [3]) gamma ray sources. The stereo technique was pioneered by HEGRA array (1996) [4]. It consisted of 6 telescopes and operated on TeV energies. The stereoscopic view allowed a full geometrical reconstruction of the air shower that improved some experimental sensitivity compared to WHIPPLE. MAGIC [5], HESS [6], VERITAS [7] are the current generation of imaging atmospheric Cherenkov telescopes. They work in the stereoscopic regime with the energy threshold lower than 100 GeV. They achieve a sensitivity which allows to detect gamma ray sources weaker than 1% of the Crab Nebulae flux. But still, only a very small fraction of objects can be studied by the Cherenkov technique. The Cherenkov Telescope Array (CTA) [8] will be a new generation of ground based Cherenkov experiments. It will operate in a wide energy range from tens of GeV to hundreds of TeV. Improved temporal, angular and energy resolution will allow to measure faint and transient γ-ray sources. The background rate limits the sensitivity in middle energy range from 100 GeV to several TeV. A high efficiency of hadron background rejection allows to improve the sensitivity which will reach 10−3 of the Crab Nebulae flux at 1 TeV energy. Further improvement of the sensitivity by rejection of hadronic showers becomes complicated. The significant part of the leftover background consists of electron induced showers which can be hardly reduced by existing methods of separation. In this work the feasibility of γ-electron separation with array of the Cherenkov telescopes is studied.

2 1 Extensive air showers

When a cosmic particle enters into the atmosphere it produces a cascade of secondary particles through interactions with nuclei. These cascades are called the Extensive Air Showers (EAS). There are two cascade sorts deﬁned by the type of primary particle: hadronic (induced by protons or heavier nucleus) and electromagnetic showers (gamma, electron or positron primary). The secondary particles are high energetic and emit Cherenkov light mainly in UV part of the spectrum. The technique of Imaging Atmospheric Cherenkov Telescopes (IACT) is based on this eﬀect. IACTs are used in the high-energy astronomy for detection of gamma-rays in energy range from tens of GeV to hundreds of TeV.

1.1 Electromagnetic showers

Electromagnetic (EM) showers can be induced by gamma-rays, electrons or positrons. All three shower types are very similar. In the following paragraph the development of gamma-ray induced EM showers are explained. The primary gamma-ray creates electron-positron pair in the ﬁeld of the atmospheric nucleus through pair production process with the characteristic length of 2 λpair ≈ 47 g/cm [9]. After pair creation the primary gamma disappears and each of the produced secondary particle gets roughly half of the primary energy. The electron and the positron continue to move through the atmosphere. They overcome approximately 36.2 g/cm2 in the distance [9] till they emit a high energy photon through Bremsstrahlung process. These steps repeat continuously until the secondary electron energy drops below critical

Ecrit = 82 MeV, when the Bremsstrahlung losses equal to the ionisation losses of the electron [10]. Often for simplification in the models of EM shower length of pair production and radiative length are equal (λpair = λbremss = X0). A simplified picture of the development of gamma induced showers is shown in fig. 1. With each step number of secondary particles (including n photons) doubles. After n = X/X0 steps the cascade consists of N = 2 secondary particles. Average energy per particle is roughly equal:

n En ' Eprim/2 , (1) where Eprim is energy of the primary particle, En is energy of the secondary particle after n steps of the shower development. As it was mentioned above, the shower develops until the energy of the secondary particles reach a critical value Ecrit. In this moment the shower achieves the maximum of development 2 hmax, from the top of the atmosphere, measured either in m or g/cm units [12]. The depth of the shower maximum can be calculated:

3 Figure 1: Schematic illustration of the electromagnetic air shower initiated by a primary gamma ray ([11]).

ln (E /E ) X = X prim crit . (2) max 0 ln 2 The depth in the atmosphere is related with the height through the barometric formula. For a standard isothermal atmosphere it can be written in the simple form:

X(h) = X(h = 0) exp (−h/H), (3) where X(h) is the depth in the atmosphere in relation from the height h, X(h = 0) is the vertical column density of the atmosphere at the sea level, H - scale height which is equal:

RT H = , (4) gµ where R [J/(K mol)] is the universal gas constant, T [K] is the absolute temperature, µ [g/mol] is the mean molecular weight, g [m/s2] is the gravitation acceleration. The location of the shower maximum depends on the primary energy. Showers with the higher energy have the maximum deeper in the atmosphere. The longitudinal development of the shower is demonstrated in fig. 2 [13]. Each curve represents a number of charged particles from the depth after first interaction for different primary energies. A maximum of each curve corresponds to the maximum of the shower. The rate of change of the shower maximum location versus the primary

4 Figure 2: Longitudinal development of the gamma-ray induced showers. The black curve illustrates results obtained with CORSIKA [14] simulations. The red curve represents longitudinal distribution described by modiﬁed Greisen formula 5 [13]. energy is called elongation rate. Analytically longitudinal development modelled by the modiﬁed Greisen formula:

a b a N (y, t) = √ exp t 1 − ln s + 2 − √ exp −t, (5) e y b − 1 y where Ne(y, t) is the number of charged particles as function of the distance to the point of the first interaction and primary energy, y = ln (Eprim/Ecrit) is energy in units of the critical energy, t = X/X0 is depth in the atmosphere in units of the radiation length, a and b are free parameters of the model, s is the shower age. The shower age is defined by the point of the first interaction, as following:

b s = , (6) 1 + c(b − 1)/t where c is depth of the shower maximum. The value of the shower age changes from 0 to 2 during shower development. In piont of the first interaction the shower age equals to ”0”. The value of ”1” corresponds to the maximum of development. Electron (or positron) induced air showers are very similar to the gamma induced ones. Main difference between them is the process in the point of the first interaction. Gamma-ray creates

5 electron-positron pair and vanishes. Unlike gammas, the primary electron still can possess enough energy to emit a second Bremsstrahlung photon. It ”stops” when its ionisation losses become dominated. Due to this electron may emit a few high energetic photons while passing through the atmosphere. This secondary photons create sub-showers. If energy of the primary electron is high enough and it does not deﬂect strongly in the Earth’s magnetic ﬁeld, then the sub-showers irradiate the same light pool on the ground. It means that such electron induced shower has a larger number of the secondary particles and accordingly a larger number of the Cherenkov photons from the high altitudes. The radiative length of the electron is smaller that the pair production length of the gamma

(λpair > λbremss). This leads to another diﬀerence between gamma induced and electron induced showers. A point of the ﬁrst interaction and, as result, a position of the maximum of development located higher in the atmosphere for the electron induced then for the gamma induced shower with the same primary energy.

