CC BY
32
UDK 537.591.15
F.A. Aharonian, A. V. Plyasheshnikov
Project of 5@5 Array of Imaging Atmospheric Cherenkov Telescopes: New Calculational Results
The performance is discussed of a powerful! future ground-based astronomical instrument, 5@5 — a 5 GeV energy threshold stereoscopic array of several large imaging atmospheric Cherenkov telescopes (lACTs) installed at a very high mountain elevation of about 5 km a.s.l. — for the study of the 7-ray sky at energies from approximately 5 to 100 GeV, where the capabilities of both the current space-based and ground-based 7-ray projects are quite limited.
In this article we analyse detailly such problems as the optimization of the field of view and the pixel size of the multichannel camera, optimization of the angular and energy resolution of the array, the detection rates of the array and influence on them of the geomagnetic cut-off, efficiency of discrirnanation of the cosmic ray background, the 7-ray flux sensitivity of the array. Beside that we discuss main aspects of the possible exploitation of this array at the HESS 1ACT array site in Namibia.
1. Introduction
In [1] (hereafter the basic article) the concept and the performance are discussed of a powerful future ground-based astronomical instrument, 5@5 — a 5 GeV energy threshold stereoscopic array of several large imaging atmospheric Cherenkov telescopes (lACTs) installed at a very high mountain elevation of about 5 km a.s.l. — for the study of the 7-ray sky at energies from approximately 5 to 100 GeV, where the capabilities of both the current space-based and ground-based 7-ray projects are quite limited. Providing a very high detection rate of 7-ray induced events such a detector could serve as an ideal "7-ray timing explorer" for the study of transient non-thermal phenomena like 7-radiat ion from AGN jets, synchrotron flares of microquasars, the high energy (GeV) counterparts of 7-ray bursts, etc. The 5@5 array also would allow detailed 7-ray spectroscopy of persistant nonthermal sources like pulsars, supernovae remnants, plerions, radiogalaxies, and others, with unprecedented for 7-ray astronomy photon statistics.
In this article we undertake an additional analysis of the 5@5 IACT array properties. We consider here problems not studied detailly in the basic paper, such as the optimization of the field of view and the pixel size of the IACT multchannel camera, optimization of the angular and energy resolutions of the array, influence of the geomagnetic cut-off and the trigger integration time gate on the basic array characteristics, etc.
2. About Simulations
IACT Array Layout and Location Site. Simulations presented here correspond to a system of 5 lACTs located at the corners and at the centre of
a square with the side length 1=100 m.
We perform our simulations for the observation altitude equal to 5 km above sea level and for geographical coordinates (23° S; 67° W) corresponding to a site chosen recently for the installation of a powerful future astronomical instrument ALMA — the Atacama Large Millimeter Array of radio antennas — being developed by the US-European astrophysical community.
IACT Configuration, It is assumed that each IACT of the array is equipped by a parabolic optical reflector focuced at infinity and having the total mirror square S equal to 600 m2. We neglect the optical abberations of the reflector and use the data of the HESS collaboration to describe the mirror reflectivity, the PMT quantum efficiency and the funnel angular response. The latter provides the photoelectron/photon conversion factor / ~ 0.11 for the wavelength region (0.28,0.60) mkm.
The main part of simulations has been carried out for a multichannel camera (MC) consisting of 631 pixels with the pixel angular size 0.12° (hereafter the basic MC configuration). Such a camera has an effective field of view ~ 3.2°. In calculations related to the optimization of MC parameters (see Sections 3 and 4) we use, besides that, a set of MC configurations with different values of the pixel size (PS) and field of view (FoV). The main parameters of these configurations are listed in Tab.l,
Integration Gate. The main part of our simulations has been performed for the trigger integration time gate r = 5 ns. Some simulations (see Section tl) have also been carried out for r =10 and 20 ns. Everywhere we assume (in accordance with the basic article) a "standard value" of the
Table 1
Configurations of the multichannel camera considered in the analysis.
NN PS, Pixel number, Effective FoV, Tail cuts, çomi:
degree inner/total degree tli/tli, ph.e. ph.e.
1 0.08 919/1387 3.13 5/7 5
2 0.10 547/817 3.00 6/9 7
3 0.12 469/631 3.16 8/10 9
4 0.15 271/397 3.14 11/13 11
4' 0.15 2107/2611 8.04 11/13 12
5 0.20 127/217 3.09 13/16 15
night sky background (NSB) flux: FNSB ^ 1-5-1012 phot/m2/sr/s. We count the arrival time of photons from the moment of registration by the camera PMTs of the first photoelectron (independently for each triggered IACT),
Selection of Events. The IACT array is supposed to be triggered if the number of triggered telescopes is greater or equal to 2. The following condition is used to simulate the hardware trigger of an individual telescope: 2nn/N > qo - at least two adjacent pixel magnitudes of the camera should exceed a given value <}o; N is the total number of pixels. The minimum available value of the parameter qo is determined by the NSB contribution to one pixel and by the total number of pixels'. For example, for a simultaneous trigger of at least two telescopes and the basic MC configuration we have tfomin ph.e.
It is requested that the image centroid of registered images belongs to a central part of the camera with FoV by as much as ~ 0.5° smaller than the total field of view (469 central pixels for the basic MC configuration). This selection criterion is goaled at the reduction of the image distortion due to the finiteness of the MC FoV.
To provide an acceptably good quality of 7-ray induced images we apply a set of additional selection criteria similar to those used by the HEGRA collaboration. In particular, we remove air showers with reconstructed cores located farther than a given distance Rq from the IACT array centre (as a rule R0 =200 m). Triggered IACTs with reconstructed impact parameters larger than Rq are also excluded from the consideration. Besides that we remove from the analysis images having the size smaller than a fixed value Sq (usually S0 =30 ph.e.).
'The value <jomin should provide the NSB trigger rate negle-giably small compared to the cosmic ray detection rate.
Tail cuts. A traditional second-moment approach is applied to evaluate parameters of the Cherenkov light image. To diminish the influence of the night sky light on image parameters we exclude from the consideration small pixel magnitudes. A two level tail cut technique (tli/th) similar to that used by the HEGRA collaboration is applied for this purpose. We choose the lower tail cut as a minimum integer number allowing to provide a reliable regection of "noisy" pixels (usually at ~99% level). A choice of the upper tail cut is related closely to the optimization of the IACT array angular resolution. It will be discussed in Section 4.
