Investigation of Energy Spectrum of EGRET
Gamma-ray Sources by an Extensive Air Shower
Experiment
M. Khakian Ghomi2, M. Bahmanabadi1,2, F. Sheidaei1, J.
Samimi1,2, A. Anvari1,2
1Department of physics, Sharif University of Technology,
P.O. box 11365 - 9161, Tehran, Iran.
2ALBORZ Observatory(http://sina.sharif.edu/∼observatory)
E-mail: sheydaei@sharif.edu
abstract
Ultra-High-Energy (UHE) (E > 100 TeV) Extensive Air Showers (EASs) have been
monitored for a period of five years (1997 − 2003), using a small array of scintillation
detectors in Tehran, Iran. The data have been analyzed to take in to account of
the dependence of source counts on zenith angle. Because of varying thickness of the
overlaying atmosphere, the shower count rate is extremely dependent on zenith angle.
During a calendar year different sources come in the field of view of the array at varying
zenith angles and have different effective observation time equivalent to zenith in a day.
High energy gamma-ray sources from the EGRET third catalogue where observed and
the data were analyzed using an excess method. Upper limits were obtained for 10
EGRET sources [1]. Then we investigated the EAS event rates for these 10 sources
and obtained a flux for each of them using parameters of our experiment results and
simulations. Finally we investigated the gamma-ray spectrum in the UHE range using
these fluxes with reported fluxes of the EGRET sources.
keywords:The EGRET sources, Extensive Air Showers (EASs), Gamma-ray sources,
Gamma-ray spectrum
http://arxiv.org/abs/0704.1122v1
http://sina.sharif.edu/~observatory
Investigation of Energy Spectrum of EGRET Gamma-ray... 2
1. Introduction
The EGRET instrument on-board Compton gamma-ray Observatory (CGRO) has
detected about 271 high energy (> 100 MeV) gamma-ray sources [2]. Effective
sensitivity of EGRET is in the energy range from 100 MeV to 30 GeV.
The EGRET gamma-ray sources in many aspects like characteristics, different energy
ranges and etc. have been investigated [3, 4, 5]. Whether the EGRET sources emit
gamma-ray at still higher energies or not, is an interesting question. Gamma-rays with
energies of about 100 TeV and more, entering the earth atmosphere, produce Extensive
Air Shower (EAS) events which could be observed by the detection of the secondary
particles of the EAS events on the ground level [6]. This gamma-ray induced EAS events
are investigated for diffuse Galactic [7] and extragalactic sources, also Galactic [8], [9]
and extragalactic [10] gamma-ray point sources have been investigated too. In this work
we have investigated 10 of these point sources.
Our small particle detector array is located at the Sharif University of Technology in
Tehran, Iran at about 1200 m above sea level (≡ 890 g cm−2). This small array is a
prototype for a large EAS array to be built at an altitude of 2600 m (≡ 756 g cm−2)
at ALBORZ Observatory (AstrophysicaL oBservatory for cOsmic Radiation on alborZ)
(http://sina.sharif.edu/ ∼observatory/) near Tehran. The results of the experiments
with this prototype observatory with about 1.7×105 recorded EAS events was reported
earlier [1] and has been shown that some of the EGRET GeV point sources are
gamma-ray emitters at energies about 100TeV. Here we report the results of our recent
investigation using the data of our earlier experiments to extend the energy spectrum of
the observed EGRET sources up to 100TeV and more. In this investigation we present
the observational results for 10 EGRET third catalogue sources. Then we investigate
the effective area and effective time of observation of each source. Finally we compare
the obtained fluxes and spectral indices with the presented fluxes and spectral indices
of the EGRET third catalogue sources at the 3rd EGRET catalogue.
2. Experimental arrangement
Our array is constructed of four slab of plastic scintillation detectors (100×100×2 cm3).
They are housed in white painted pyramidal boxes [11] which arranged in a square; at
51◦ 20
E and 35◦ 43
N, elevation 1200 m (≡ 890 g cm−2). Two different experimental
configurations were used in the experimental set up. The first (E1) and the second (E2)
experimental configurations are identical except the size of the square array. In E1 the
size is 8.75 m × 8.75 m and in E2 the size is 11.30 m × 11.30 m. More details of the
experimental setup is given in the reference [1].
http://sina.sharif.edu/
Investigation of Energy Spectrum of EGRET Gamma-ray... 3
3. Data Analysis
The logged time lags between the scintillation detectors and Greenwich Mean Time
(GMT) of each EAS event were recorded as raw data. We synchronized our computer to
GMT (http://www.timeanddate.com). Our electronic system has a recording capability
of 18.2 times per second. If an EAS event occurs, its three time lags will be recorded and
if it does not occur ’zero’ will be recorded. Therefore the starting time of each experiment
and the count of records gives us the GMT of each EAS event. We estimated the energy
threshold and the mean energy of our experiment and also we calculated the statistical
significance of 98 of the 3rd EGRET sources which were in the Field Of View (FOV) of
our array.
The complete analysis procedure [1] is itemized as follows:
• The local coordinates: zenith and azimuth angles of each EAS event (z, ϕ)
were calculated using a least-square method based on the logged time lags and
coordinates of the scintillators. A zenith angle cut off of 60◦ is implemented to
increase the significance [12].
• The distributions of the local angles of the EAS events were investigated to
understand the general behavior of these events. We fitted these distributions
with the two functions as follows [13]:
dN = Az sin z cos
n zdz (1)
where Az = 95358 and n = 5.00, and also
f(ϕ) = Aϕ +Bϕ cos(ϕ− ϕ1) + Cϕ cos(2ϕ− ϕ2) (2)
where Aϕ = 1, Bϕ = 0.081 , Cϕ = 0.069, ϕ1 = 95
◦ and ϕ2 = −193
• Celestial coordinates (RA,Dec) of each EAS event were calculated using its
local coordinates, the GMT of the event and geographical latitude of our
array (http://tycho.usno.navy.mil/sidereal.html). Then we calculated galactic
coordinates (l,b) of each EAS event from its equatorial coordinates for epoch J2000
[14].
• We estimated the errors in (l,b) of the investigated EGRET sources from the error
factors in the array. In this stage we obtained r̄e = 4.35
◦ ± 0.82◦ as the mean
angular error of our experiment.