6 1.2 Hadronic showers

Another type of the showers is the hadronic showers. These showers are caused mainly by the protons and relatively smaller part from other heavy hadron. When a cosmic proton enters the atmosphere it collides with a nucleus. Only one or two nucleons participate in the interaction with the high energy proton [11]. They leave the nucleus in the highly excited state. The highly excited nucleus emits fragments. These fragments are called spallation fragments. The interaction can produce all types of pions, strange particles and hadrons. Light particles (pions, hadrons, strange particles) are produced within the cone. A width of the cone is connected to the primary hadron energy. Schematically the process is depictured in ﬁg. 3.

Figure 3: Schematic illustration of the cosmic ray interaction with the nucleus in the atmosphere. [11].

The secondary nucleons and pions move through the atmosphere and they create jet of the particles due to the interaction with other nucleons. This process continues while the primary energy per nucleon bigger than the threshold for the pion production (around 1 GeV). The process of energy transition from primary particle to the pions is called pionisation. 0 −16 The neutral pions π have short lifetime τπ0 = 1.78 · 10 s and decay into two gammas π0 → 2γ. Each of these gammas produces electromagnetic shower. The lifetime of the charged −8 pion is bigger and equal τπ± = 2.551·10 s. These pions mainly decays into muons and neutrinos:

π+ → µ+ + ν , µ (7) − − π → µ + νµ.

7 Figure 4: Schematic representation of the hadronic air shower [11].

High energetic muons can be produced in the higher layers of the atmosphere where the typical length of the nuclear interaction is bigger than the decay length of the pion. These muons can penetrate deep into the atmosphere and even reach the ground level. They form the muon component of the shower. Another part of the muon component decays as:

µ+ → e+ + ν + ν , e µ (8) − − µ → e + νe + νµ. Neutrinos produced during evolution of the shower forms the penetrative component. All components of the hadronic shower schematically shown in ﬁg. 4.

8 Figure 5: Comparison of gamma-ray (left) and proton (right) induced extensive air shower. Top images illustrate vertical development and bottom images illustrate lateral development of the showers. Red color represent photon, electron and positron tracks, blue color - hadron tracks, green color - muon tracks [15].

9 The main diﬀerences between the hadronic and the electromagnetic showers are:

• the hadronic showers have bigger lateral distribution due to a transverse momentum of the secondary particles [16]. The comparison between a gamma induced (at left) and a proton induced (at right) showers in ﬁg. 5. Both showers have the primary energy equal to 100 GeV.

• in the hadronic showers the main sources of the Cherenkov light are electromagnetic sub- showers. Electromagnetic component is created mainly after the neutral pion decays. All types of the pions are produced almost in the equal amount. Due to this the neutral pions and consequently the electromagnetic sub-showers get only part of the energy of the primary particle. As consequence the hadronic showers looks fainter than electromagnetic ones with the same primary energy. This diﬀerence also can be seen in ﬁg. 5;

• if the shower is initiated by heavy particle it can have a multi-core structure. After collision with the atmospheric nucleus the heavy cosmic ray continues to move with a jet of the relativistic spallation fragments, protons and neutrons [11]. The high energy fragments can create the sub-showers and lead to a multi-core structure in the main shower. A comparison on the single core structure of the proton shower (at left) and multi-core structure of the heavy hadron shower (at right) is illustrated in ﬁg. 6.

Figure 6: Distribution of particle density in central region of proton single core (a) and heavy hadron multi-core (b) showers [12].

10 1.3 Cherenkov radiation

Charged particles emit the Cherenkov light if they move quicker than the phase velocity of light in the medium. Every point of the particle track may be considered as a source of the electromagnetic waves which are emitted in all directions. The refraction index of the medium is equal n. The velocity of waves is c/n, where c is the speed of light in the vacuum. According to the Huygen’s principle the coherent radiation from each element of the track can be cancelled or amplified. It depends on the emission angle of the waves [16]. Two points of the particle track (A and B in fig. 7) radiate the light under the angle θ. Path difference of this waves is equal [17]:

c c AB AC 1 mλ ∆x = (t − t ) = − n = AB − cos θ = , (9) n 2 1 n v c βn 2 where v is a velocity of the particle, λ is radiation wavelength, t1 is a time which is needed to light for the passage of the piece AC, t2 is a time which is needed to particle move from A to B, if m = 1, 3, ... (odd value) then waves cancel each other, if m = 0, 2, ... (even value) then waves are ampliﬁed. Thus waves are distributed only in case cos θ = 1/βn. Otherwise, it is always possible to ﬁnd the size of the segment AB for which m is odd value. Only particles with the velocity above some threshold emits the Cherenkov light. The emission angle of such waves is minimal θ = 0. The velocity threshold is equal to:

βth = 1/n. (10)

Figure 7: Schematic illustration of direction of the Cherenkov radiation [17].

11 Figure 8: Dependence of the Cherenkov emission angle on electron energy [16].

The maximum emission angle exists. It is called the Cherenkov angle and can be reached in the ultra relativistic case i.e. when β → 1:

θmax = arccos (1/n). (11)

Fig. 8 illustrates changes of the Cherenkov emission angle versus the kinetic energy of electrons in the air at diﬀerent altitudes. The losses due to Cherenkov radiation are negligible and amount only 0.1% fraction of the total energy losses. The energy dE radiated per unit of path dl is equal:

dE ze2 Z 1 = 4π 1 − 2 2 ωdω, (12) dl c βn>1 β n where ze is a charge of the particle, ω is an angular frequency of Cherenkov photons. A number of photons Nph emitted along the length l equal: 2 1 1 1 Nph = 2πz αl − 1 − 2 2 , (13) λ1 λ2 β n where α = e2/~c ' 1/137 is the ﬁne structure constant.