Simulation Codes. The main part of simulations has been performed with the help of the ALTAI simulation code [2]. Besides that some simulations have been made by means of the CORSIKA code (version 6.019) [3]. The Madrid version of the CORSIKA Cherenkov light option is used. To simulate hadron interactions with CORSIKA we use the HDPM option in the high energy region (Slab > 80 GeV) and the GHEISHA option in the low energy region (£tab < 80 GeV).
Primary particle flux. To calculate the rate of air showers registered by an IACT array one needs an input on the energy spectra and the mass composition of primary particles. For 7-rays we usually assume a power low energy spectrum
^ = F0E~a* (1)
dE
or a power law spectrum with the exponential cut-off
^l = F()E-2exp(-E/Ec) (2)
ah
with the flux normalized at 3-10~~3phot/m2/s above 1 GeV. Usually a7 =2.5 in formula (1).
To describe the energy dependence of the CR electron flux (measured in m~2 s-1 sr"1 GeV-1)
Table 2
The contribution of different CR nucleus groups to the all-particle flux.
Nucleus group P a LM HVH
Atomic number range 1 4 5-20 21-56
Proportion in the CR flux_0.41 0.27 0.12 0.20
we use the following formula from the basic article [1):
^^lS.e-iTMl + tiJ/SGeV)2-2]-1 (3)
For CR particles we assume for simplicity that all nucleus groups give an energy-independent contribution to the all-particle CR flux
dFcR/dE = 0.25 • £T2-7(ssr m2 TeV)~l (4)
The data on this contribution are presented in Tab.2. Each value given in the table is the proportion of the respective nucleus group in the all-particle flux.
In our study we consider the IACT detection rates corresponding to four groups of CR primary particles — protons, a-particles, 'low+medium' (LM) and 'heavy+very heavy' (HVH) nuclei. For LM and HVH groups we assume for simplicity that all air showers of these groups are induced by nuclei with the same value of the atomic number (oxygen and iron nuclei, respectively).
3. Field of View
We define the optimum field of view of the multichannel camera as a minimum FoV providing a sufficiently large detection area for 7-ray induced air showers and a reasonably small distortion of images due to the FoV finiteness. In Fig.l — 3 we present the calculational results allowing to estimate the value of the optimum FoV. In particular, in Fig.l we show the radial distributions of the Cherenkov light, whereas in Fig.2 and 3 we demonstrate the radial dependence of some image parameters for the case of a point 7-ray source. These are the DIST parameter defining the location of image centroide and the basic shape parameters — WIDTH and LENGTH. The MC configuration with a very wide FoV is considered here (see Tab.l) to avoide a distortion of images.
In the energy region near the IACT energy threshold only air showers are registered which have the core location presumably within the Cherenkov light pool, i.e. showers with R < 100 m. Image centroids of such showers (see Fig.2) are located in the central part of the camera with FoV~ 1.5°. To avoide the distortion of images
located at the edge of the camera, one should increase the FoV by as much as the double angular size of the image (i.e. by ~ 0.5° according to Fig.3). So, near the energy threshold the optimum FoV of the camera is ~ 2°.
I02
E
c/:
C
O
O
■C
o_
10
fl£
Cl
1
10
0 50 100 150 200 250 300 350 400 450
R, m
Figure 1. Radial distributions of the Cherenkov light for vertical air showers. Different values of the energy of primary 7-rays are considered (indicated at the curves). Habs = 5 km a.s.l.
u 1.6
u
u.
OO
■S 1.4 f—
£2 1.2
1
0.8 0.6 0.4 0.2 0
0 50 100 150 200 250 300 350
R, m
Figure 2. The radial dependence of the mean value of DIST for different values of the energy of primary 7-rays (indicated at the curves). The MC configuration number 4' is considered (see Tab.l).
85 0 2
on 0.18 v
0.16
H 0.14 Q
g 0.12 * 0.1 0.08 0.06 0.04 0.02 0
85 GeV
85 GeV
a o.M 00
•g 0.32
X (1.3 f-
O 0.28 z
03 0.26 0.24 0.22 0.2 0.18 0.16
Figure 3. The radial dependence of the mean values of WIDTH (left) and LENGTH (right) for different values of the energy of primary 7-rays (indicated at the curves). The MC configuration number 4' is considered (see Tab.l).
In the high energy region (Ey ~ 100 GeV) air showers with larger impact parameters can be registered. Assuming a reasonably good quality of registered images (e.g. Size> 100 ph.e.) one can find out from Fig.l that in the enegry region near 100 GeV impact parameters of registered air showers can reach a few hundred meters. For such showers we have the following estimate of an optimum field of view: FoVopt ~ 2-(1.5°+0.2°) ~ 3.5°.
Thus, for a practically interesting energy interval E-f < 100 GeV and for point 7-ray sources the optimum FoV of the 5@5 array cameras does not exceed ~ 3.5°. For extended 7-ray sources an estimate of the optimum FoV is somewhat larger (< 4 — 4.5°).
4. Pixel Size and Angular Resolution
The distortion of an image parameter due to a finiteness of the pixel size (PS) depends essentially on its nature. In particular, the orientation angle ALPHA is more sensitive to the PS variation than the basic shape parameters WIDTH and LENGTH (see e.g. [4]). In this relation1, we define the optimum value of the pixel size as a maximum PS providing an acceptably good angular resolution of the IACT array.
It should be noted that a technique described in [5] is used by us to reconstruct the air shower arrival direction. We define the angular resolution (50) by the following way: for a certain percentage of registered air showers (usually 50% or 67%) the angle between the real and reconstructed shower arrival directions should be smaller than 80.
In Fig. 4 we present the energy dependence of the angular resolution 59 of the 5@5 IACT array. Calculational results presented in this figure correspond to the mentioned above two level tail cut
'Keeping in mind that the arrival direction of an air shower is reconstructed on the basis of the orientation o( images.
technique (tli/th) and illustrate dependence of 50 on the value of the upper tail cut {tli)2- It is seen that the angular resulution is rather sensitive to the t/2 value. To provide a good angular resolution one should keep £/2 > 10 ph.e. This feature of the angular resolution can be explained by the following way.
