SciPost Phys. Proc. 13, 033 (2023)

Update on the angular resolution of GRAPES-3
experiment based on Moon shadow analysis
D. Pattanaik1, 2⋆ , S. Ahmad3 , M. Chakraborty1 , S. R. Dugad1 , U. D. Goswami4 ,S. K. Gupta1 , B. Hariharan1 , Y. Hayashi5 , P. Jagadeesan1 , A. Jain1 , P. Jain6 ,S. Kawakami5 , H. Kojima7 , S. Mahapatra2 , P. K. Mohanty1 , R. Moharana8 ,Y. Muraki9 , P. K. Nayak1 , T. Nonaka10 , A. Oshima7 , B. P. Pant8 ,M. Rameez1 , K. Ramesh1 , L. V. Reddy1 , S. Shibata7 , F. Varsi6 and M. Zuberi1
1 Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Utkal University, Bhubaneshwar 751004, India
3 Aligarh Muslim University, Aligarh 202002, India
4 Dibrugarh University, Dibrugarh 786004, India
5 Graduate School of Science, Osaka City University, Osaka 558-8585, Japan
6 Indian Institute of Technology Kanpur, Kanpur 208016, India
7 College of Engineering, Chubu University, Kasugai, Aichi 487-8501, Japan
8 Indian Institute of Technology Jodhpur, Jodhpur 342037, India9 Institute for Space-Earth Environmental Research, Nagoya University,Nagoya 464-8601, Japan
10 Institute for Cosmic Ray Research, Tokyo University, Kashiwa, Chiba 277-8582, Japan⋆ diptiranphy@gmail.com

21st International Symposium on Very High Energy Cosmic Ray Interactions(ISVHECRI 2022)
Online, 23-28 May 2022
doi:10.21468/SciPostPhysProc.13

Abstract
GRAPES-3 is an extensive air shower array located at Ooty (11.6◦ N, 76.7◦ E, 2200 ma.s.l.) in southern India. Recently, the angular resolution of the GRAPES-3 array has
been improved by correcting the shower front curvature based on the shower size andage. Here, we present the results of the angular resolution and pointing accuracy of
the array through observation of the Moon shadow. We have analyzed the data for theperiod of 2014-2016 containing ∼ 3×109 air shower events with a median energy of 15
TeV. A significant improvement in the angular resolution has been observed compared tothe earlier analysis by the group through the Moon shadow method and is comparable
to the arrays located at a 2 km higher altitude than the GRAPES-3 experiment.
Copyright D. Pattanaik et al.
This work is licensed under the Creative Commons
Attribution 4.0 International License.
Published by the SciPost Foundation.

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Received 01-09-2022
Accepted 22-06-2023
Check forupdates
Published 29-09-2023
doi:10.21468/SciPostPhysProc.13.033

SciPost Phys. Proc. 13, 033 (2023)

1

Introduction

In the last decade, there has been a significant advancement in the field of very high energy
gamma-ray astronomy. Due to the large area and more than 90% duty cycle, the ground based
air shower observatories are well equipped to detect the very high energy gamma rays. The fluxof the gamma rays is small compared to the large cosmic-ray background. This generally makes
the detection of gamma rays challenging. However, improving the angular resolution canreject large cosmic-ray backgrounds. In addition, efficient gamma-hadron separation can leadto a further reduction in the background. With these two methods, ground based experiments
are able to detect gamma rays. Large extensive air shower array experiments like Tibet ASγ [1],HAWC [2], and LHAASO [3, 4] have already implied the presence of Pevatrons (PeV electronaccelerators) by detecting gamma rays above 100 TeV up to several PeV.
An excellent angular resolution of the air shower array can be obtained by precise measurement of the arrival time of the air shower. A recent result from the GRAPES-3 experimenthas shown that the shower front curvature depends on the shower size and age [5]. If appropriately corrected, the angular resolution can be further improved. The angular resolution canbe determined from the Moon shadow method, as suggested by Clark in 1957 [6]. In addition, the Moon shadow method also determines the absolute pointing of the detector, which
describes the offset in the location of any point source. In this work, we have observed theMoon shadow in the cosmic rays and determined the angular resolution and pointing accuracyof the GRAPES-3 air shower array.

2The GRAPES-3 experiment

GRAPES-3 is an extensive air shower array located in Ooty (11.4◦ N, 76.7◦ E, and 2200 ma.s.l.), southern India. There are 400 scintillator detectors deployed over an area of 25000
m2 [7], and a large area muon telescope (560 m2 ) [8] is located near the periphery of thearray. Fig.1 shows the schematic representation of the GRAPES-3 array with the scintillator
detectors arranged in a hexagonal geometry with an inter detector separation of 8 m and thelarge area muon telescope. The area enclosed within the dashed line is the fiducial area of thearray, which covers about an area of 14500 m2 . Each scintillator detector is designed to record
the charge content as well as the arrival time of the air showers. Recently, the commerciallyavailable Time to Digital Converter (TDC) units have been replaced by more advanced High
Performance Time to Digital Converter (HPTDC), which exhibits excellent linearity within adynamic range of 3.5 µs with an accuracy of 195 ps. Due to this upgrade, the shower arrival
time can be measured more precisely.