12 2 Cherenkov technique

The energy losses by the Cherenkov radiation are negligible in comparison with all energy losses of the ultra relativistic charged particle. But these losses are very important for the High energy astrophysics. The Imaging Atmospheric Cherenkov Telescopes (IACT) can image the short ﬂashes of the Cherenkov light from air showers. It allows to explore the very high energy gamma-rays which cannot be studied by the satellite experiments due to their very low ﬂux.

2.1 Cherenkov telescopes

The Imaging Atmospheric Cherenkov Telescopes (IACTs) use the Cherenkov light from air showers for the high energy gamma-rays detection. The 10 m telescope Whipple in Arizona was the first IACTs and was mounted in 1968. WHIPPLE operated in the energy range 300 GeV - 10 TeV. The current systems of the Cherenkov telescopes, such as MAGIC, HESS and VERITAS work in the stereo regime and can measure the lower energies (from tens of GeV) with high sensitivity. The Cherenkov Telescopes Array (CTA) is a one of the new generation of the ground based experiments and now it is in the design phase. The optical part of the Cherenkov telescopes consists of a reflector which focuses photons into the camera at the focal plane. For costs reasons, the telescope reflector consists of the individual small mirrors [18]. The typical telescopes with the threshold around 100 GeV have the reflectors with the effective areas approximately equal 100 m2 and are segmented on 350-400 elements. The average reflectivity of the mirrors is >80% for the wavelengths in the range 300-600 nm.

Camera of the telescope The telescope camera consists of the arrays of photomultiplier tubes (PMT). Fig. 9 illustrates the shower image (primary energy 460 GeV) observed from the same impact distance (190 m) by the same telescope (6◦ field of view) but with the different pixel size (0.07, 0.1, 0.14, 0.2, 0.28◦) [19]. The accuracy of the event reconstruction depends on the pixel size (more about reconstruction can be found in section 2.3). The very small (0.07◦) and very big (0.28◦) pixels should not be used for the observation of the low-energy showers. In the first case the event can not be triggered because the signal is not contiguous in the adjacent pixels. In the second case the little light can not trigger the enough number of pixels. The pixel size is limited by the point spread function (PSF) of the reflector. In the ideal case, the PSF should be smaller then the pixel size over the entire field of view (FoV) [20]. There are gaps between the PMTs and for the avoiding a leakage of the light each pixel has a special funnel on the front side [21]. These funnels are called Winston cones. It also reduces

13 Figure 9: Imaging of 460 GeV gamma-ray shower with different pixel sizes (0.07, 0.1, 0.14, 0.2, 0.28◦). Observations are cared by 420 m2 telescope with 6◦ FoV at 190 m core distance [19]. a stray light from the night sky which can incident from the large angles. The reflectivity of the Winston cones is close to the reflectivity of the mirror facets (more than 80%).

Field of view The current generation of the Cherenkov telescope systems consists of the several telescopes and have small ﬁeld of view (5◦ for HESS, 3.5◦ for VERITAS). The distance of the image from the camera centre scales with the distance of the shower axis from the telescope position. Therefore, a large FoV is necessary for the large telescope array which will work with the high energies [19]. The increasing of the FoV results in the increase of the number of pixels. Also it requires the improving of the f/d ratio in the single-mirror telescope for obtaining an acceptable point spread function. This is mechanically diﬃcult due to the heavy camera. For the large FoVs, a two-mirror telescope design (for example Schwarzschild-Couder) can be used.

Davies-Cotton and parabolic layout Most reﬂectors of the Cherenkov telescope have a spherical (Davies-Cotton) or a parabolic design [22]. In the Davies-Cotton design all mirrors are arranged on the sphere with the diameter d. Each of the mirrors has the focal length d which is equal to the focal length of the whole telescope. In the parabolic design spherical mirrors are arranged on the paraboloid z = r2/4f. The focal length of the facets changes with a distance from the optical axis. For the small perfect mirrors both layouts provide a point-like focus for the rays parallel to the

14 Figure 10: Left: PSF of the Davies-Cotton design for diﬀerent f/d ratio from 0.8 (top curve) to 1.4 (bottom curve) with step 0.1. Right: Comparison of the Davies-Cotton design with f/d = 1.2 (bottom curve) and the parabolic design (top curve) [22].

Figure 11: Comparison of the time profile of the Cherenkov light reflected by parabolic (dotted) and Davies-Cotton (dashed) designs for impact distance 100 m (left) and 150 m (right). Real profile of Cherenkov light is shows by solid line. Both telescopes have a 20 m diameter and were simulated at an altitude 5 km. The energy of the primary gamma-ray is 10 GeV. [23]. optical axis. Both of them have a significant aberrations for the rays which incident at an angle to the optical axis. In this regard the parabolic reflectors suffer more than the Davies-Cotton types. The PSF for the Davies-Cotton design is represented at the left image of the fig. 10. The different curves indicate the different ratio f/d. The comparison of the parabolic (top curve) and Davies-Cotton design with f/d ratio 1.2 (bottom curve) is illustrated at the right image. The reflector introduces some time dispersion [23]. It should be not bigger than the intrinsic spread of the Cherenkov wavefront. The parabolic reflector is isochronous. Only individual mirrors

15 Figure 12: Illustration of the optical system for the Schwarzschild-Couder design [24].

Figure 13: Comparison of PSF for different configuration of the Schwarzschild-Couder design [24]. introduce relatively small time dispersion due to their spherical shape. Whereas in the Davies- Cotton design light from the different part of the reflector needs a different time to reach the focal plane. Fig. 11 shows comparison of the time profile of the Cherenkov light which hit the telescope dish (solid line) and which were reflected into the focal plane with the parabolic (dotted line) and the Davies-Cotton (dashed line) telescope designs. The last criteria is the most important for the measurement of the low energy gamma-rays which produce a few of Cherenkov photons. In the ideal case the pulse integration gate should be comparable with the real time of the light pulse from the shower. A pulse time of the photons reflected by the parabolic dish close to the real time profile. Small integration gate allows to

16 suppress a level of detected background from the NSB and, as result, to lower the telescope threshold.

Schwarzschild-Couder layout The Schwarzschild-Couder layout has never been used for the Cherenkov telescope design. It consists of two aspherical mirrors. The basic geometry of the optical system in shown in ﬁg. 12 [24].