Er GeV
Figure 4. The energy dependence of the angular resolution of the 5@5 IACT array. The basic MC configuration is considered for different tail cut combinations (indicated at the curves in ph.e.). So =30 ph.e.; q0=12 ph.e.; R0 =200 m; ©0 = 30°.
The two level tail cut technique used here assumes that all MC pixels having magnitudes M > £/2 are involved in the evaluation of image parameters. Therefore, if tl2 is not high enough, some standing alone "noisy" pixels are included in the analysis. Such pixels (due to the usage of the second moment approach to the image parameters evaluation) can affect seriously the image parameters (among them the orientation angle APLHA). As a result the angular resolution becomes worser. So, an optimum value of i/2 should provide a reliable suppression of standing alone "noisy" pixels.
2A "standard" value providing a reliable rejection of "noisy" pixels is choosen for the lower cut (t/i =8 ph.e.).
Simple calculations based on the Poissonian statistics show that for t/2 = 10 ph.e. (providing in accordance with Fig.4 an angular resolution nearly un-influenced by the NSB) no more than a few per cent of registered images have standing alone "noisy" pixels.
Calculational results presented in Fig.5 demonstrate another way of improving the angular resolution. This figure corresponds to the following conditions. Reconstructing the arrival direction of air showers we remove image pairs having the angle (©) between the major axes smaller than a fixed value ©o. It is seen that an exclusion of intersection angles © < 30° improves considerably the angular resolution. At the same time, the selection criterion 0 > 30° does not reduce seriously the 1ACT array detection rate (see Tab.3).
Er GeV
Figure 5. The energy dependence of the angular resolution of the 5@5 IACT array for different cuts applied to the image axis intersection angle (© > ©o). The values of ©o are indicated at the curves. The basic MC configuration is considered. So =30 ph.e.; tail cuts: 8/10 ph.e.; R0 =200 m; <jo = 10 ph.e.
Table 3
The ratio of differential detection rates of 7-ray induced air showers calculated with and without usage of selection criterion 0 > B0. The basic MC configuration is considered.
Ey, GeV 3 5 10 20 30 100
©o e0 = 30° = 45° 0.88 0.74 0.90 0.78 0.92 0.82 0.93 0.83 0.94 0.84 0.94 0.84
In Fig.6 we also present the energy dependence of the angular resolution of the 5@5 array. Calculational results of this figure correspond to 5 different configurations of the multichannel camera (they are listed in Tab.l) having the FoV close to the optimum one and the pixel size within 0.08 - 0.20°. For each configuration we use a
"standard" value of the lower tail cut (see the footnote number 3) and the value of the upper tail cut providing a reliable suppression of standing alone "noisy" pixels. To reduce an influence of the hardware triggering (2nn/N > qo\ it also depends considerably on the pixel size) we exclude from the analysis images of small size (< 70 ph.e.).
67% event acceptance
0.20'
r o.oá^^s: 0.15"
: i iiii U u - ---- 0.10* i l i i i 1 1 l
10
Er GeV
Figure 6. The energy dependence of the angular resolution of the 5@5 IACT array for MC with different pixel size (indicated at the curves), go — th\ So = 70 ph.e.; R0 =200 m; ©0 = 30°.
It is seen from Fig.6 that a reduction of the pixel size leads to a rapid improvement of the angular resolution. At the same time, for PS< 0.15° the angular resolution becomes insensitive (within the statistical and systematic errors of our calculations1) to the PS value. So, from the point of view of the angular resolution PS~ 0.15° can be considered as an optimum value of the MC pixel size. However, according to recommendations of the basic article [1] one should keep PS « 0.1° to provide an effective suppression of the NSB (by using a "multiple" hardware triggering m/N > qo with m > 2). That is why we use for the basic MC configuration the value of the pixel size equal to 0.12°.
Calculational results of Fig.7 also present the energy dependence of 89 for the basic MC configuration. These results illustrate the variation of the angular resolution with the So parameter. Is is easy to understand from the figure that using a dynamic cut SIZE > So in which the parameter So increases with the air shower energy one could have the angular resolution compared to that received in the basic article (see the dashed curve at the bottom panel of Fig.7).
In Fig.8 we compare different strategies of the angular resolution optimization. The angular resolution calculated under standard conditions (curve 1) is compared here with results of two other
'For example, the difference between results on 66 received with the help of ALTAI and CORS1KA codes can reach 15-20%.
Figure 7. The energy dependence of the angular resolution of the 5@5 IACT array for 50% level (left panel) and 67% level (right panel) of the event acceptance and different values of the So parameter (indicated at the curves). The basic MC configuration is considered. Vertical arrows indicate the efffective energy threshold of the array. Solid curves — our calculations; dashed curve — results of the basic article [1]. q0 =10 ph.e.; R0 =200 m; 0O = 30°; tail cuts; 8/10 ph.e.
Figure 8. The energy dependence of the angular resolution of the 5@5 IACT array. The basic MC configuration is considered. Curve 1 — standard calculation conditions: tl\ -- th — Qo =10 ph.e.; Ro =200 m; S0 =30 ph.e.; ©0 = 30°. Curves 2,3 - images with SIZE/SIZEmax < d0 are removed; do =0.15 (2); do =0.30 (3). Curve 4 — do =0.30; an additional dynamic tail cut is used: tla = ro-Mmax > Qo, where Mmax is the maximum pixel magnitude, r0=0.!5.
approaches. First of them (see curves 2 and 3) consists in removing from the consideration images of small size (SlZE/SIZEmax < d0, where SIZEmixx is the size of the most intensive image); in the second one (curve 4) an additional dynamic tail cut proportional to the maximum pixel magnitude is applied to the registered images. It is seen that both approashes are effective in the energy region above >15-20 GeV. Particularly, near the primary energy value Ey =100 GeV a simultaneous application of these approashes provides 89 ss 0.05° and 0.1° for 50% and 67% levels of the event acceptance, respectively. This agrees with predictions of paper [5] for IACT arrays with an effective energy threshold ~100 GeV. At low energies (<15-20 GeV) the angular resolution with difficulties gives way to its optimization. Here it has a magnitude ~ 0.2° for the 50% level of the event acceptance and ~ 0.3 - 0.4° for the 67% level.