• We investigated cosmic-ray initiated EAS events by simulations based on a
homogeneous distribution of primary charged particles. These simulations
incorporated all known parameters of the experiment. [1]
• We investigated the statistical significance of 98000 random sources and also 98
sources of the 3rd EGRET catalogue, using the method of Li & Ma (Li & Ma 1983)
we derived the best-known locations for the EGRET sources in the TeV range [1].
http://www.timeanddate.com
http://tycho.usno.navy.mil/sidereal.html
Investigation of Energy Spectrum of EGRET Gamma-ray... 4
3.1. Shadow of the moon
Observing the shadow of the moon in EAS experiments which usually might have a much
larger error circle than the disk of the moon is a very difficult task and requires a careful
scrutinization of the data. The difficulty is compounded since a realistic radius for the
error circle of the experiment is only obtained by the observation of the shadow which
could be indicated as a deficit of shower counts falling in the error circle centered about
the moving location of the moon as compared to the average shower counts falling in
error circles centered at other positions in sky during the observation time. To carry out
the scrutinization of our data, we have proceeded as follows.We have divide our data into
sequential time segments and for each time segment we have used the mean values of the
local coordinates of moon (θm, ϕm) moving over our observatory site. These coordinates
were obtained using the information provided by the http://aa.usno.navy.mil. Now
for an assumed radius of circle of error, angular radius ρerr ranging from 0.5
◦ to 15◦
incremented by 0.5◦, we have calculated the number of showers falling in each circle. This
has been done by calculating the angular separations Θs between the arrival direction
of each shower event (θs, ϕs) and the direction of the moon at the time of recording of
that event, using the following equation from spherical geometry:
cosΘs = cos θm cos θs + sin θm sin θs cos(ϕm − ϕs) (3)
Obviously if Θs < ρerr that shower is counted as falling in the moon’s error circle. In
order to compare the obtained result with random sampling and scrutinize the difference
for each value of ρerr we have chosen 1000 random locations in the sky denoted by
local coordinates (θr, ϕr) and have calculated the number of showers falling in the error
circles countered about each of the 1000 random locations. This was similarly done
by calculating the angular separation of each shower arrival direction (θs, φs) with the
direction of the center of the randomly chosen error circle (Θr) from above equation with
(θm, ϕm) replaced by (θr, ϕr). If for any shower event Θr < ρerr that shower is counted
as falling in the error circle of that random position. In these computations (both for
the moon as well as for the random locations) a weight factor was used for each of the
shower events in order to account for the site-specific effects in our data which depend
on the arrival directions of shower events. These effects are :
(1) The different thickness and density of the overlying atmosphere which are effective
in shower development and hence its detectability at the height of the observatory.
(2) The geomagnetic effect on the azimuthal arrival direction of the showers. These
effects which are specific for each observation site, were separately and independently
determined for our site and are reflected in the dependence of the number of shower
events on zenithal and azimuthal angles which are given by equations 1 and 2,
respectively [13]. To take account of these effects in our observed data, we have assigned
a weight factor to each shower arrival direction which is the product of these two
independent factors. The weight factor is thus:
W (θs, ϕs) = cos
n θs(Aϕ +Bϕ cos(ϕ− ϕ1) + Cϕ cos(2ϕ− ϕ2)) (4)
http://aa.usno.navy.mil
Investigation of Energy Spectrum of EGRET Gamma-ray... 5
where the constants n, Aϕ,Bϕ and Cϕ are given below Eqs.1 and 2.
It should be remembered that in our earlier work, [1] reporting the observation of
EGRET gamma-ray point sources in TeV data by excess method, both of these
effects were carefully taken into account by determining the exposure map of our
observations by simulations incorporating these effects along with other particularities
of our observations and by correcting of our observed data by dividing it by the exposure
map in galactic coordinates.
3.2. Distributions of number of EAS events in error circles
Here we discuss the distribution of number of EAS events falling in the error circles
of different radii as determined according to the aforementioned procedure. We first
present the results for each of the sets of 1000 randomly chosen error circles. Fig.2
shows the histogram of frequency of occurrence of number of circles with respect to the
number of EAS falling in the error circle. The histograms distributions corresponding
to different radii of error circles are shown here as illustration. These for other radii
show similar distributions and all these distributions nearly fit gaussian distributions
with a mean and a variance which increase with increasing radius. This result is very
assuring and shows the correctness of our sophisticated numerical procedure and the
validity of using the mean number of events, in these randomly chosen locations of
error circles in the sky to compare with the number of events falling in the error circle
countered about the moving moon. Fig.3 shows the variation of the mean number of
events of these distribution as a function of the chosen radius of the error circles. It is
seen that these calculated means show a nearly exact dependence on the square of the
radius. This result is not surprising and is exactly what one would expect to get from
a correct random sampling of statistical data. However, in view of the complexity and
sophistication involved in our entire procedure (with inclusion of the weight factors),
this result is again very assuring and shows that we can use these mean number of
events to compare with that falling in the error circles centered about the moving moon
and rule out the possibility of the deficit in the number of events falling in the moon
centered circle as due to statistical fluctuation. In Fig.3 we have also shown the number
of events falling in the moon-countered circles for comparison with the means of the
random samplings. It is seen that in every case( for every chosen error circle radius) the
deficit of number of EAS from the direction of the moving moon is quite significant as
compared to the error bars of the mean of random sampling( Fig.3) which is taken as
the variance of nearly gaussian distributions of Fig.2. As seen here the deficit which is
from 1.6 to about 7.1 times the standard deviation of the mean of random distributions
is quite significant and since it is definitely associated with the moving moon it must be
associated with some moon- related phenomenon. We will not discuss this phenomenon
here and rather simply call it the shadow of the moon in our EAS observed data.
Investigation of Energy Spectrum of EGRET Gamma-ray... 6
3.3. Estimation of energy thresholds
Our detected EAS events are a mixture of cosmic-ray and gamma-ray events. In E1 the
total number of EAS events was 53,907 and the duration of the experiment was 501,460
seconds. So the mean event rate of the first experiment was 0.1075 events per second.
The distribution of the time between successive events was investigated and found to be
in good agreement with an exponential function, indicating that our event sampling is
completely random [16]. In E2 the total number of events was 173,765 and the duration
of the second experiment was 2,902,857 seconds, so its mean event rate was 0.05986
events per second.
We refined the data to separate out the acceptable events. Events are acceptable if
there is a good coincidence between the four scintillator pulses, also we omitted the
events with zenith angles more than 60◦ because of their less accuracy. Therefore after
these separations we obtained smaller data sets of 46,334 and 120,331 events for E1 and
E2 respectively. Since we cannot determine the energy of the showers on an event by
event basis, we estimate our lower energy threshold by comparing our event rate to the
following cosmic-ray integral spectrum [17],
J(E) = 2.78× 10−5E−2.22 + 9.66× 10−6E−1.62
− 1.94× 10−12 40 ≤ E ≤ 5000 TeV (5)
The obtained lower energy limits are 39 TeV in E1 and 54 TeV in E2. The
calculated mean energies with above energy spectrum are 94 and 132 TeV in E1 and
E2, respectively. Since the distribution of cosmic-ray events within the array around
these energy ranges is homogeneous and isotropic, we used an excess method [18] to find
signatures of the EGRET 3rd catalogue gamma-ray sources. This method was used for
both E1 and E2.
4. Calculation of effective area and time
Number of secondary particles in the growth profile of EAS events increases in
atmosphere until the shower maximum and then decreases after it. In energy of about
100 TeV the shower maximum height is at about 500g cm−2 and a fraction of these
secondary particles arrive to the ground level particle detectors of our array at Tehran
level (1200 m≡ 890 g cm−2).