Dp, Fp are the diameter and the focal length for the primary mirror, analogically Ds, Fs are for the secondary mirror and Df , Ff are the diameter and the focal plane curvature. α is the position of the secondary mirror in units of the primary focal length. The secondary mirror is placed inside the focus of the primary mirror (α < 1). But unlike the traditional two-mirror systems (Cassegrain design) which has the convex secondary mirrors for the magnification, Schwarzschild-Couder design has the concave mirror to reduce the size of the image. The Schwarzschild-Couder design is free from the coma and the spherical (aplanatic system) aberrations with relatively big field of view [25]. It is isochronous and can be optimized to have no vignetting across the FoV. The PSF as a function of the FoV angle is shown in fig. 13 for the three different configurations. The first configuration (conf1) constructed to achieve the largest effective area and the soft requirement to imaging. The second configuration (conf2) should provide the largest FoV with a uniform response. To do so secondary mirror is extended on 25%. The third configuration (conf3) should have a large FoV with a good PSF. A Schwarzschild-Couder design is more compact in the comparison with usual singe-mirror telescope. But it has large secondary mirror which shadows a big part of the primary mirror. Also the aspheric mirrors are complicated to produce.

17 2.2 Cherenkov Telescope Array

The Cherenkov Telescope Array (CTA) is a one of the new generation of the ground-based experiments (ﬁg. 14). This instrument will work in a wide energy range (from some tens of GeV to above 100 TeV). For covering the whole range, the array will consist of three type of the telescopes [8]:

• the Large-Size Telescopes (LSTs) - 24 m telescopes with the ﬁeld of view (FoV) of 4-5 degrees, will work at the low energies (from a few tens of GeV up to about a hundred GeV);

• the Medium-Size Telescopes (MSTs) - 10-12 m telescopes for the ”core” energy range from 100 GeV to 5 TeV with the FoV of 6-8 deg;

• the Small-Size Telescopes (SSTs) - 4-6 m telescopes with the FoV 10 deg., which will operate over 5 TeV.

Figure 14: CTA (The Cherenkov Telescope Array).

Initially it was proposed that the CTA would be located in two hemispheres: northern and southern. The northern array will consist of 2 larger telescope types (LSTs and MSTs). There is easy to observe the extragalactic objects. Whereas in the southern hemisphere the Milky Way is located on the small zenith distance which promotes the observations of the galactic gamma-ray sources. The southern part of the CTA should involve all telescope types. At current development stage of the CTA project there are two large-scales simulations: Prod1 [19] and Prod2 [26]. Each simulation includes several possible configuration of the telescopes location which are shown at Appendix A. Prod1 consists of 275 telescopes, in Prod2 this number was reduced to 168 telescopes. The improved telescope characteristics are used in the new version of the simulation. The comparison of the mirrors reflectivity and the telescope quantum efficiency in Prod1 and Prod2 are shown in fig. 15 and fig. 16 respectively.

18 Figure 15: Mirror reﬂectivity simulated in prod1 (red curve) and in prod2 (green curve) [26].

Figure 16: Quantum eﬃciency simulated in prod1 (green curve) and in prod2 (red curve) [26].

The LSTs will follow the parabolic design with Rc = 2f. The MSTs design will be close to the Davies-Cotton with Rc = 1.2f. The SSTs will include two types of the telescopes: the single reflector (Davies-Cotton like MST) and the two-mirror Schwarzschild-Couder design. The schematic representation of the parabolic, the Davies-Cotton and the Schwarzschild-Couder designs can be found at Appendix A. The CTA will have improved temporal, angular and energy resolution. It will allow to resolve the fine structure of the extended sources, which can not be probed with the current generation of the Cherenkov telescopes. The CTA will be able to register the flaring and the time-variable

19 Figure 17: Angular resolution for B, C and E arrays in comparison of current telescope array HESS [19]. emission on the small time scales. The angular resolution is shown in fig. 17. The results were obtained for the array B (blue), C (green) and E (red) which are the candidate configurations for the CTA in prod1 layout. Illustration of this configurations can be found in Appendix A. The red dotted line show result for the array E with the more advanced method of the event reconstruction which uses the time of the photons arrival. The black dashed line illustrates HESS angular resolution as the reference. Fig. 18 shows the energy resolution for the same arrays. For all of them resolution change in a range of 10% - 30%. The improvement of the array sensitivity allows to register the fainter sources, which cannot be seen by the current telescope arrays. Fig. 19 shows the sensitivity for the CTA candidates arrays B, C, E. The goal sensitivity curve is shown by the grey color. The sensitivity of all configurations is close to the desired values even with the standard analysis methods. The array C is the most sensitive on high energies. But due to a large distance between telescopes it can not provide a good sensitivity below 100 GeV. Fig. 20 shows that the sensitivity scales linearly with the observed time. The results are illustrated for the array E for 50 h, 5 h and 0.5 h. Two alternative analysis are shown for 50 h time curve. Thus the weakest sources the for current telescopes with flux around 2% of the Crab Nebula flux would be observed with the array E in over 30 minutes. Fig. 21 illustrates the limiting factors of the instrument sensitivity (blue line), which is calculated as the minimal detectable flux of the Crab nebulae per energy band. At high energies the

20 Figure 18: Energy resolution of the CTA candidate arrays B,C,E [19].

Figure 19: Sensitivity of the CTA candidate arrays B,C,E in comparison of the goal sensitivity values [19]. sensitivity is limited by number of the gamma-rays (black), at medium range by the hadron (green) and the electron (red) background rates and at low energies by the systematic background ﬂuctu- ations (purple). Quality of the gamma-hadron separation is very high what leads that the electron

21 Figure 20: Sensitivity of the CTA candidate arrays B,C,E for the diﬀerent observation times [19].

Figure 21: Limiting of the sensitivity. High energies - gamma ray flux (black), medium energies - electron (red) and proton (green) background rate, low energiws - beckground fluctuations (purple) [19]. background becomes a very important constraining factor for the CTA sensitivity. In fig. 22 the background rate (solid curve) is shown. The dashed curve illustrates only proton background and dotted only electron background. As result, reducing even a part of the electron induced showers

22 1

10•1

10•2

•3

background rate [1/s] 10

10•4

10•5

10•6

10•2 10•1 1 10 102 energy [TeV] Figure 22: Background rate. Solid line - full rate, dashed - proton background, dotted - electron background. would improve the instrument sensitivity at medium energy range.