Table 4
The ratio of differentia! detection rates corresponding to different values of parameter d0. See for an explanation the caption of Fig.8.
~T~tGeV r0"T0~T2.5"~25 60~T25~ i?(0.15)/i?(0) 1.00 1.00 0.99 0.97 0.90 0.81 fl(0.30)/.R(0) 0.99 0.97 0.95 0.88 0.77 0.65
5. Energy Resolution
Reconstructing the primary energy of 7-ray induced air showers we use the image size (for a known distance between the IACT and the air shower core location) as a measure of this energy. We calculate a general estimate of the primary energy averaging energy estimates received for individual IACTs triggered by a given air shower.
We define the energy resolution (5E) by the following way: for a certain percentage of registered
air showers (50% or 67%) the absolute value of difference between the real and reconstructed energy values should be smaller than 5E.
Some calculational results related to the energy resolution are presented in Fig.9-12. Particularly, in Fig.9 we present results on a basic parameter defining the accuracy of the energy reconstruction — the fluctuations in the total number of photoelec-trons constituting a 7-ray induced image. It is seen that in the primary energy region considered here the Cherenkov light fluctuations are much larger compared to the TeV energy region. However these fluctuations decrease rapidly with the primary energy. The minimum of fluctuations is located near the region of impact parameter values R ~150 m. This minimum ranges within ~ 25 - 120%.
•j1 c o
e5 3
t> 3
50 45 40
35 :
30 ;
25 ; 20
15 >
10 i
5 i
0 !
50-
67%
Er GeV
100 125 150 175 200 225
R, m
Figure 9. The fluctuations in the total number of photoelectrons of the image as a function of the shower impact parameter for FoV=oo and different energies of the primary 7-ray (indicated at the curves). No cuts on pixel magnitudes have been applied. The NSB contribution has been neglected.
In Fig.10 we present calculational results on another basic parameter affecting the energy resolution. This is the statistical error (8R) of reconstruction of the air shower core location. Besides the results obtained with the help of a traditional algorithm of the core reconstruction (see e.g. (5)) we give here results received by means of a special reconstruction algorithm valid for point 7-ray sources [6]. It is seen that the usage of a special algorithm gives a possibility to reduce considerably the core location error. However, even in this case the error is much larger than that in the TeV region1.
In Fig.11 we present examples of the probability distributions of the reconstructed 7-ray energy. It is seen that these distributions are rather broad and have a long tail towards large values of the reconstructed energy.
Figure 10. The air shower core location error (one projection) via the energy of primary 7-ray. The 50% and 67% levels of the event acception are presented. Solid curves — the traditional algorithm of the core reconstruction; dashed curves — a special reconstruction algorithm valid only for point 7-ray sources. The basic MC configuration is considered. th/tl2 =8/10 ph.e.; 50 =30 ph.e.; q0 =10 ph.e.
In Fig.12 we demonstrate possibilities of ap-proashes aimed at the optimisation of the energy resolution. These are: curve I — a traditional approach described in [5]; curve 2 — an improved approach (6] with usage of the reconstructed value of #max2; curve 3 - conditions of curve 2, but a special algorithm of the core reconstruction valid for point 7-ray sources is considered; curve 4,5 -conditions of curve 1 + removement of small size images.
It is seen from Fig.12 that neither the usage of
2WmM is the altitude at which the maximum amount of the Cherenkov light is emitted.
'Near I TeV calculations of |5j give for SR the value ~ 3 m at 67% of the event acceptance for an arbitraty 7-ray source.
Figure 11. Probability distributions of the reconstructed 7-ray energy for two different primary energy intervals (indicated at the figure). The basic MC configuration is considered. The energy reconstruction technique for an arbitrary 7-ray source with the usage of information on Hmax is applied. th/th =8/10 ph.e.; Rq =200 rn; S0 =30 ph.e.; q0 =10 ph.e.
Figure 12. The energy resolution of the 5@5 1ACT array for different approaches to the 7-ray energy reconstruction. The basic MC configuration is considered. Rq =200 m; <?o =10 ph.e. So=50 ph.e. (curves 1,2,3); 300 ph.e. (curve 4); 500 ph.e. (curve 5). Curves 1,4,5 — traditional approach for an arbitrary 7-ray source; curve 2 — conditions of curve 1 + the usage of information on Hmax; curve 3 - conditions of curve 2, however a special algorithm of the core reconstruction valid for point 7-ray sources is applied. Arrows indicate the effective energy threshold of the IACT array.
Hmax no reduction of the core location error due to the algorithm [6] provide dramatic improvement of the energy resolution. At the same time, remove-ment of small size images considerably improves the energy resolution providing in the energy region near 100 GeV results comparable with predictions of [5]. However, the latter approach increases essentially the energy threshold of the IACT array. Thus, at low energies the approaches considered here can not provide the energy resolution better than ~ 40% at 50% level of event acceptance and ~ 50% at 67% acceptance level.
6. Detection Rates
In Fig.13 we present the energy dependence of the portion ol air showers registered by the 5@5 IACT array and having real cores inside a circle of a given radius R centered at the central telescope of the array. Different values of R are considered for 7-ray and proton induced showers, It is seen that in the primary energy region 5-100 GeV, interesting for us, an overwhelming majority of registered 7-showers has cores located within ~250 m from the centre of the array. For primary protons the core distribution is somewhat broader; in this case the shower cores are concentrated within R ~500 m.
In Fig.14 we present differential detection rates of air showers registered by the 5@5 IACT array. The following primary particles are considered — 7-rays from a point source with a power-law energy spectrum; CR electrons with an isotropical angular distribution; different isotropically distributed primary nuclei. Two different computational codes (ALTAI and CORSIKA) have been applied to obtain these results. In Tab.5 we give the values of the efffective energy threshold of the 5@5 array
for different primary particles. In Tab.6 the relative contributions of different nucleus groups to the CR total detection rate of the array are presented. The following conclusions can be reached from the
■uvi
Figure 13. The energy dependence of the portion of 7-ray (upper panel) and proton (lower panel) induced air showers registered by the 5at5 IACT array and having location of the real core inside a circle of radius R. Different values of R (indicated at the curves in m) and the basic MC configuration are considered. Rma.x=600 m; So =0 ph.e.; <jo =10 ph.e.