3Analysis method

To study the Moon shadow, we used three years of air shower data from 1 January 2014 to31 December 2016. A total of 2.98×109 events were recorded with a live time of 994.1 days.
The lateral particle density distribution was fitted with the Nishimura-Kamata-Greisen (NKG)
function. Only the adequately fitted events were considered for further analysis. In addition
to that, another cut was imposed on shower age (defined as the developmental stage of an airshower) to be within 0.2 to 1.8. To remove the contamination due to the large showers fallingoutside the array, the showers landing within the fiducial area (shown in Fig.1) are selected.
The zenith angle of the showers was restricted up to 40◦ .

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SciPost Phys. Proc. 13, 033 (2023)

EY (m)

500−50−100−50050SX (m)

Figure 1: A schematic plot of the GRAPES-3 array showing the scintillator detectors(solid blue markers) and the muon telescope (empty red squares). The dashed line
represents the fiducial area of the array covering about 14500 m2 .
A total of 10 different fake-Moon (background) regions were considered to find the cosmic
ray background level. Out of 10 fake-Moon regions, five regions are selected along negative
azimuthal (φ) directions, and other regions are selected along positive φ direction with a6◦ successive shift (±6◦ , ±12◦ , ±18◦ , ±24◦ , ±30◦ ). The zenith angles (θ ) of the fake-Moonregions were kept the same as Moon. The average of the background level was considered tobe the reference background. Then the relative deficit in the cosmic rays from the direction of
the Moon was calculated using the method explained in [9, 10].
In Fig.2, the cosmic ray flux deficit (%) from the Moon direction is shown as a function ofangular distance (ψ) from the Moon center. An apparent deficit in the flux can be observed atboth E > 50 TeV and E > 100 TeV. The relative deficit plot was then fitted with a 2-dimensionalGaussian function where the standard deviation (σ) represents the angular resolution. The2-d Gaussian expression is given in Eq.(1),N (ψ) = N0

ψ2M−ψ2(1)2σwhere ψ is the space angle measured from the center of the Moon, ψ M is the angular radiusof the Moon (0.26◦ ), and σ represents the angular resolution of the array. The angular resolution at energy above 50 TeV and 100 TeV was found to be 0.44◦ ± 0.07◦ and 0.38◦ ± 0.06◦
respectively.

4e 2σ2 ,2Results

The angular resolution was obtained at different integral energy bins. The energy dependenceof the angular resolution is shown in Fig.3. Obtained values are compared with the earlier
Moon shadow analysis done by GRAPES-3 using 2000 to 2003 data [11]. A significant improvement in the angular resolution in the recent analysis can be observed, particularly in low
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SciPost Phys. Proc. 13, 033 (2023)

5

Cosmic ray flux deficit (%)

0−5

E > 50 TeV

−10
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.50−10E > 100 TeV−20
0.00.5

1.0

1.5

2.0

2.5

3.0

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Angular distance from Moon, ψ (degree)

Figure 2: The relative deficit (%) in the cosmic rays flux from the direction of theMoon is shown as a function of angular distance from the Moon center for Energy
above 50 TeV and 100 TeV. The deficit plot is fitted with a 2-dimensional Gaussianfunction to determine the angular resolution.
energies. It has to be noted that the earlier analysis was carried out considering a constantslope value of the shower front curvature, while in this analysis, the shower front curvature
was corrected based on the shower size and age. The improved angular resolution agrees withthe angular resolution estimated using the Left-Right array division method. In the Left-Rightmethod, the entire array is divided into two sub-arrays based on the line joining the array
center and the shower core. By comparing the angle reconstructed from the sub-arrays, theangular resolution is estimated. The detailed method is explained in [5]. This confirms theobservation made by the GRAPES-3 experiment that the angular resolution of the array canbe improved by the shower size and age based curvature correction.
The other important aspect of studying the Moon shadow is to determine the absolute
pointing accuracy of the detector. For this, the GRAPES-3 event coordinates (θ and φ) weretransformed into the equatorial coordinates (α = right ascension and δ = declination). Using
the HEALPix framework, a 2-dimensional relative intensity map was generated between ∆δ(∆δ = δevent - δ M oon ) and ∆α (∆α = αevent − α M oon ). By subtracting the Moon coordinatesfrom the events, the position of the Moon was shifted to the center of the map. From thedeviation in the observed Moon shadow position from the center, the pointing in α and δ wasestimated [10]. In Fig.4, the relative intensity map is shown, where the blue marker represents
the center of the map while the red circle is an ideal representation of the Moon. From theposition of the maximum deficit, the pointing in α and δ was obtained to be 0.032◦ ± 0.004◦
and 0.09◦ ± 0.003◦ .