Monte Carlo simulations There are several Monte Carlo tools for the air showers simulations. One of them is the shower generator CORSIKA [14]. It is used for all current IACT and was chosen for CTA. This code creates a detailed three-dimensional simulation of the showers induced by different primary particles. Hadron initiated showers are the most complicated because they require a correct description of the hadronic interaction [27]. The package ”IACT/ATMO” allows the Cherenkov light simulation for the chosen telescopes array. The Cherenkov photons are collected in each pre-defined place for the telescope position and serve for usage in the package for the telescope simulations (sim telarray). The detector simulation includes reflection of the photons by the mirrors into the PMTs, all electronics and the signal digitization. The NSB signals are simulated separately and added. The results of the simulations by the chosen packages are in good agreement with other codes [27].

23 2.3 Air shower reconstruction

The telescope dish reflects not only Cherenkov photons which are emitted by the air cascade. The light from the night sky constantly illuminates the camera and should be reduced. Also the gamma induced showers should be selected from the air showers induced by the charged particles. Due to the randomly oriented magnetic field in the Galaxy the cosmic rays are deflected and does not point exactly to their sources. They are background for the gamma-ray astrophysics. The efficient background rejection and the correctness of the event reconstruction are the keys to accuracy for the astrophysical studies.

Trigger The image of the shower looks like a compact object in contrast to the night sky background (NSB) which has a lot of ﬂuctuation. The trigger system selects a potentially useful shower event among the NSB. The trigger consist of two parts [28]:

• a local trigger works for the individual telescope. It searches for compact groups of the pixels i.e. several connected pixels with the signals above some threshold (a few photoelectrons) within a short time window. Usually, the groups of three or four neighbour pixels are used. They are called 3 nn (next neighbour) or 4 nn triggers.

• a central trigger gets a signal from each telescope, analyze it and searches for coincidences. If two or more telescopes were triggered, i.e. the stereo reconstruction is possible, such event is recorded by the data acquisition system.

Image cleaning The trigger logic only selects events which could be air showers. The image cleaning separates shower images from the ambient background. The shower image consists of two parts: core and boundary pixels. The core is the central part of the image. It is a compact group of the channels with large photon densities. The boundary pixels are the part of the image around the core. It consists of the pixels with smaller number of detected photons. Usually two level image cleaning is used [29]. At the ﬁrst level the core of the image is sought. It should consists of several connected pixels with a signal level larger than the core-threshold qcore. The task for the second level is to ﬁnd the bound. It should consist of the pixels connected to the core with a signal level higher then the bound-threshold qbound (qbound < qcore). The pixels, which are connected to the previous layer of the boundary pixels and satisfy the condition, are also considered as the boundary pixels.

24 Hillas parameters For the reconstruction and the analysis it is convenient to parametrize the shower image. The images of the gamma ray showers are very close to the elliptical shape. For this purpose second moments of the images are used. They are called Hillas parameters.

If ωi is a statistical weight of the i-th pixel, i.e. number of the photoelectrons in the pixel, and xi, yi are coordinates of this pixel, then the ﬁrst moments of the image are:

N N X X xiωi yiωi hxi = i=1 , hyi = i=1 . (14) N N X X ωi ωi i=1 i=1 The second moments are:

N N N X 2 X 2 X xi ωi yi ωi xiyiωi hx2i = i=1 , hy2i = i=1 , hxyi = i=1 . (15) N N N X X X ωi ωi ωi i=1 i=1 i=1 The standard deviations are:

var(x2) = hx2i − hxi2, var(y2) = hy2i − hyi2, (16) covar(xy) = hxyi − hxihyi.

The covariance matrix is:

! var(x2) covar(xy) M = . (17) covar(xy) var(y2) Using the covariance matrix in the diagonal form, the longitudinal (LENGTH) and the transverse (WIDTH) second moments of the image can be found (ﬁg. 23). Auxiliary variables for the ﬁnding parameters LENGTH and WIDTH:

d = var(y2) − var(x2), z = pd2 + 4covar2(xy), d u = 1 + , (18) z v = 2 − u, w = hxi2hy2i − 2hxihyi + hyi2hx2i.

25 Figure 23: Hillas parameters [30].

Then LENGTH and WIDTH:

LENGT H = pvar(x2) + var(y2) − z, (19) WIDTH = pvar(x2) + var(y2) + z, (20)

Other helpful Hillas parameters are:

DIST = p(hxi2 + hyi2), 2var(xy)hxihyi MISS = 0.5(uhxi2 + vhyi2) − , (21) z MISS ALP HA = arcsin , DIST N X SIZE = ωi. i=1

LEAKAGE parameter Cameras of the telescope have a finite size. For low and medium energies it is large enough, but the images from high energy showers often do not fit fully into the camera (especially for large impact parameters). Therefore the large part of the information about the shower will be lost and this will bring large errors to the event reconstruction. It is better not to take into account the images where a significant part is lost. Parameter

26 Figure 24: Shower reconstruction [32].

LEAKAGE determines usefulness of the image [31] and equals:

X qi LEAKAGE = border , (22) SIZE X where qi - total signal from the border pixels of the camera. Usually if LEAKAGE > 0.1 border then this image is not used.

Reconstruction of the shower core position If several images of the shower are available, a stereoscopic reconstruction of the event becomes possible. It is convenient to use a slanted coordinate system related to the ground, like it is shown in ﬁg. 24a. In this system a xy-plane coincides with the camera plane and a z-axis directed along the telescope axis. The point of the intersection of the shower axis and the xy-plane is a shower core position. It is one of the most important event parameters. The direction can be reconstructed ”in the camera”

27 Figure 25: Dependence of photon density as a function of distance to shower core for each primary energy. by the intersection of the image directions i.e. big axes of the ellipses which describe the shower images [32]. The schematic stereoscopic reconstruction is shown in fig. 24b. If there are more than two images, the directions of the ellipses intersect in a pair. And then the crossing should be averaged with the weights to one point. The weight depends on the size of the images, angle between them and elongation of the images (WIDTH/LENGTH). Thus big long images are more significant for the reconstruction. The shower core position ”on the ground” can be calculated analogically to the reconstruction ”in the camera” (fig. 24c). In this case, a continuation of the major axes of the ellipses should be crossed starting from the positions of the telescopes. Subsequent algorithm is similar.