Table 5
The effective energy threshold of the 5@5 IACT array for vertical air showers created by different primary particles. The basic MC configuration is considered. S0=30 ph.e.; /îo=200 m;
<7o = 10 ph.e.
Primary particle 7 e P_a__0_Fe
~Et h, GeV ~5 ~4Ô ~ 150 -500 ~ 2000
Table 6
The contribution of different CR nucleus groups to the CR detection rate of the 5@5 IACT array. The basic MC configuration is considered. So=30 ph.e.; Ro=200 m; q0 = 10 ph.e.
CR nucleus group P a LM HVH
Atomic number range 1 4 5-20 21-56
Proportion in the detection rate 0.81 0.17 0.016 0.004
figure and tables.
> 10 2 u £ jg 10
e
r
0 e 1 y
0
8 10 r
O .2 10 r
10 _
E, GeV
Figure 14. The differential detection rates for vertical air showers created by different primary particles. Basic MC configuration is considered. So = 30 ph.e.; R0 =200 m; q0 = 10 ph.e.; a7=2.5. Solid curves — simulations with ALTAI; dashed curves — simulations with CORS1KA.
• Despite of usage of additional cuts providing a better quality of images (cuts on Ro and So parameters) the effective energy threshold of the array is located near 5 GeV for 7-ray induced air showers.
• According to both computational codes (ALTAI and CORSIKA) the energy threshod (£th) of the array is ~ 40 GeV for the primary proton. This contradicts strongly the results of the basic article [1] where a much larger value has been received for this quantity (~200 GeV).
• Only a modest sensitivity of calculational results to the hadron interaction model is observed.
• The energy threshold Eth increases rapidly with the atomic number (A) of registered CR
nuclei. Roughly, Eth is proportional to A. In the TeV energy region dependence E^{A) is essentially weaker (~ A1/2 according to [7)).
• An overwhelming majority of CR nuclei detected by the 5@5 IACT array are protons (81% according to Tab.6) and a-particles (17%). The contribution of L.M nuclei to the total detection rate is only ~ 2%; for HVH nuclei this contribution is about 0.5%. All this is a direct consequence of a rapid growth of Eth with A,
7. Geomagnetic Cut-off
The theory of the motion of cosmic ray particles in the geomagnetic field (see e.g. [8]) leads to the conclusion (in a dipole approximation of the geomagnetic field) that in an arbitraty point of the Earth, at the geomagnetic latitude A, at zenith angle £ and azimuth all particles with the rigidity g =pc/Zel (measured in 1010V) smaller than
9min — 6 cos4 A[1 4- \Jl - sin £ cos <p cos3 A] 2 (5)
can not reach the Earth surface. So, the geomagnetic energy cut-off (£g) takes place for charged cosmic ray particles. The value of this cut-off depends rather complicately of the arrival direction of the particle. According to (1) the cut-off value ranges for the ALMA site (A ~ 9°2) within ~10-40 GeV (in the case of a relativistic particle). For the vertical incidence of particles E& ~14 GeV.
In Fig.15 we illustrate the influence of the geomagnetic cut-off on the detection rates of electron and proton induced air showers. In this fig-
11n this formula p is the momentum, Ze is the charge of the particle.
2Tliis value corresponds to the south geomagnetic pole lo-
cated at (75°S, 120° E).
>
<u
s
X
-1
s 10 i
2 10
w
4J T3
10
10
-4
r —E.-0
= E,= 20 GeV
-............S N N. \\ \
» \ 1 N.
1 1 1 1 1 1 1 1 N v. 1 111 ENV 1.
10
Erec GeV
> to
a "ft DC
Si
^ 10
i> T3
iS 10'-
10
Erec-GeV
Figure 15. The differential detection rates via the reconstructed shower energy for showers created by the primary 7-ray (solid curves), electron (dashed curves, upper panel) and proton (dashed curves, lower panel). Different values of the geomagnetic cut-off energy (Eg) are considered (indicated at the curves). The energy resolution corresponds to the curve 2 of Fig.12. The angular resolution (Fig.8, curve 4)
provides an energy independent 7-ray acceptance factor So=30 ph.e.; #o=200 m; q0 = 10 ph.e.
y=0.5. The basic MC configuration. q7=2.5;
c 25
0
1 22.5
5 20
I' 17.5
I 15
I 12.5
I -
% 7.5 5
2.5 0
ALTAI
Full boxes --7-ray Open boxes — proton Triongles — iron nucleus
0.04 0.06 0.08
0.12 0,14 0,16 0.18 0.2 WIDTH, degree
0.02 0.04 0.06 0.08 0.1
0.12 0.14 0.16 0.18 0.2 WIDTH, degree
Figure 16. The probability distribution of the WIDTH parameter for vertical air showers created by different primary particles. The basic MC configuration is considered. So=30 ph.e.; Rq=200 m; qo = 10 ph.e.; tail cuts: 7/9 ph.e.
ure we present the differential detection rates via the reconstructed energy of the shower using for all events the look-up tables coresponding to the primary 7-ray. It should be noted also that a cut on the air shower arrival direction is put here which provides an energy independent acceptance efficiency of 7-rays k;7=0.5.
It is seen from Fig. 15 that the detection rate of CR protons can suffer only a modest influence of the geomagnetic field. At the same time, the detection rate of CR electrons can be reduced dramatically (especially in the low energy region). In particular, for vertical air showers (Eg ~14 GeV) the geomagnetic field reduces the CR electron detection rate near the energy threshold of the 5@5 IACT array more than by an order of magnitude.
8. Image Parameter Distributions
In Fig.16-20 we present calculational results on the probability distributions of basic image parameters as registered by the 5@5 IACT array These results have been received with the usage of both computational codes (ALTAI and CORSIKA) and correspond to different primary particles - 7-ray, proton and iron nucleus.
Some differences are observed between image probability distributions corresponding to the primary 7-ray and proton (or the nucleus). In particular, the probability distributions for CR-induced air showers are broader and have longer tails. For the ifmax parameter a noticeable dependence of the
'We define the DENS parameter as the ratio of the SIZE parameter to the total number of pixels having non-zero magnitudes after application oi the tail cut cleaning technique.
most probable value on the atomic number takes place. However, the mentioned above differences are much smaller than those in the TeV energy region. In this relation, an effective software rejection of CR-induced air showers on the basis of image parameters seems to be problematic, at least near the energy threshold of the 5@5 array.