For calculating the effective surface of each experiment (E1 and E2) we used Greisen
lateral distribution of electrons which is known the NKG formula [19] and CORSIKA
simulation code [20] for the simulation of the two sets of proton showers with energy
thresholds of 39 TeV and 54 TeV respectively for E1 and E2 at our array level. From
our logged EAS events we obtained a zenith distribution function for E1 and E2, which
the mean zenith angles are 26◦ for both of them. Also we calculated the z̄ which was
obtained from the weight curve of the zenith distribution dN/dz ∝ cosn z sin z and we
obtained the 26◦ too. This weight curve was obtained by fitting the function dN/dz to
Investigation of Energy Spectrum of EGRET Gamma-ray... 7
our data in the E1 and E2 with n = 5.00. So in the first approximation we used the
effective thickness of the passed atmosphere as 890g cm−2/ cos(26◦) = 980g cm−2. In
the thickness, the average number of the secondary particles for the two experiments
are NE1 = 5265 and NE2 = 8571, these two numbers obtained from 1000 simulated
proton showers for each energy threshold. So based on the NKG formula the mean
effective surfaces of EAS events at Tehran level are 965 m2 and 2173 m2 for E1 and
E2 respectively. With these results we could obtain the mean effective surface of our
array in the upper level of the atmosphere (The surface that if a primary particle passes
through it, the array could detect its EAS events) 718m2 and 1751m2 for E1 and E2
respectively.
For calculation of the effective time of observation of each source in every 24 hours, we
used the spherical geometry and the track of each source in the local coordinates. Each
source with its celestial coordinates right Ascention, Declination (RA,Dec) is introduced
in the 3rd EGRET catalogue. Time duration of each source is calculated by reaching the
source to the zenith angle of 60◦ from the direction of east to the same zenith angle from
the west, and the distribution function dN/dz =∝ cosn z sin z which is related to the
zenith distribution effect [1]. Finally we obtained the mean effective time of observation
of our array for all 10 sources equivalent to 4h,28
(equivalent to existence of 4h,28
the source at zenith) for every 24 hours. The FOV of our array with the 60◦ zenith
angle cutoff is π steradian. With these calculated factors we obtained fluxes(events
cm−2s−1sr−1) for each of the 10 sources in E1 and E2 which are shown in Table 1.
5. Results
Our results have been compared with the EGRET results. For each source we have
fluxes and energies from EGRET, E1 and E2, so we extracted a spectral index for each
source and compared it with the reported spectral index of EGRET. Some information
about the 10 EGRET sources like Name, RA, Dec, and spectral index and its error,
(γ ± ∆γ)EGT , are from the 3rd EGRET catalogue [2]. Other information like mean
energy for E1 and E2 which are 94TeV and 132TeV respectively (are not shown in the
table), fluxes of the two experiments and spectral indexes and their errors, (γ±∆γ)OUR,
have been calculated in this analysis. The last column shows the agreement of our
spectral indices to its in the 3rd EGRET catalogue.
5.1. Result of Energy Analysis with Simulated Showers
For further energy analysis of our measured data of EAS events observed at our
site we have used the CORSIKA code[20] to simulate showers with the inclusion
of geomagnetic field pertinent to the location of our site from data provided by
http://www.ngdc.noaa.gov. We have simulated a total of 7350 showers entering the
top of atmosphere at various zenith angles (0◦, 15◦, 30◦, 45◦, 60◦) and for each zenith
angle at 12 various azimuth angles ranging from 0◦ to 360◦ every 30◦. For each angle
http://www.ngdc.noaa.gov
Investigation of Energy Spectrum of EGRET Gamma-ray... 8
the simulations were repeated 10 times for energies less than 50 TeV and 5 times for
energies greater than 50 TeV with separately 10 TeV intervals from 10 TeV to 100 TeV.
These simulations were carried out similarly for entering protons as well as gamma-
rays. For each simulation the number of secondary charged particles of the simulated
shower at the height of observation of our site was determined from CORSIKA code.
In order to make an energy analysis comparing gamma-ray initiated showers with those
initiated by protons in our observations we have calculated a mean number of secondary
shower particles for each energy by averaging over all the angles using the site-specific
weight factor discussed in sec 3.1(Eq. 4). The ratio of angle-averaged mean of number
of secondary charged particles in gamma-ray initiated showers to that of the mean for
proton-initiated showers is shown in Fig.4 as a function of energy in the energy range of
our simulations. The ratio shown here incorporates almost all of related particularities of
our experiments. Since in our observations we have used exactly identical experimental
procedure, equipment, thresholds and set-ups for all of the recorded showers irrespective
of the nature of the radiation which initiates the shower the relative detection efficiency
of our array and observations could only depend on the ratio of these means depicted in
Fig.4. Now we use the relative detection efficiency calculated from simulated data and
shown in Fig.4 to estimate the relative number of gamma-ray initiated showers to that
initiated by protons, using the known energy spectrum of proton showers of the form
= Np10(
10TeV
)−Γp. (6)
Where dNp is the number of proton showers in the energy interval E to E + dE, Np10
is a constant and Γp is the spectral index of EAS producing protons. Now denoting our
array’s relative detection efficiency by η(E), we can write for the expected differential
number of gamma-ray initiated showers:
= η(E)Np10(
10TeV
)−Γγ (7)
where Γγ is the spectral index of EAS producing gamma- rays. Dividing Eq.7 by Eq.6
and upon integration from a threshold energy to infinity, the ratio of observed gamma-
ray EAS events to that initiated by protons is obtained. Thus we write:
NγEAS
NpEAS
η(E)E−Γγ dE
E−Γp dE
where Et is assumed threshold energy. For the energy range covered in this analysis,
we use Γp = 2.7 and for gamma-ray spectral index we use the mean value of the
spectral indices that we have estimated above (Table.1) for the sources with the highest
statistical significance (those observed at a statistical significance level of higher than
1.5σ). Thus using our estimations of table 1 we have Γγ = 2.3. In order to carry out
the integrations in Eq.8 we are forced to impose a truncation since with our rather
limited computer shower simulations we only have η(E) for 10TeV < E < 100TeV . For
the sake of numerical consistency, we have imposed this truncation to E=100 TeV in
Investigation of Energy Spectrum of EGRET Gamma-ray... 9
Name(3EG J) RA,Dec ID (γ ±∆γ)EGT logFE1 logFE2 (γ ±∆γ)OUR |γOUR − γEGT |
0237+1635 39.3,16.5 A 1.85±0.12 -11.25 -11.53 1.90±0.27 0.05
0407+1710 61.8,17.1 2.93±0.37 -10.77 -11.45 4.20±0.40 1.27
0426+1333 66.6,13.5 2.17±0.25 -11.11 -11.28 1.15±0.48 1.02
0808+5114 122.1,51.2 a 2.76±0.34 -11.01 -11.58 3.87±0.42 1.11
1104+3809 126.1,38.1 A 1.57±0.15 -11.10 -11.72 4.21±0.50 2.64
1308+8744 197.0,87.7 2.17±0.66 -10.96 -11.53 3.87±0.45 1.70
1608+1055 242.1,10.9 A 2.63±0.24 -10.92 -11.72 4.34±0.50 1.71
1824+3441 276.2,34.6 2.03±0.50 -10.65 -11.25 4.07±0.35 2.04
2036+1132 309.1,11.5 A 2.83±0.26 -11.08 -11.73 4.41±0.53 1.58
2209+2401 332.4,24.0 A 2.48±0.50 -10.91 -11.31 2.71±0.42 0.23
Table 1. Comparison of our spectral indices of the 10 sources with the spectral indices
of them which is introduced by the 3rd EGRET catalogue. The last column shows
agreement of our spectral indices to EGRET spectral indices.
the denominator of Eq.8 as well as its numerator. The result of these calculations
obviously depend on the value of an assumed threshold energy, Et, therefore the
numerical calculations were repeated for values of Et from 10 TeV to 100 TeV with
10 TeV intervals. The result of these calculations, that is, the ratio of the number of
gamma-ray EAS events to that of proton EAS events expected to be detected in our
experiments at our site is shown as a function of the threshold energy in Fig.5. Here
we see that this ratio shows a maximum at a value of Et = 40 TeV which very nearly
corresponds to the lower value of the two threshold energies of our two experiments.