Reconstruction of the primary energy The number of the Cherenkov photons that enter into the camera (and therefore the number of photoelectrons) depend on energy of the primary particle and the impact parameter of the telescope. Fig. 25 shows this relation. The xy-plane illustrates the photon density (size of image) as function of the distance to the shower axis. The primary energy (in logarithm) is represented by the different colors, i.e. one color in figure is one bin of the energy. For each energy in the figure curve of the shower light pool can be seen. Around the distances of 120 m there is typical break of the curve. The size of the image and the telescope impact parameter are enough for simple reconstruction

28 procedure. The energy can be reconstructed for each telescope and then averaged with the weights. The telescope weight can be chosen similar to the weights for the reconstruction of the shower core position. Usually the maximum of the height distribution is used for improving the accuracy of the energy reconstruction. The location of the shower maximum in the atmosphere fluctuates a lot. And the photon density at the ground level strongly depends on it. Usage of the shower maximum for the energy reconstruction makes corrections in relation to the image size fluctuations. The lookup tables are used for the reconstruction [29]. It contains mean values of the afore- mentioned parameters for the Monte Carlo simulations of the gamma rays. The lookup tables are built for the different zenith angles. Resulting energies for each telescope are estimated by the interpolation in the field of the several parameters and then averaged for all reconstructed telescopes.

Gamma-hadron separation The air showers induced by the cosmic rays are background for the Imaging Atmospheric Cherenkov Telescopes (IACTs). The quality of rejection of the background is one of the key aspects that determines the sensitivity of the IACTs. The diﬀerence between electromagnetic and hadronic showers were described in section 1.2. The values based on Hillas parameters are usually used for the separation. One of the separation parameters is a mean reduced scaled width (MRSW) [33]:

1 X MRSW = X · (SCWi · ωi), (23) ω i i∈Ntel i∈Ntel where SCW = (Wi −hWii)/σi is a scaled width for i telescope; hWii is the mean expected width for the gamma-ray (Monte Carlo simulations); Wi is a measured width; σi is a spread of the expected 2 2 width; ωi = hWii /σi is a weighting factor. Analogically a mean reduced scaled length (MRSL) can be calculated.

An important parameter is the maximum of the shower development Xmax. Due to different characteristic lengths before the interaction, the gamma induced and the hadron induced showers have different location of the first interaction points and the maximum of the shower. Also the hadronic showers have an irregular structure. Because of that, energy may be reconstructed dif- ferently for the telescopes on the different impact parameters. The parameter ∆E/E is calculated as the averaged spread in the reconstructed energy between the triggered telescopes and is used as another separation parameter. ∆E is an averaged absolute error of reconstructed energy. Com- parison of the separation parameters is shown in fig. 26. The distributions for the gamma induced showers are marked by the black color and the hadron inducer ones are marked by the red color. The distributions were built for the energy range 500 GeV - 1 TeV and zenith angles 15 - 25 deg.

29 Figure 26: Distribution of separation parameters, black color - gamma induced, red color - hadron induced showers [33].

30 3 γ-electron separation with telescope arrays

3.1 Hybrid array

First, the feasibility of the gamma-electron separation should be studied. The Hybrid array was introduced for such studies [34]. It consists of two types of telescopes, in total 61 telescopes: 25 of Davies-Cotton and 36 of Schwarzschild-Couder design. The telescopes are located within distances of 120 m from each other which corresponds to the light pool radius of air showers. The layout of the Hybrid array is depicted in ﬁg. 27.

Figure 27: Hybrid array layout. SC - Schwarzchild-Couder design, DC - Davies-Cotton design.

The air showers were simulated by the CORSIKA [14]. The gamma-rays were simulated from ◦ ◦ a point source located at the zenith angle θz = 20 and the azimuth angle θaz = 90 . Electron primaries are simulated with diffuse initial direction. To be closer to the ideal case, the telescopes were simulated with 50% quantum efficiency and the real response of the electronic was not simulated. It means that the half of all Cherenkov photons are reflected by the telescope dish and saved. For the feasibility tests the Night sky background (NSB) was not simulated as well. The Schwarzchild-Couder telescopes have a point spread function (PSF) three times better than the

31 telescopes of the Davies-Cotton design. This improves the accuracy of the event reconstruction and, as result, accuracy of the height distribution. As consequence, the separation parameters can be calculated with higher precision.

Event reconstruction All the procedures of the event reconstruction and analysis were performed by the scripts written in ROOT [35]. The telescope camera was not simulated, but was replaced by a the two dimensional histogram. The size of the histogram and its bins are comparable to the true angular size of the camera (8 deg) and the pixels (Davies-Cotton - 0.0283 deg2, Schwarzchild-Couder - 0.0044 deg2) respectively. Very low energy events and events simulated far from the telescopes array can not be reconstructed in reality. The next neighbour (3nn) trigger was used to reduce this type of events. The trigger threshold is assumed to be diﬀerent for diﬀerent mirror areas and pixel sizes of the telescope (i.e. bigger area collects more light). The thresholds are set:

trig sc = 5 [phot/pix], (24) trig dc = 8 [phot/pix].

The precision of the photon height calculation (and hence the possibility of the gamma-electron separation) depends on the quality of the event reconstruction. Therefore the image cleaning should be optimal. The two level image cleaning with dynamic thresholds was chosen. The threshold for the photon number in the pixel changes with Monte Carlo (MC) primary energy. A constant values for the cleaning threshold are not eﬀective for all events in the wide energy range. A soft threshold saves more and it is better to use it for reconstruction of the low-energy showers. But the high-energy events with big and bright image will be reconstructed worse. And conversely a hard threshold gives a good precision for the high-energy events, but it cuts a bigger part of the low-energy ones. The thresholds for the central parts of the shower images are:

E 0.76 core sc = 6 [phot/pix], (25) 100 E 0.76 core dc = 12 [phot/pix], 100 where E is the MC primary energy in GeV. The thresholds for the boundary part of the shower image are:

bound sc = 0.5core sc [phot/pix], (26) bound dc = 0.5core dc [phot/pix].