<».5 r
'5
4
■o
J? 5
M J O
Ë. 2.5
Ê 2 D
1.5
ALTAI
Full boxes — y-ray Open boxes — proton Triangles — iron nucleus
u:
I
0.5 0
0.4 0.5 0.6
LENGTH, degree
Figure 17. The probability distribution of the LENGTH parameter for vertical air showers created by different primary particles. The basic MC configuration is considered. So=30 ph.e.; i?o=200 m; qQ = 10 ph.e.; tail cuts: 7/9 ph.e.
ALTAI
Full boxes — y-ray Open boxes — proton Triongles — iron nucleus
T3
0.14
>> 11.12 I 01
a.
VI
Z 0.1» UJ
a
ALTAI
Full boxes — y-ray Open boxes -- proton Triangles — iron nucleus
DENS, ph.e./pixel
Figure 19. The probability distribution of the DENS parameter for vertical air showers created by different primary particles. The basic MC configuration is considered. So=30 ph.e.; Ro=200 m; (jo = 10 ph.e.; tail cuts: 7/9 ph.e.
pool of the whole air shower is splitted into a set of non-overlapping (or weakly overlapping) sub-pools produced by individual neutral pions. So, the ICRC array registers under such conditions electromagnetic cascades created by single neutral pions, which and very similar in properties to 7-ray induced air showers.
On the other hand, according to a well-known superposition model an air shower created by a nucleus with atomic number A and energy E can
Figure 18. The probability distribution of the SIZE parameter for vertical air showers created by different primary particles. The basic MC configuration is considered. ¿>o=30 ph.e.; i?o=200 m; qo = 10 ph.e.; tail cuts: 7/9 ph.e.
A weak dependence of the image probability distributions on the nuture of air shower at low energies can be explained by the following way. In CR induced air showers an overwhelming majority of the Cherenkov light is emitted in sub-cascades created by neutral pions generated, in their turn, in inelastic hadron collisions. For low energy cascades such pions have large enough emission angles (inversely proportional to the energy of colliding hadrons). As a result the Cherenkov light
X
ALTAI
Full boxes — y-ray Open boxes -- proton Triangles — iron nucleus
"1-
X;:.....
I I I . I I 1 L I I 1 , I I I I
5 7.5 10 12.5 15 17.5 20 22.5 25
H , km
max'
Figure 20. The probability distribution of the reconstructed Hmax parameter for vertical air showers created by different primary particles. The basic MC configuration is considered. So=30 ph.e.; i?o=200 m; q0 = 10 ph.e.; tail cuts: 7/9 ph.e.
Table 7
Parameters related to the efficiency of the CR background rejection with the help of the scaled width technique. Different tail cuts and the basic MC configuration are considered for vertical air showers. The image size cut So =1000 ph.e. W0 is the scale width cut.
Tail cut, ph.e. 100 70 50 30 20 15 10
W0 1.1 1.1 1.1 1.0 1.1 1.0 1.0
^ 0.549 0.592 0.585 0.329 0.511 0.335 0.320
«CR 0.098 0.106 0.080 0.021 0.067 0.047 0.060
Q = 1.75 1.82 2.06 2.26 1.97 1.54 _13^1__
Table 8
Optimum values of parameters related to the efficiency of the CR background rejection with the help of the scaled width technique. Different values of the image size cut (So) and the basic MC configuration are considered for vertical air showers. The tail cut is equal to 30 ph.e.
So, ph.e. 1000 700 500 300 200 150
¿?th-y. GeV -100 -80 -60 —45 -35 -25
Wo 1.0 1.2 1.1 1.3 1.4 1.5
rC'y 0.329 0.716 0.563 0.806 0.846 0.878
« CR 0.021 0.156 0.137 0.333 0.468 0.609
Q = «7/VK CR 2.26 1.81 1.52 1.40 1.24 1.13
be replaced, in a rather good approximation, by an ensemble of A nucleón induced showers having the same primary energy E/A. Thus, the energy spectra of individual neutral pions do not exhibit a noticeable dependence on A. That is why the image probability distributions do not show such a dependence as well.
In Tab.7 and 8 we present some results on the efficiency of CR background rejection with the help of a standard scaled width technique. Aplying different cuts on the SIZE parameter we analyse here the evolution of the efficiency with the effective energy threshold of the IACT array. The following conclusions can be made from the tables.
• A more or less effective rejection of CR induced air showers can be achieved only the region of relatively high energies (above —30 GeV). This contradicts results of the basic paper [1] where an effective CR background rejection is obtained in the energy region Eth7 >5 GeV.
• The tail cut providing an optimum efficiency of the background rejection is equal to —30 ph.e., i.e. considerably larger than tail cuts optimizing the angular resolution (8/10 ph.e.).
• In the energy region above —30 GeV the rejection efficiency grows rapidly with energy. Near 100 GeV this efficiency becomes compa-
rable with predictions of paper [5].
9. Sensitivities
We define the sensitivity of the IACT array as a minimum 7-ray flux (integral or differential) which could be detected by the array at a fixed confidence level a (usually 0=3) during a fixed observation time T. To calculate the sensitivity for the integral 7-ray flux we use the following formula
Emin(^ Er
F{0)(>Er
min V — -"-r
TV2 • ET)
(6)
where Er is the reconstructed energy of the air
shower, Ran — the detection rate of CR induced
(0) (0)
air showers with energy larger than Er\ F7', R\ 1 — the integral flux and detection rate corresponding to a "standard" 7-ray source with an energy spectrum defined by formulae (I) or (2).
For calculation of the differential flux sensitivity we apply the following expression
/ni in ( Er ) = /^'„(fir)
err
1/2 CR
[26E ■ T]1/2
where
r = dR/dE, f = df/dE
(7)
(8)
are the differential detection rate and differential flux, correspondingly; 5E is the energy resolution.
Calculating sensitivities we use a cut applied to the shower arrival direction and providing an energy independent 7-rav acceptence factor k7=0.5. This cut corresponds to the optimized (Fig.8, curve 4) angular resolution. For the energy resolution we use the non-optimised results (Figl2, curve 2).