6. Concluding remarks
We believe the main reasons for success in these observations and investigations on
EGRET gamma-ray point sources despite the low statistics of ∼ 3 × 105 EAS events
from our small array of ALBORZ prototype observatory, relies on the following two
favorite points of strength:
(1) we have intensively studied the location- dependent factors which influence shower
development and shower count from various angular bins in the sky. These factors
are the mass of the overlying atmosphere and anisotropy in azimuth angles which it is
attributed to the effect of the geomagnetic field [21], [13], [22]. For our particular site
we investigated these effects which are in form of Eqs. 1 and 2. We carefully refined our
data from these effects finally the investigation of the EGRET gamma-ray point sources
are based on the corrected data.
(2) Our site and the duration of our observations in the data set have been such that 10
of the EGRET gamma-ray point sources have crossed our site at small enough zenith
angles to make their observation possible at least with a statistical significance of 1.5σ
with Li and Ma criterion in the excess method which we have used[1]. In order to
Investigation of Energy Spectrum of EGRET Gamma-ray... 10
investigate this rather fortunate point for our site and the time of these observations,
we have calculated the average zenith all angle of passage of each of 271 EGRET gamma-
ray point sources during our entire observation period, for each of these sources. We
have also calculated the statistical significance(number of sigma) for excess counts from
these sources. The result is shown here in Fig.1 and it convincingly shows an inverse
correlation between the statistical significance of excess shower counts from the EGRET
point source location and the average zenith angle of the transit of the source over our
site. The computed coefficient of this correlation(correlation between inverse statistical
significance and z) is 0.77.
Obviously the EGRET sources investigated here are those with highest statistical
significance corresponding to the lowest zenith angles of the passage of the source over
our site.
Our results shows that our spectral indices within error limits are in agreement with
EGRET spectral indices for most of the considered here.
For the calculation of the effective area of the EAS events at first , we calculated the
primary particle energy, then we extracted the number of the secondary particles from
a set of CORSIKA simulations, and finally we used the Greizen lateral distribution for
these particles. In the near future with a larger array and larger set of logged EAS
events at ALBORZ observatory we hope to calculate these results more accurately.
It is worth remarking that due to increased probability of pair- production interaction of
VHE and UHE gamma-rays with various low energy universal photons, the absorption
of these gamma-rays becomes significant for sources located at cosmological distances.
This absorption has been studied extensively [23, 24, 25]. The lack of observation of
VHE and UHE gamma-rays from extragalactic EGRET gamma-ray sources has been
generally attributed to the absorption of the gamma-rays from these sources which are
located at cosmological distances.
Stecker and De Jager (1997) gave a parametric relation for optical depth (τj) as a
function of the source gamma energy (ETeV ) and red shift (z) for the two models (j=1,2)
they have studied. For the 39TeV energy threshold of our experiments, we use their
parametric relation with an optical depth of unity to calculate the red shift of the
sources we have observed in our EAS experiments and have investigated here(Table 1).
The result is z=0.0032 for their model 1 and z=0.0024 for their model 2. Ong,[26] have
listed the red shifts of two classes of EGRET extragalactic sources and the calculated red
shifts for the sources investigated here is smaller than red shifts listed for these classes
of objects. However, we should remark that the recent discovery of the unexpected by
hard spectra of the Blazar sources observed in HESS data [27] bear as the possibility of
observation of EGRET gamma-ray point sources at higher energies. It would be open
for future ground-base observations.
The energy analysis carried out here using simulated shows with CORSIKA has shown
that the ratio of number of gamma-ray generated EAS events expected to be detected
at our site relative to the number of proton- generated EAS events show a maximum at
a value of 40 TeV for the threshold energy of observation of EAS events at our site. The
Investigation of Energy Spectrum of EGRET Gamma-ray... 11
fortunate fact that this value corresponds to the lower value of the threshold energies of
our two experiments, provides further support for the fact that the data collected in our
experiments at our site has had this extra advantageous attribute for the observation of
gamma-ray initiated EAS events in the 10 TeV to 100 TeV energy range and thus the
extra advantage for observing gamma-ray point sources in this range.
7. acknowledgements
This research was supported by a grant from the national research council of Iran for
basic sciences. The many useful and conductive comments by anonymous referee is very
much appreciated. Also many thank from Prof. James Matthews for his comments and
attentions to our works at ICRC 2005, Pune, India.
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[15] Li, T., Ma, Y., 1983, ApJ, 272, 317
[16] Bahmanabadi, M., et al. 2003, Experimental Astronomy, 15, 13
[17] Borione, A., et al. 1997, ApJ, 481,313
[18] Amenomori, M., et al., 2002, ApJ, 580, 887
[19] Kamata, K., Nishimura, J. (1958) Prog. Theor. Phys.(kyoto) suppl. 6, 93
[20] Heck, D., et al., Report FZKA 6019(1998), Forschungszentrum Karlsruhe
http://www-ik.fzk.de/corsika/physics-description/corsika-phys.html
[21] Ivanov, A.A. et al., 1999, JETP Let. 69, 288-293
[22] He, H.H., Sun, B.G., Zhou, Y., 2005, ICRC, India, 6, 5-8
[23] Stecker, F.W, Cosmic Gamma ray, Moro Book Corp., Baltimore (1971)
[24] Fazio, G.G., Stecker, F.W., 1970, Nature, 226, 135
[25] Stecker, F.W., De Jager, O.C, 1997, ApJ, 476, 716
[26] Ong, R.A., et al., 2001, ICRC, Germany, 2593.
[27] Aharonian , F., et al., Nature 440(2006) 1018-1021
http://www-ik.fzk.de/corsika/physics-description/corsika-phys.html
Investigation of Energy Spectrum of EGRET Gamma-ray... 12
Figure 1. Distribution of statistical significance versus average zenith angle of transit
of calculated for 271 EGRET gamma-ray sources over our site(only sources with
significance > 1.5σ are shown.).
Investigation of Energy Spectrum of EGRET Gamma-ray... 13
Figure 2. Histograms show the frequency of circles of error with radius ρ and random
chosen centers in the sky vs. the number of EAS events falling in each error circle.
Investigation of Energy Spectrum of EGRET Gamma-ray... 14
Figure 3. Dependence of the mean number of EAS events falling in the random error
circles as a function of the radius of the error circle, ρ. Smooth curve shows a ρ2
dependence. Error bars are the standard deviation of the distribution shown in Fig.2,
and statistical errors for the moon. Open circles (◦) are random error circles. Filled
circles(•) are error circles centered about the location of the moving moon.