Fig. 28 illustrates the angular resolution of the Hybrid array. In the real situation good

32 0.2 SC 0.18 DC 0.16 full array 0.14

0.12

0.1

0.08 Angular resolution (68%) [deg] 0.06

0.04 0.02 0 1.5 2 2.5 3 3.5 4 4.5 log (Primary energy [GeV])

Figure 28: Angular resolution. Red points - resolution for full array, blue points - Davies-Cotton telescope design, green points - Schwarzchild-Couder telescope design. resolution is achieved through usage of the gamma-hadron separation. It cuts not only hadronic events but also a part of gammas, which were badly reconstructed. In our case these values of the angular resolution are result of the dynamic image cleaning which was optimally chosen for each energy. The deterioration of the resolution can happen for very bright events with large impact parameters. The part of the distant image can be lost due to limited size of the camera. A telescope catches only ”tail” of the image and it introduces errors into event reconstruction. To minimize this effect images with LEAKAGE > 0.1 were excluded from the subsequent reconstruction and the analysis. The efficiency is one of the important values for choosing the image cleaning parameters. It is calculated by taking the ratio between a number of the triggered and the reconstructed events. The efficiency of the current image cleaning is shown in fig. 29. Here, only results for the full array are shown. Similar figures for the Schwarzchild-Couder and the Davies-Cotton parts of the array are shown in Appendix B (fig. 39 and 40 respectively). The dependence of the image size on the energy and the impact parameter was used for the reconstruction of the shower energy (see section 2.3 for more details). The energy was defined for each telescope separately and then averaged with the weights:

s wtel = √ , (27) s + σ2 where s is sum of the charges of all pixels after the image cleaning, σ is uncertainty of the mean for energy in ﬁg. 25. The energy resolution deﬁned as 68% of average spread in the reconstructed

33 ×103 450

400 triggered

350 reconstructed

300

250

200

150

100

0 1 1.5 2 2.5 3 3.5 4 4.5 5 log (Primary energy [GeV])

0.8

0.7 Efficiency [%] 0.6

0.5

0.4

0.3

0.2

0.1

0 1 1.5 2 2.5 3 3.5 4 4.5 5 log (Primary energy [GeV])

Figure 29: Top: comparison of triggered (blue line) and reconstructed (green line) events; bottom: efficiency of the image cleaning for full array. energy and is shown in fig. 30. A comparison between the MC and the reconstructed energy can be found in Appendix B fig. 41.

Gamma-electron separation As it was mentioned in section 1.1, an electron primary cannot be vanished after the interaction with the nucleus in the atmosphere. It may emit more than one high energy photons before the

34 Figure 30: Energy resolution. energy losses become ionization-dominated. Therefore the electron induced showers have bigger number of the Cherenkov photons from the higher layers of the atmosphere. The main idea for the separation of the gamma from the electron initiated showers is based on this assumption. One of the possible parameters is the asymmetry A of the distribution of heights:

Nbins Nbins X X 2 Hiwi Hiwi i=1 i=1 A = hHiw − hHiw2 = − , (28) Nbins Nbins X X 2 wi wi i=1 i=1 where hHiw = Hmean is the mean of the distribution of heights (the maximum of the shower development), hHiw2 is the mean with square weights, wi is a number of photons from the same height Hi. A height of each photon can be found as:

I h = , (29) tan Θ where I is distance to the telescope, Θ is angular distance of the current photon. All calculations are held in the coordinate system related with the shower. The distribution of the heights was built using all photons in the camera plane (not after the image cleaning) to save more information about the development of the shower. Two cases were considered:

35 Figure 31: HYBRID array, green color indicate central part of array where core position should located in case ”cut array”.

• all reconstructed events participate in the separation;

• ”cut array” – only events with the shower-core position in the central part of the array. This region has a radius of 350 m and is marked green in ﬁg. 31. It allows to save more information about the shower and to increase the detecting possibility of the photon from the high layers of the atmosphere.

Fig. 32 illustrates the gamma-electron separation with usage of Cherenkov photons. Both cases are presented: all reconstructed events (at the left) and ”cut array” only (at the right). The x axis of the graph denotes a cut value of the asymmetry. A saved fractions of gamma and electron induced showers are marked by blue and red colors respectively. The quality of the separation is called quality factor and marked by the black curve. The quality factor is calculated:

s QF = √ , (30) b where s is the fraction of the gamma induced showers after the cut, b is the fraction of the electron induced ones. The maximum of the black curve shows the best cut-value. The value of the maximum bigger than one means a reasonable separation and an improvement of the sensitivity.

36 Figure 32: Separation with photons. Left image - all events, right image - ”cut array”.

Figure 33: Separation with a pixelated camera. Left image - all events, right image - ”cut array”.

A real camera has pixels and can not accurately register the location of each photon. Analogi- cally to the case with the Cherenkov photons, studies of the separation with the pixelated camera were done. The image cleaning which was used for the reconstruction of the event has a high threshold values. The thresholds which were used for the separation:

core sc = 4, bound sc = 2 [phot/pix], (31) core dc = 6, bound dc = 3 [phot/pix].

37 A number of the high altitude photons is small and they trigger only one or few pixels and there is a lot of light from the maximum of the shower. The high altitude pixels play a negligible role in the distribution of heights in comparison with the shower maximum. To avoid this the pixels content was not used for building of the height distributions for the following results with pixelated camera. Pixels worked in regime ”yes/no”. If pixel collect some number of photons (does not matter how much) it participate in distribution of heights with weight one. It makes high altitude pixels more significant for the asymmetry calculation. The results of the gamma- electron separation with the pixalated camera are shown in fig. 33. The left hand side corresponds to the case with all reconstructed events and the right hand side shows the ”cut array” case. The high quantum efficiency and the high quality of the shower reconstruction leads to a good separation even with the pixelated camera.

38 3.2 The Cherenkov Telescope Array

The Cherenkov telescope array (CTA) will be a new generation of the Cherenkov instruments. This experiment is still under the development and currently several possible layouts of the CTA are discussed. For tests of the gamma-electron separation the ”array E” layout was chosen [27]. It is shown in ﬁg. 34. The array consists of 4 large (LST - red color), 23 middle (MST - blue color) and 32 small size telescopes (SST - green).

Figure 34: One of candidate conﬁgurations — array E.