In Fig.21 we present some results illustrating dependence of the differential flux sensitivity on the spectral index of the 7-ray flux (a7) and the geomagnetic cut-off (£"g). This dependence takes place due to a finiteness of the energy resolution of the array. It is seen that the variation of a7 or Eg (or both of them simultaneously) does not influence dramatically the sentitivity value.
Er, GeV
Figure 21. The differential flux sensitivities of the 5@5 IACT array via the reconstructed EAS energy for 1 and 25 h observation times (£g =10 GeV; a-y =2.5). The expected sensitivity of GLAST for 30 day continuous observation is shown by a solid straight line. The basic MC configuration is considered. So=30 ph.e.; i?o=200 m; qo = 10 ph.e.
In Fig.22 we also present the differential flux sensitivities of the 5@5 IACT array for 1 and 25 h observation times. The expected sensitivity of the GLAST detector for 30 days of continuous observations is showed here for comparison. Besides that, in this figure, also for comparison, hard power-law 7-ray spectra are presented (see formula (2)) having an exponential cut-off at E = Ec (five diferent values of Ec are considered) and assuming the flux normalization (3 ■ 10~7 phot/cm2/s above 1 GeV) corresponding approximately to an upper limit of EGRET 7-ray sources.
Figure 22. The differential flux sensitivities of the 5@5 IACT array via the reconstructed EAS energy for different geomagnetic cut-offs (left panel; a7=2.5) and different spectral indexes of the 7-ray flux (right panel; Eg =10 GeV.). The observation time T = 25 h. The basic MC configuration is considered. 50=30 ph.e.; i?o=200 m; q0 = 10 ph.e.
Er, GeV
Figure 23. The integral flux sensitivities of the 5@5 array via the reconstructed EAS en-ergy for 25 h observation time, assuming power-law 7-ray spectra with indexes ay=1.5, 2 and 2.5 (Eg =10 GeV). The sensitivity of GLAST for 1 year continuous observation time is also shown. The basic MC configuration. So=30 ph.e.; Ro=200 m; qo = 10 ph.e.
In Fig.23 we present the integral flux sensitivities of the 5@5 IACT array via the reconstructed air shower energy, assuming power-law 7-ray spectra with different spectral indexes. The sensitivity of GLAST for 1 year continuous observation time is also shown for comparison.
In Fig.24 we show the minimum time tm¡n required for detection of GeV 7-ray flares with a given energy flux /(£') at four different 7-ray energies (indicated at the figure). The calculations correspond to the 3o- signal at each energy E within interval 2SE (SE is the energy resolution), provided that the number of detected 7-rays exceeds 10. In the regime of low fluxes, typically / < 10~9erg/cm2/s, the 7-rays are detected in the presence of the heavy CR background. Therefore ¿mm oc fFor fluxes larger than 10~~9erg/cm2/s, the detection occurs under almost background-free conditions, and therefore imin oc /"'.
C/Ï
u
£ Í0 2
1
s
.2
10
0
«
«
Q 1
-1 10
10 "
10
: \r* 1 - 2-4 GeV
1 v \ H»5.0 km 2-4-8 GeV
fV, 3 - 8-15 GeV
r \ 4 - 100-150 GeV
r
L
1 ........! . .....it • ' "
that both effects are connected closely with variation of an effective depth propagated by air showers in the process of their development.
In Fig.25 we demonstrate the influence of noted above effects on the differential detection rates of air showers created by 7-rays and protons, whereas in Fig.26 - on the differential flux sensitivity of the IACT array. Results of both figures correspond to a pure power-law spectrum of primary 7-rays. In Fig.27 we give results on the angular and energy resolutions used in calculations of the sensitivity. The following conclusions can be reached.
proton
¡U
O 10
I - H^-5.0 km, 0 = 0* - - N„.-1.8 km. 0=0* 3 - 0 km. 0 = 45'
102, Energy flux, erg/cm /s
Figure 24. Minimum observation time required for detection of 7-rays for a given energy flux (SED) in four energy bands centered at 2.5, 6.0, 12.5 and 125 GeV with a width equal to 2SE.
Actually, the results of Fig.24 demonstrate the capability of 5@5 for detection of GeV counterparts of GRBs. The detection of >5 GeV episodic events with typical GRB fluxes between 1CT8 and 10~"6/erg/cm2/s would require only 0.1 s observation time.
10. Results for Inclined Showers and HESS Elevation Altitude
In this section we analyse the influence on IACT array characteristics of two following effects — variations of the air shower arrival direction and of the observation level altitude. For this purpose we compare the IACT array characteristics for two different shower inclination angles (0° and 45°) and two different elevations of the observation altutude — 5.0 km and 1.8 km, the latter of which corresponds to the HESS site in Namibia. It is obvious
E, Ge\
Figure 25. Differential detection rates of the 5@5 IACT array for different obsevation altitudes (Hab¡¡) and different inclination angles (9). The basic MC configuration is considered. So =30 R0 =200 m; q0 =10 ph.e.; a7 =2.5. Hob, = 5.0 km, G = 0°; 2 - Hobs = 1 e = 0°; 3 - //obs = 5.0 km, 9 = 45°.
ph.e.; 1 -i km,
B
m 11
eel 0 a
m
IIJ
1 - Bfc.=s 0 km, 0=0"
2 - 1.8km. 8=0*
3 - H^-5.0 km. (.=>=45*
10
I GeV '
Figure 26. The minimum detectable 7-ray differential fluxes corresponding to different obsevation altitudes and different inclination angles. The basic MC configuration is considered. So =30 ph.e.; Ro =200 m; q0 =10 ph.e.; Eg =10 GeV; 2.5. The calculational results on the angular and energy resolutions presented in Fig.27 are used in the cal-cucations.
• Both effects lead to an increase of the effective energy threshold of the array (approximately
>0.35
g1 0.3 ■o
cO.25
J2 0.2 o
KO. 15 Ï-.