Investigation of Energy Spectrum of EGRET Gamma-ray... 15
Figure 4. The ratio of the mean number of secondary charged particles at the location
of our site produced in gamma-ray generated simulated Extensive Air Shower to that
produced by proton generated showers as a function of the energy of the primary
radiation( Gamma-ray and proton) entering the top of the atmosphere.
Investigation of Energy Spectrum of EGRET Gamma-ray... 16
Figure 5. The ratio of the mean number of gamma-ray generated showers to that
of proton generated showers expected to be observed at our site as a function of the
threshold energy of our experiments.
	Introduction
	Experimental arrangement
	Data Analysis
	Shadow of the moon
	Distributions of number of EAS events in error circles
	Estimation of energy thresholds
	Calculation of effective area and time
	Results
	Result of Energy Analysis with Simulated Showers
	Concluding remarks
	acknowledgements

  Ultra-High-Energy (UHE) ($E>100 $TeV) Extensive Air Showers (EASs) have been
monitored for a period of five years (1997-2003), using a small array of
scintillation detectors in Tehran, Iran. The data have been analyzed to take in
to account of the dependence of source counts on zenith angle. Because of
varying thickness of the overlaying atmosphere, the shower count rate is
extremely dependent on zenith angle. During a calendar year different sources
come in the field of view of the array at varying zenith angles and have
different effective observation time equivalent to zenith in a day. High energy
gamma-ray sources from the EGRET third catalogue where observed and the data
were analyzed using an excess method. Upper limits were obtained for 10 EGRET
sources. Then we investigated the EAS event rates for these 10 sources and
obtained a flux for each of them using parameters of our experiment results and
simulations. Finally we investigated the gamma-ray spectrum in the UHE range
using these fluxes with reported fluxes of the EGRET sources.

Introduction
The EGRET instrument on-board Compton gamma-ray Observatory (CGRO) has
detected about 271 high energy (> 100 MeV) gamma-ray sources [2]. Effective
sensitivity of EGRET is in the energy range from 100 MeV to 30 GeV.
The EGRET gamma-ray sources in many aspects like characteristics, different energy
ranges and etc. have been investigated [3, 4, 5]. Whether the EGRET sources emit
gamma-ray at still higher energies or not, is an interesting question. Gamma-rays with
energies of about 100 TeV and more, entering the earth atmosphere, produce Extensive
Air Shower (EAS) events which could be observed by the detection of the secondary
particles of the EAS events on the ground level [6]. This gamma-ray induced EAS events
are investigated for diffuse Galactic [7] and extragalactic sources, also Galactic [8], [9]
and extragalactic [10] gamma-ray point sources have been investigated too. In this work
we have investigated 10 of these point sources.
Our small particle detector array is located at the Sharif University of Technology in
Tehran, Iran at about 1200 m above sea level (≡ 890 g cm−2). This small array is a
prototype for a large EAS array to be built at an altitude of 2600 m (≡ 756 g cm−2)
at ALBORZ Observatory (AstrophysicaL oBservatory for cOsmic Radiation on alborZ)
(http://sina.sharif.edu/ ∼observatory/) near Tehran. The results of the experiments
with this prototype observatory with about 1.7×105 recorded EAS events was reported
earlier [1] and has been shown that some of the EGRET GeV point sources are
gamma-ray emitters at energies about 100TeV. Here we report the results of our recent
investigation using the data of our earlier experiments to extend the energy spectrum of
the observed EGRET sources up to 100TeV and more. In this investigation we present
the observational results for 10 EGRET third catalogue sources. Then we investigate
the effective area and effective time of observation of each source. Finally we compare
the obtained fluxes and spectral indices with the presented fluxes and spectral indices
of the EGRET third catalogue sources at the 3rd EGRET catalogue.
2. Experimental arrangement
Our array is constructed of four slab of plastic scintillation detectors (100×100×2 cm3).
They are housed in white painted pyramidal boxes [11] which arranged in a square; at
51◦ 20
E and 35◦ 43
N, elevation 1200 m (≡ 890 g cm−2). Two different experimental
configurations were used in the experimental set up. The first (E1) and the second (E2)
experimental configurations are identical except the size of the square array. In E1 the
size is 8.75 m × 8.75 m and in E2 the size is 11.30 m × 11.30 m. More details of the
experimental setup is given in the reference [1].
http://sina.sharif.edu/
Investigation of Energy Spectrum of EGRET Gamma-ray... 3
3. Data Analysis
The logged time lags between the scintillation detectors and Greenwich Mean Time
(GMT) of each EAS event were recorded as raw data. We synchronized our computer to
GMT (http://www.timeanddate.com). Our electronic system has a recording capability
of 18.2 times per second. If an EAS event occurs, its three time lags will be recorded and
if it does not occur ’zero’ will be recorded. Therefore the starting time of each experiment
and the count of records gives us the GMT of each EAS event. We estimated the energy
threshold and the mean energy of our experiment and also we calculated the statistical
significance of 98 of the 3rd EGRET sources which were in the Field Of View (FOV) of
our array.
The complete analysis procedure [1] is itemized as follows:
• The local coordinates: zenith and azimuth angles of each EAS event (z, ϕ)
were calculated using a least-square method based on the logged time lags and
coordinates of the scintillators. A zenith angle cut off of 60◦ is implemented to
increase the significance [12].
• The distributions of the local angles of the EAS events were investigated to
understand the general behavior of these events. We fitted these distributions
with the two functions as follows [13]:
dN = Az sin z cos
n zdz (1)
where Az = 95358 and n = 5.00, and also
f(ϕ) = Aϕ +Bϕ cos(ϕ− ϕ1) + Cϕ cos(2ϕ− ϕ2) (2)
where Aϕ = 1, Bϕ = 0.081 , Cϕ = 0.069, ϕ1 = 95
◦ and ϕ2 = −193
• Celestial coordinates (RA,Dec) of each EAS event were calculated using its
local coordinates, the GMT of the event and geographical latitude of our
array (http://tycho.usno.navy.mil/sidereal.html). Then we calculated galactic
coordinates (l,b) of each EAS event from its equatorial coordinates for epoch J2000
[14].
• We estimated the errors in (l,b) of the investigated EGRET sources from the error
factors in the array. In this stage we obtained r̄e = 4.35
◦ ± 0.82◦ as the mean
angular error of our experiment.