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Angular resolution (degrees)

SciPost Phys. Proc. 13, 033 (2023)

1.5

Moon shadow (Oshima et al., 2010)
Moon shadow (Pattanaik et al., 2022)
Left-Right (Pattanaik et al., 2022)

1.00.50.0102
Energy (TeV)

10Δδ (δevent – δMoon) (degree)

Figure 3: Variation of the angular resolution obtained from the Moon shadow method
is shown (red circles) as a function of energy. A clear improvement in the angularresolution can be observed from the earlier Moon shadow analysis (blue squares).
The values obtained from the new analysis method are consistent with the angularresolution obtained from the Left-Right method (green triangles).

Δα (αevent – αMoon) (degree)

Figure 4: Relative intensity map of the Moon shadow between ∆δ and ∆α.

5ConclusionCompared to the earlier reconstruction method, the new method with shower size and age
dependent corrections to the shower front has significantly improved the angular resolution.
The angular resolution of the array was obtained to be 0.83◦ ± 0.09◦ with a pointing accuracyof 0.032◦ ± 0.004◦ and 0.09◦ ± 0.003◦ along α and δ, respectively. The pointing accuracy issmaller than the uncertainty in the angular resolution. Even though the GRAPES-3 experimentis located at an altitude of 2200 m, the angular resolution is comparable to the other experiments which are located at twice the altitude of GRAPES-3. In addition to that, the angular
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SciPost Phys. Proc. 13, 033 (2023)

resolution of the array improves to about less than half a degree above 50 TeV energies. Hencethe GRAPES-3 experiment is suitable for detecting multi-TeV (E > 50 TeV) gamma rays fromthe southern as well as northern sky due to its equatorial location.

Acknowledgements
We are grateful to D.B. Arjunan, A.S. Bosco, V. Jeyakumar, S. Kingston, N.K. Lokre, K. Manjunath, S. Murugapandian, S. Pandurangan, B. Rajesh, R. Ravi, V. Santoshkumar, S. Sathyaraj,M.S. Shareef, C. Shobana, R. Sureshkumar for their role in the efficient running of the experiment.
Funding information We acknowledge the support of the Department of Atomic Energy,
Government of India, under Project Identification No. RTI4002. This work was partially
supported by grants from Chubu University, ISEE of Nagoya University and ICRR of Tokyo
University, Japan.

References[1] M. Amenomori et al., First detection of photons with energy beyond
100 TeV from an astrophysical source, Phys. Rev. Lett. 123, 051101 (2019),
doi:10.1103/PhysRevLett.123.051101.
[2] A. U. Abeysekara et al., Measurement of the Crab Nebula spectrum past 100 TeV withHAWC, Astrophys. J. 881, 134 (2019), doi:10.3847/1538-4357/ab2f7d.
[3] Z. Cao et al., Peta-electron volt gamma-ray emission from the Crab Nebula, Science 373,425 (2021), doi:10.1126/science.abg5137.
[4] Z. Cao et al., Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ-ray galactic
sources, Nature 594, 33 (2021), doi:10.1038/s41586-021-03498-z.
[5] V. B. Jhansi et al., The angular resolution of GRAPES-3 EAS array after improved timing
and shower front curvature correction based on age and size, J. Cosmol. Astropart. Phys.
024 (2020), doi:10.1088/1475-7516/2020/07/024.
[6] G. W. Clark, Arrival directions of cosmic-ray air showers from the northern sky, Phys. Rev.
108, 450 (1957), doi:10.1103/PhysRev.108.450.
[7] S. K. Gupta et al., GRAPES-3 – A high-density air shower array for studies on the structurein the cosmic-ray energy spectrum near the knee, Nucl. Instrum. Methods Phys. Res. A 540,311 (2005), doi:10.1016/j.nima.2004.11.025.
[8] Y. Hayashi et al., A large area muon tracking detector for ultra-high energy cosmic rayastrophysics – The GRAPES-3 experiment, Nucl. Instrum. Methods Phys. Res. A 545, 643(2005), doi:10.1016/j.nima.2005.02.020.
[9] M. G. Aartsen et al., Observation of the cosmic-ray shadow of the Moon with IceCube, Phys.
Rev. D 89, 102004 (2014), doi:10.1103/PhysRevD.89.102004.
[10] D. Pattanaik et al., Validating the improved angular resolution of the GRAPES-3 air shower
array by observing the Moon shadow in cosmic rays, Phys. Rev. D 106, 022009 (2022),
doi:10.1103/PhysRevD.106.022009.
033.6

SciPost Phys. Proc. 13, 033 (2023)[11] A. Oshima et al., The angular resolution of the GRAPES-3
the shadows of the Moon and the Sun, Astropart. Phys. 33,
doi:10.1016/j.astropartphys.2009.12.004.

033.7

array from97 (2010),