The array E was simulated under real conditions: with the NSB, the quantum eﬃciency, the realistic camera with the photoelectrons. The standard analysis procedures were applied for the event reconstruction (see in section 2.3). The analysis was performed with the Eventdisplay (special

39 Figure 35: Separation results for the CTA candidate array E. Left - standard image cleaning, right - improved image cleaning. software package for the analysis of the data from the Cherenkov telescopes) [36]. Usually the standard two level image cleaning is used for the background rejection. The standard method reduce faint part of the image together with background using only pixels content. Increase of the information amount about the showers leads to improvement of gamma-electron separation. The improved image cleaning method was used for this purpose [37]. It uses the photon arrival time for the separation of a useful signal from the NSB light. It allows to save parts of the image with low content which is comparable with the NSB fluctuations and would be cut by the standard image cleaning. It is very important to catch as more high altitude photons as possible. But it is difficult with the smallest telescopes of the array. SSTs have small dish and a big distance between each other. Thus the condition for the separation in the case of the ”realistic simulations” is presence of the shower image in more than 2 MSTs. The meaning of this condition is similar to the case of ”cut array” for the Hybrid array. As for the Hybrid array, gamma-rays were simulated from point source and the electron- primaries are diffuse. It leads to the restriction of the shower direction, which should be within the radius 3◦ from the camera center. A lack of statistics does not allow to make this camera-cut smaller. In figure 35 the results of the gamma-electron separation are shown for the standard (left) and the improved (right) image cleaning methods. There are no explicit maximum of the quality factor for the both variants of the image cleaning. It means that there is no reasonable separation and, as result, no improvement of the instrument sensitivity for the current technical characteristics. The

40 fraction of the saved electrons and gammas are almost coincide for the standard image cleaning. It means, that there are no clues of the separation. However the improved image cleaning suits better for the purpose. It allows to keep around 10-20% more gamma showers then electron induced ones. The current quantum efficiency of the Cherenkov telescopes is low and does not allow to achieve a reasonable gamma-electron separation with the asymmetry of the height distribution. But telescopes quantum efficiency can be increased by further development of the technologies. The second version of the CTA layouts Prod2 is under development. The telescopes have higher quantum efficiency in new simulations. In fig. 16 (section 2.2) there is the comparison between the quantum efficiency of Prod1 (same as HESS quantum efficiency) and of Prod2 simulations. Increased telescopes quantum efficiency would allow to improve the gamma-electron separation.

41 Summary

The sensitivity is one of the most important characteristics of Cherenkov telescopes. It determines the brightness of the source, which can be detected by the experiment. Only the brightest objects can be studied with current Cherenkov systems. In the middle energy range sensitivity is limited mainly by the proton background rate. A rejection of the hadron events lead to improvement of the sensitivity. Present methods of the gamma-hadron separation and large effective area of future arrays of the Cherenkov telescopes will allow to reduce the proton background as well. As result, electron induced showers become to constitute a significant part of the full background rate. A rejection of the electron induced showers is a key for further improvement of the sensitivity of the Cherenkove telescope arrays. But they are very similar to the gamma induced ones. Both primaries produce electromagnetic cascades which can not be separated by the image shape like it is done with the hadronic cascades. The main difference between gammas and electrons is their interaction with nucleus in the atmosphere. A primary gamma creates electron-positron pair in field of the nucleus. Whereas an electron primary emits a high energy photon and continues its passage through the atmosphere. An electron primary may emit a few high energy photons before its ionisation losses become dominant. It leads to a higher number of the Cherenkov photons from the high altitudes in case of the electron induced shower. The feasibility of gamma-electron separation with large arrays of the Cherenkov telescopes was studied in this work. The asymmetry of the distribution of heights of Cherenkov photons was chosen as a parameter for the gamma-electron separation. The asymmetry is bigger if the shower has an more photons from high altitudes. First, the feasibility of the separation was tested in almost the ideal case. For this purpose the Hybrid array was used. It was simulated without night sky background and with a high quantum efficiency. 50% of the photons reflected by the telescope dish were saved in the focal plane of the telescopes. This allows to study the gamma-electron separation using each photon location with and the pixelated camera. The feasibility of the separation was tested with all reconstructed showers and with usage of the showers which hit the ground in the region within 350 m radius from the array center. Both case shows the reasonable results of the separation with usage of true photon coordinates and with pixelated camera. The following step was to test the separation in the realistic conditions. The simulation of array E was used for this purpose. It is one of the possible candidates for the CTA. The realistic quantum efficiency and the night sky background were simulated in this case. The separation was compared for standard and improved methods of the image cleaning. The improved image cleaning showed better separation results is not sufficient for the improvement of the array sensitivity. Nevertheless the described methods have a perspective. The technological progress does not

42 stand still and there are possibilities to increase the quantum eﬃciency of the telescopes. This would allow to improve the gamma-electron separation. As a result, the sensitivity of the future instruments could be improved with the rejection of part of the electron background. The gamma-electron separation has another application in the future telescopes arrays.It would make possible the studies of the cosmic electron spectrum with improved accuracy. However, this is out of the scope of this study and required an additional investigation.

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46 Appendix A

Figure 36: Top: Prod1 layout of the CTA. Red color - 24 m telescopes, black and green - 12 m, pink - 10 m, blue - 7 m. Bottom: three candidate conﬁgurations (B, C and E array).

47 Figure 37: Prod2 layout of the CTA.

48 Figure 38: Possible designs of the telescopes: top - parabolic, bottom left - Davies-Cotton and bottom right - Schwarzschild-Couder layout.

49 Appendix B

×103 220 triggered 200 180 reconstructed 160 140 120 100 80 60 40 20 0 1 1.5 2 2.5 3 3.5 4 4.5 5 log (Primary energy [GeV])

0.8

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Figure 39: Top: comparison of triggered (blue line) and reconstructed (green line) events; bottom: eﬃciency of the image cleaning only for Schwarzchild-Couder design telescopes.

50 ×103

300 triggered reconstructed 250

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Figure 40: Top: comparison of triggered (blue line) and reconstructed (green line) events; bottom: eﬃciency of the image cleaning only for Davies-Cotton design telescopes.

51 Figure 41: Comparison of MC and reconstructed energy.