• We investigated cosmic-ray initiated EAS events by simulations based on a
homogeneous distribution of primary charged particles. These simulations
incorporated all known parameters of the experiment. [1]
• We investigated the statistical significance of 98000 random sources and also 98
sources of the 3rd EGRET catalogue, using the method of Li & Ma (Li & Ma 1983)
we derived the best-known locations for the EGRET sources in the TeV range [1].
http://www.timeanddate.com
http://tycho.usno.navy.mil/sidereal.html
Investigation of Energy Spectrum of EGRET Gamma-ray... 4
3.1. Shadow of the moon
Observing the shadow of the moon in EAS experiments which usually might have a much
larger error circle than the disk of the moon is a very difficult task and requires a careful
scrutinization of the data. The difficulty is compounded since a realistic radius for the
error circle of the experiment is only obtained by the observation of the shadow which
could be indicated as a deficit of shower counts falling in the error circle centered about
the moving location of the moon as compared to the average shower counts falling in
error circles centered at other positions in sky during the observation time. To carry out
the scrutinization of our data, we have proceeded as follows.We have divide our data into
sequential time segments and for each time segment we have used the mean values of the
local coordinates of moon (θm, ϕm) moving over our observatory site. These coordinates
were obtained using the information provided by the http://aa.usno.navy.mil. Now
for an assumed radius of circle of error, angular radius ρerr ranging from 0.5
◦ to 15◦
incremented by 0.5◦, we have calculated the number of showers falling in each circle. This
has been done by calculating the angular separations Θs between the arrival direction
of each shower event (θs, ϕs) and the direction of the moon at the time of recording of
that event, using the following equation from spherical geometry:
cosΘs = cos θm cos θs + sin θm sin θs cos(ϕm − ϕs) (3)
Obviously if Θs < ρerr that shower is counted as falling in the moon’s error circle. In
order to compare the obtained result with random sampling and scrutinize the difference
for each value of ρerr we have chosen 1000 random locations in the sky denoted by
local coordinates (θr, ϕr) and have calculated the number of showers falling in the error
circles countered about each of the 1000 random locations. This was similarly done
by calculating the angular separation of each shower arrival direction (θs, φs) with the
direction of the center of the randomly chosen error circle (Θr) from above equation with
(θm, ϕm) replaced by (θr, ϕr). If for any shower event Θr < ρerr that shower is counted
as falling in the error circle of that random position. In these computations (both for
the moon as well as for the random locations) a weight factor was used for each of the
shower events in order to account for the site-specific effects in our data which depend
on the arrival directions of shower events. These effects are :
(1) The different thickness and density of the overlying atmosphere which are effective
in shower development and hence its detectability at the height of the observatory.
(2) The geomagnetic effect on the azimuthal arrival direction of the showers. These
effects which are specific for each observation site, were separately and independently
determined for our site and are reflected in the dependence of the number of shower
events on zenithal and azimuthal angles which are given by equations 1 and 2,
respectively [13]. To take account of these effects in our observed data, we have assigned
a weight factor to each shower arrival direction which is the product of these two
independent factors. The weight factor is thus:
W (θs, ϕs) = cos
n θs(Aϕ +Bϕ cos(ϕ− ϕ1) + Cϕ cos(2ϕ− ϕ2)) (4)
http://aa.usno.navy.mil
Investigation of Energy Spectrum of EGRET Gamma-ray... 5
where the constants n, Aϕ,Bϕ and Cϕ are given below Eqs.1 and 2.
It should be remembered that in our earlier work, [1] reporting the observation of
EGRET gamma-ray point sources in TeV data by excess method, both of these
effects were carefully taken into account by determining the exposure map of our
observations by simulations incorporating these effects along with other particularities
of our observations and by correcting of our observed data by dividing it by the exposure
map in galactic coordinates.
3.2. Distributions of number of EAS events in error circles
Here we discuss the distribution of number of EAS events falling in the error circles
of different radii as determined according to the aforementioned procedure. We first
present the results for each of the sets of 1000 randomly chosen error circles. Fig.2
shows the histogram of frequency of occurrence of number of circles with respect to the
number of EAS falling in the error circle. The histograms distributions corresponding
to different radii of error circles are shown here as illustration. These for other radii
show similar distributions and all these distributions nearly fit gaussian distributions
with a mean and a variance which increase with increasing radius. This result is very
assuring and shows the correctness of our sophisticated numerical procedure and the
validity of using the mean number of events, in these randomly chosen locations of
error circles in the sky to compare with the number of events falling in the error circle
countered about the moving moon. Fig.3 shows the variation of the mean number of
events of these distribution as a function of the chosen radius of the error circles. It is
seen that these calculated means show a nearly exact dependence on the square of the
radius. This result is not surprising and is exactly what one would expect to get from
a correct random sampling of statistical data. However, in view of the complexity and
sophistication involved in our entire procedure (with inclusion of the weight factors),
this result is again very assuring and shows that we can use these mean number of
events to compare with that falling in the error circles centered about the moving moon
and rule out the possibility of the deficit in the number of events falling in the moon
centered circle as due to statistical fluctuation. In Fig.3 we have also shown the number
of events falling in the moon-countered circles for comparison with the means of the
random samplings. It is seen that in every case( for every chosen error circle radius) the
deficit of number of EAS from the direction of the moving moon is quite significant as
compared to the error bars of the mean of random sampling( Fig.3) which is taken as
the variance of nearly gaussian distributions of Fig.2. As seen here the deficit which is
from 1.6 to about 7.1 times the standard deviation of the mean of random distributions
is quite significant and since it is definitely associated with the moving moon it must be
associated with some moon- related phenomenon. We will not discuss this phenomenon
here and rather simply call it the shadow of the moon in our EAS observed data.
Investigation of Energy Spectrum of EGRET Gamma-ray... 6
3.3. Estimation of energy thresholds
Our detected EAS events are a mixture of cosmic-ray and gamma-ray events. In E1 the
total number of EAS events was 53,907 and the duration of the experiment was 501,460
seconds. So the mean event rate of the first experiment was 0.1075 events per second.
The distribution of the time between successive events was investigated and found to be
in good agreement with an exponential function, indicating that our event sampling is
completely random [16]. In E2 the total number of events was 173,765 and the duration
of the second experiment was 2,902,857 seconds, so its mean event rate was 0.05986
events per second.
We refined the data to separate out the acceptable events. Events are acceptable if
there is a good coincidence between the four scintillator pulses, also we omitted the
events with zenith angles more than 60◦ because of their less accuracy. Therefore after
these separations we obtained smaller data sets of 46,334 and 120,331 events for E1 and
E2 respectively. Since we cannot determine the energy of the showers on an event by
event basis, we estimate our lower energy threshold by comparing our event rate to the
following cosmic-ray integral spectrum [17],
J(E) = 2.78× 10−5E−2.22 + 9.66× 10−6E−1.62
− 1.94× 10−12 40 ≤ E ≤ 5000 TeV (5)
The obtained lower energy limits are 39 TeV in E1 and 54 TeV in E2. The
calculated mean energies with above energy spectrum are 94 and 132 TeV in E1 and
E2, respectively. Since the distribution of cosmic-ray events within the array around
these energy ranges is homogeneous and isotropic, we used an excess method [18] to find
signatures of the EGRET 3rd catalogue gamma-ray sources. This method was used for
both E1 and E2.
4. Calculation of effective area and time
Number of secondary particles in the growth profile of EAS events increases in
atmosphere until the shower maximum and then decreases after it. In energy of about
100 TeV the shower maximum height is at about 500g cm−2 and a fraction of these
secondary particles arrive to the ground level particle detectors of our array at Tehran
level (1200 m≡ 890 g cm−2).