■i 0.1 <0.05
50% event occeptance
1 - H*,=5.0km. ©=0e
2 - H*,= 1.8l,m, 0=0"
3 - HoM=5.0km. 0=45°
10
ErGeV>°
0.6
a o.?
o
S-1 oc
LU
0.4
0.1
50°1 event acceptance
3____i
i
1 - HOM=5.0 km, 9=0°
2 - Ho6,= 1.8 km. 0=0°
3 - H«,,=5.0 km. 0=45°
10
Figure 27. The energy dependence of the angular (left panel) and energy (right panel) resolutions of the 5@5 IACT array for different obsevation altitudes (HQbs) and different inclination angles (6). The basic MC configuration is considered. S0 =30 ph.e.; R0 =200 m; q0 =10 ph.e. 1 — Hobs = 5.0 km, 9 = 0°; 2 - Hobs = 1.8 km, 9 = 0°; 3 - Hoba = 5.0 km, © = 45°.
by a factor of two for conditions considered here).
• The differential detection rate of 7-rays drops seriously in the low energy region with the growth of the shower arrival angle or with the reduction of the elevation altitude. Near the energy threshold of the 5@5 array (5 GeV) this dropping reaches approximatetely one decade.
• Both effects lead to losses tn the 7-ray flux sensitivity. However these losses are dramatically large (a factor of two near the energy threshold) for a power-law 7-ray spectrum considered here.
The latter item of the itemizing list can explained by the following way. The differential detection rates are involved in the sensitivity calculations as functions of the reconstructed energy ET. So, a non-perfect energy resolution of the IACT array leads to smoothing the detection rate energy dependence. As a result the influence of the elevation and inclination effects is diminished, especially in the low energy region.
In Fig.28, 29 and Tab.9 we present some calcula-tional results for 7-ray sources with energy spectra having an exponential cut-off (see formula (2))1 and the flux normalization at 3- 10~7phot/cm2/s above 1 GeV. Particularly, we present for such sources the total detection rates, the time needed for registration at the 3cr confidence level and the gain in the flux sensitivity achieved by the high elevation of the IACT array. The following conclusions can be made.
• The 5@5 effective energy threshold for such
'It is expected that the GRB episodical events and some of 7-ray sources from the EGRET catalogue could have such type of spectra.
§ 1
10
<u
S 10 Q
10
E, Ge>i0
Figure 28. The differential detection rates for vertical air showers created by 7-rays with the energy spectrum described by formula (2). Different values of parameter Ec are considered (indicated at the curves). The basic MC configuration is considered. S0 = 30 ph.e.; q0 = 10 ph.e.
7-ray sources depends essentially on the cutoff location and ranges within ~2-10GeV.
• The gain in the sensitivity induced by the high elevation effect is much larger tnan that for pure p ower-law 7-ray sources and increases
Table 9
The total detection rate (Rand the time (T) needed to reveal a 7-ray source at the 3<7 confidence level. The 7-ray energy spectra with different values of the exponential cut-off are considered (see formula (2)). Eg ==10 GeV; <70 =10 ph.e.; Sa =30 ph.e.; R0 =200 m.
Ec, GeV Ry, Hz T, s
1
0.99 9700
3 4.04 570
10
11.6 70
30 20.2 23
00 33,7
Table 10
Dependence of some basic quantities on the trigger integration time gate. The basic MC configuration is considered. Rq = oo; So = 0; a7=2.5.
T0, ns gomin. ph^e. Tail cuts, ph.e. Ry, Hz Rp,Hz E^, GeV Ethp, GeV
5 9 8/10 31.1 1460 ~ 3 ~ 30
10 12 12/14 18.7 1080 ~ 40
20 18 18/21 12.3 810 ~ 5 ~ 50
Figure 29. The ratio of minimum detectable integral 7-ray fluxes corresponding to the 1.8 km (nominator) and 5 km (denominator) a.s.l. location of the 1ACT array. The primary 7-ray differential energy spectra defined by formula (2) are considered with different values of the cut-off energy Ec (indicated at the curves). ¿?0=200 m; So =30 ph.e.; % =10 ph.e.
rapidly with the reduction of the cut-off energy Ec.
• The time of the source registration also depends strongly on the cut-off position and ranges (for a "standard" flux normalization) from a few hours (small cut-offs) to a few seconds (large cut-offs).
11. Trigger Integration Time Gate
The calculational results presented in the previous sections have been received for the trigger integration time gate r =5 ns. Such a small value of the time gate provides a good rejection of the NSB and, therefore, a low energy threshold of the IACT array. However, this value of the time gate assumes the usage of a very fast (and expensive) electronics for the trigger and readout systems. So, it is important to investigete an optimum choice of the trigger integration time gate (r).
In Tab.10 and Fig.30-31 we present some calculational results illustrating dependence of basic characteristics of the 5@5 IACT array on the value of the r parameter. To see a pure effect of the r influence we do not apply here cuts on the Ro and So
Figure 30. Differential detection rates for air showers created by primary 7-rays and protons. Different values of the trigger integration time gate (indicated at the curves) and the basic MC configuration are considered, a-, =2.5; Ro = 00; So = 0.
parameters (goaled at the improvement of the image quality). All results presented in this section correspond, besides that to a minimum available value of the hardware triggering parameter go-
in Tab. 10 and Fig.30 we show calculational results on the total and differential detection rates. It is seen that growing r parameter leads to a considerable increase of the energy threshold Eth oi the IACT array. At the same time, the total detection rate of the array reduces essentially.
£ .1 .....
I i V 1 - »«,,(10 ns)/l„(5ns)
C 2 - U.(20 ns)/f^,(b ns) !
"S 2
o
Figure 31. The ratio of minimum detectable 7-ray differential fluxes corresponding to different values of the trigger integration time gate. The basic MC configuration is considered. Ro = 00; So = 0; Eg =10 GeV; a,=2.5.
Fig.31 shows the losses (or the gain) in the differential flux sensitivity for r= 10 and 20 nse in comparison with r=5 ns. The following conclusions can be reached.
• The sensitivity reduces with r in the low energy region (<10 GeV). On the contrary, in the upper part of the energy interval 1 100 GeV some improvement of the sensitivity takes place.
• The value r=20 ns (compared with 5 ns) leads to rather essential losses in the sensitivity (up to a factor of 2-3 in the low energy region). At the same time, for r=10 ns the gain in the flux sensitivity is not very large.
Acknowlegements. A.P. is very indebted to the administration of Max-Planck-Institut of Nuclear Physics (Heidelberg) for hospitality.
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