For calculating the effective surface of each experiment (E1 and E2) we used Greisen
lateral distribution of electrons which is known the NKG formula [19] and CORSIKA
simulation code [20] for the simulation of the two sets of proton showers with energy
thresholds of 39 TeV and 54 TeV respectively for E1 and E2 at our array level. From
our logged EAS events we obtained a zenith distribution function for E1 and E2, which
the mean zenith angles are 26◦ for both of them. Also we calculated the z̄ which was
obtained from the weight curve of the zenith distribution dN/dz ∝ cosn z sin z and we
obtained the 26◦ too. This weight curve was obtained by fitting the function dN/dz to
Investigation of Energy Spectrum of EGRET Gamma-ray... 7
our data in the E1 and E2 with n = 5.00. So in the first approximation we used the
effective thickness of the passed atmosphere as 890g cm−2/ cos(26◦) = 980g cm−2. In
the thickness, the average number of the secondary particles for the two experiments
are NE1 = 5265 and NE2 = 8571, these two numbers obtained from 1000 simulated
proton showers for each energy threshold. So based on the NKG formula the mean
effective surfaces of EAS events at Tehran level are 965 m2 and 2173 m2 for E1 and
E2 respectively. With these results we could obtain the mean effective surface of our
array in the upper level of the atmosphere (The surface that if a primary particle passes
through it, the array could detect its EAS events) 718m2 and 1751m2 for E1 and E2
respectively.
For calculation of the effective time of observation of each source in every 24 hours, we
used the spherical geometry and the track of each source in the local coordinates. Each
source with its celestial coordinates right Ascention, Declination (RA,Dec) is introduced
in the 3rd EGRET catalogue. Time duration of each source is calculated by reaching the
source to the zenith angle of 60◦ from the direction of east to the same zenith angle from
the west, and the distribution function dN/dz =∝ cosn z sin z which is related to the
zenith distribution effect [1]. Finally we obtained the mean effective time of observation
of our array for all 10 sources equivalent to 4h,28
(equivalent to existence of 4h,28
the source at zenith) for every 24 hours. The FOV of our array with the 60◦ zenith
angle cutoff is π steradian. With these calculated factors we obtained fluxes(events
cm−2s−1sr−1) for each of the 10 sources in E1 and E2 which are shown in Table 1.
5. Results
Our results have been compared with the EGRET results. For each source we have
fluxes and energies from EGRET, E1 and E2, so we extracted a spectral index for each
source and compared it with the reported spectral index of EGRET. Some information
about the 10 EGRET sources like Name, RA, Dec, and spectral index and its error,
(γ ± ∆γ)EGT , are from the 3rd EGRET catalogue [2]. Other information like mean
energy for E1 and E2 which are 94TeV and 132TeV respectively (are not shown in the
table), fluxes of the two experiments and spectral indexes and their errors, (γ±∆γ)OUR,
have been calculated in this analysis. The last column shows the agreement of our
spectral indices to its in the 3rd EGRET catalogue.
5.1. Result of Energy Analysis with Simulated Showers
For further energy analysis of our measured data of EAS events observed at our
site we have used the CORSIKA code[20] to simulate showers with the inclusion
of geomagnetic field pertinent to the location of our site from data provided by
http://www.ngdc.noaa.gov. We have simulated a total of 7350 showers entering the
top of atmosphere at various zenith angles (0◦, 15◦, 30◦, 45◦, 60◦) and for each zenith
angle at 12 various azimuth angles ranging from 0◦ to 360◦ every 30◦. For each angle
http://www.ngdc.noaa.gov
Investigation of Energy Spectrum of EGRET Gamma-ray... 8
the simulations were repeated 10 times for energies less than 50 TeV and 5 times for
energies greater than 50 TeV with separately 10 TeV intervals from 10 TeV to 100 TeV.
These simulations were carried out similarly for entering protons as well as gamma-
rays. For each simulation the number of secondary charged particles of the simulated
shower at the height of observation of our site was determined from CORSIKA code.
In order to make an energy analysis comparing gamma-ray initiated showers with those
initiated by protons in our observations we have calculated a mean number of secondary
shower particles for each energy by averaging over all the angles using the site-specific
weight factor discussed in sec 3.1(Eq. 4). The ratio of angle-averaged mean of number
of secondary charged particles in gamma-ray initiated showers to that of the mean for
proton-initiated showers is shown in Fig.4 as a function of energy in the energy range of
our simulations. The ratio shown here incorporates almost all of related particularities of
our experiments. Since in our observations we have used exactly identical experimental
procedure, equipment, thresholds and set-ups for all of the recorded showers irrespective
of the nature of the radiation which initiates the shower the relative detection efficiency
of our array and observations could only depend on the ratio of these means depicted in
Fig.4. Now we use the relative detection efficiency calculated from simulated data and
shown in Fig.4 to estimate the relative number of gamma-ray initiated showers to that
initiated by protons, using the known energy spectrum of proton showers of the form
= Np10(
10TeV
)−Γp. (6)
Where dNp is the number of proton showers in the energy interval E to E + dE, Np10
is a constant and Γp is the spectral index of EAS producing protons. Now denoting our
array’s relative detection efficiency by η(E), we can write for the expected differential
number of gamma-ray initiated showers:
= η(E)Np10(
10TeV
)−Γγ (7)
where Γγ is the spectral index of EAS producing gamma- rays. Dividing Eq.7 by Eq.6
and upon integration from a threshold energy to infinity, the ratio of observed gamma-
ray EAS events to that initiated by protons is obtained. Thus we write:
NγEAS
NpEAS
η(E)E−Γγ dE
E−Γp dE
where Et is assumed threshold energy. For the energy range covered in this analysis,
we use Γp = 2.7 and for gamma-ray spectral index we use the mean value of the
spectral indices that we have estimated above (Table.1) for the sources with the highest
statistical significance (those observed at a statistical significance level of higher than
1.5σ). Thus using our estimations of table 1 we have Γγ = 2.3. In order to carry out
the integrations in Eq.8 we are forced to impose a truncation since with our rather
limited computer shower simulations we only have η(E) for 10TeV < E < 100TeV . For
the sake of numerical consistency, we have imposed this truncation to E=100 TeV in
Investigation of Energy Spectrum of EGRET Gamma-ray... 9
Name(3EG J) RA,Dec ID (γ ±∆γ)EGT logFE1 logFE2 (γ ±∆γ)OUR |γOUR − γEGT |
0237+1635 39.3,16.5 A 1.85±0.12 -11.25 -11.53 1.90±0.27 0.05
0407+1710 61.8,17.1 2.93±0.37 -10.77 -11.45 4.20±0.40 1.27
0426+1333 66.6,13.5 2.17±0.25 -11.11 -11.28 1.15±0.48 1.02
0808+5114 122.1,51.2 a 2.76±0.34 -11.01 -11.58 3.87±0.42 1.11
1104+3809 126.1,38.1 A 1.57±0.15 -11.10 -11.72 4.21±0.50 2.64
1308+8744 197.0,87.7 2.17±0.66 -10.96 -11.53 3.87±0.45 1.70
1608+1055 242.1,10.9 A 2.63±0.24 -10.92 -11.72 4.34±0.50 1.71
1824+3441 276.2,34.6 2.03±0.50 -10.65 -11.25 4.07±0.35 2.04
2036+1132 309.1,11.5 A 2.83±0.26 -11.08 -11.73 4.41±0.53 1.58
2209+2401 332.4,24.0 A 2.48±0.50 -10.91 -11.31 2.71±0.42 0.23
Table 1. Comparison of our spectral indices of the 10 sources with the spectral indices
of them which is introduced by the 3rd EGRET catalogue. The last column shows
agreement of our spectral indices to EGRET spectral indices.
the denominator of Eq.8 as well as its numerator. The result of these calculations
obviously depend on the value of an assumed threshold energy, Et, therefore the
numerical calculations were repeated for values of Et from 10 TeV to 100 TeV with
10 TeV intervals. The result of these calculations, that is, the ratio of the number of
gamma-ray EAS events to that of proton EAS events expected to be detected in our
experiments at our site is shown as a function of the threshold energy in Fig.5. Here
we see that this ratio shows a maximum at a value of Et = 40 TeV which very nearly
corresponds to the lower value of the two threshold energies of our two experiments.
6. Concluding remarks
We believe the main reasons for success in these observations and investigations on
EGRET gamma-ray point sources despite the low statistics of ∼ 3 × 105 EAS events
from our small array of ALBORZ prototype observatory, relies on the following two
favorite points of strength:
(1) we have intensively studied the location- dependent factors which influence shower
development and shower count from various angular bins in the sky. These factors
are the mass of the overlying atmosphere and anisotropy in azimuth angles which it is
attributed to the effect of the geomagnetic field [21], [13], [22]. For our particular site
we investigated these effects which are in form of Eqs. 1 and 2. We carefully refined our
data from these effects finally the investigation of the EGRET gamma-ray point sources
are based on the corrected data.
(2) Our site and the duration of our observations in the data set have been such that 10
of the EGRET gamma-ray point sources have crossed our site at small enough zenith
angles to make their observation possible at least with a statistical significance of 1.5σ
with Li and Ma criterion in the excess method which we have used[1]. In order to
Investigation of Energy Spectrum of EGRET Gamma-ray... 10
investigate this rather fortunate point for our site and the time of these observations,
we have calculated the average zenith all angle of passage of each of 271 EGRET gamma-
ray point sources during our entire observation period, for each of these sources. We
have also calculated the statistical significance(number of sigma) for excess counts from
these sources. The result is shown here in Fig.1 and it convincingly shows an inverse
correlation between the statistical significance of excess shower counts from the EGRET
point source location and the average zenith angle of the transit of the source over our
site. The computed coefficient of this correlation(correlation between inverse statistical
significance and z) is 0.77.
Obviously the EGRET sources investigated here are those with highest statistical
significance corresponding to the lowest zenith angles of the passage of the source over
our site.
Our results shows that our spectral indices within error limits are in agreement with
EGRET spectral indices for most of the considered here.
For the calculation of the effective area of the EAS events at first , we calculated the
primary particle energy, then we extracted the number of the secondary particles from
a set of CORSIKA simulations, and finally we used the Greizen lateral distribution for
these particles. In the near future with a larger array and larger set of logged EAS
events at ALBORZ observatory we hope to calculate these results more accurately.
It is worth remarking that due to increased probability of pair- production interaction of
VHE and UHE gamma-rays with various low energy universal photons, the absorption
of these gamma-rays becomes significant for sources located at cosmological distances.
This absorption has been studied extensively [23, 24, 25]. The lack of observation of
VHE and UHE gamma-rays from extragalactic EGRET gamma-ray sources has been
generally attributed to the absorption of the gamma-rays from these sources which are
located at cosmological distances.
Stecker and De Jager (1997) gave a parametric relation for optical depth (τj) as a
function of the source gamma energy (ETeV ) and red shift (z) for the two models (j=1,2)
they have studied. For the 39TeV energy threshold of our experiments, we use their
parametric relation with an optical depth of unity to calculate the red shift of the
sources we have observed in our EAS experiments and have investigated here(Table 1).
The result is z=0.0032 for their model 1 and z=0.0024 for their model 2. Ong,[26] have
listed the red shifts of two classes of EGRET extragalactic sources and the calculated red
shifts for the sources investigated here is smaller than red shifts listed for these classes
of objects. However, we should remark that the recent discovery of the unexpected by
hard spectra of the Blazar sources observed in HESS data [27] bear as the possibility of
observation of EGRET gamma-ray point sources at higher energies. It would be open
for future ground-base observations.
The energy analysis carried out here using simulated shows with CORSIKA has shown
that the ratio of number of gamma-ray generated EAS events expected to be detected
at our site relative to the number of proton- generated EAS events show a maximum at
a value of 40 TeV for the threshold energy of observation of EAS events at our site. The
Investigation of Energy Spectrum of EGRET Gamma-ray... 11
fortunate fact that this value corresponds to the lower value of the threshold energies of
our two experiments, provides further support for the fact that the data collected in our
experiments at our site has had this extra advantageous attribute for the observation of
gamma-ray initiated EAS events in the 10 TeV to 100 TeV energy range and thus the
extra advantage for observing gamma-ray point sources in this range.
7. acknowledgements
This research was supported by a grant from the national research council of Iran for
basic sciences. The many useful and conductive comments by anonymous referee is very
much appreciated. Also many thank from Prof. James Matthews for his comments and
attentions to our works at ICRC 2005, Pune, India.
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Investigation of Energy Spectrum of EGRET Gamma-ray... 12
Figure 1. Distribution of statistical significance versus average zenith angle of transit
of calculated for 271 EGRET gamma-ray sources over our site(only sources with
significance > 1.5σ are shown.).
Investigation of Energy Spectrum of EGRET Gamma-ray... 13
Figure 2. Histograms show the frequency of circles of error with radius ρ and random
chosen centers in the sky vs. the number of EAS events falling in each error circle.
Investigation of Energy Spectrum of EGRET Gamma-ray... 14
Figure 3. Dependence of the mean number of EAS events falling in the random error
circles as a function of the radius of the error circle, ρ. Smooth curve shows a ρ2
dependence. Error bars are the standard deviation of the distribution shown in Fig.2,
and statistical errors for the moon. Open circles (◦) are random error circles. Filled
circles(•) are error circles centered about the location of the moving moon.
Investigation of Energy Spectrum of EGRET Gamma-ray... 15
Figure 4. The ratio of the mean number of secondary charged particles at the location
of our site produced in gamma-ray generated simulated Extensive Air Shower to that
produced by proton generated showers as a function of the energy of the primary
radiation( Gamma-ray and proton) entering the top of the atmosphere.
Investigation of Energy Spectrum of EGRET Gamma-ray... 16
Figure 5. The ratio of the mean number of gamma-ray generated showers to that
of proton generated showers expected to be observed at our site as a function of the
threshold energy of our experiments.
	Introduction
	Experimental arrangement
	Data Analysis
	Shadow of the moon
	Distributions of number of EAS events in error circles
	Estimation of energy thresholds
	Calculation of effective area and time
	Results
	Result of Energy Analysis with Simulated Showers
	Concluding remarks
	acknowledgements
