30 TH I NTERNATIONAL C OSMIC R AY C ONFERENCE

Influence of hadronic interaction models on the muon multiplicity distribution of airshowers observed with the GRAPES-3 experiment at Ooty
H. TANAKA1 , S.K. GUPTA1 , K. HAYASHI2 , Y. H AYASHI2 , N. I TO2 , A. I YER1 , P. JAGADEESAN1 ,A. JAIN1 , S. K ARTHIKEYAN1 , S. K AWAKAMI2 , H. KOJIMA3 , T. M ATSUYAMA2 , M. M INAMINO2 ,P.K. MOHANTY1 , S.D. M ORRIS1 , P.K. NAYAK1 , T. N ONAKA2 , S. O GIO2 , T. O KUDA2 , A. O SHIMA2 ,B.S. R AO1 , K.C. RAVINDRAN1 , M. S ASANO2 , N. S HIMIZU2 , K. SIVAPRASAD1 , S.C. T ONWAR1 ,T. YOSHIKOSHI2
1Tata Institute of Fundamental Research
2Osaka City University
3Nagoya Women’s University
tanaka@tifr.res.in
Abstract: The GRAPES-3 experiment observes extensive air showers using a high-density array ofscintillation detectors and a large area tracking muon detector. We have studied the relationship between
the muon multiplicity distribution and shower size for the GRAPES-3 data taken during the period of2000 - 2001. In order to extract the spectra for various nuclear groups namely H, He, N, Al and Fe fromthese observations, Monte Carlo simulations using CORSIKA code have been performed. SIBYLL 2.1,
QGSJET01 and QGSJET-II hadronic interaction models have been used for this investigation and ourresultant spectra were compared with the direct measurements obtained from balloon and satellite borne
experiments. Less of distinction was found between the results expected from SIBYLL and QGSJET-II.

Introduction
There is a rather sudden change in index of energy
spectrum of primary cosmic rays (PCRs) around1015 eV, so it is called the “knee”. Some modelsof “knee” claim that the composition of the PCRs
should change in this energy region.
We noticed through Monte Carlo simulations (MC)that the muon multiplicity distribution (MMD) inlarge detectors can help in the studies on energy
spectrum of various nuclear component of PCRs.
The PCR energy spectrum can be estimated from
EAS’s size (total number of charged particles)
spectrum. So, to obtain the precise size of EASdense array of detectors is desirable. Since MMDs
strongly depend on nuclear species of PCRs, one
can utilize the MMDs to find out the relative abundance of primary nuclear components, such as Proton, Helium, N, Al and Fe groups.
Different nuclear interaction models in MC yield
different MMDs, so we have tried to find out theproper nuclear interaction model by comparing ourobserved data with the data of direct measurements. Since we introduced dense array of scintillation detectors and large area muon detectors at
the mountain altitude, it has become possible.

GRAPES-3 experiment
The GRAPES-3 experiment is being operated atOoty (11.4◦ N, 76.7◦ E, 2200 m a.s.l.) in southern India. The EAS array consists of 257 scintillators, each 1 m2 in area with inter-detector separation of only 8 m (fig. 1). The 560 m2 GRAPES3 muon detector consists of 16 tracking modules(each 35 m2 in area and energy threshold of 1 GeV
for vertical muons), which provides reliable measurement of muon multiplicity even for low energy
EAS. [1, 2]
A total of 6×108 EAS collected over a live-time of4.71 × 107 s have been analyzed. Triggering rate
was about 13 Hz during this period. Various conditions (yellow shaded area) were imposed in selec-

I NFLUENCE OF HADRONIC INTERACTION MODELS ON THE MUON MULTIPLICITY DISTRIBUTION

Figure 3: Red, blue and green lines show distributions of the numbers of muons with SIBYLL,QGSJET-II and QGSJET01, respectively.

Figure 1: 257 Scintillation Detectors N (each 1 m2 )and 16 Muon Detectors  (each 35 m2 )tion of EAS for getting size spectrum and MMDsin fig. 1.

EAS simulation
The EAS events were generated through CORSIKA (v6.50) [3] MC simulation by using SIBYLL(v2.1) [4] and QGSJET-II (v03) [5] interaction
models for high energy interactions and GHEISHA
for interactions below 80 GeV in order to evaluate the composition of PCRs. MC EASs using
QGSJET01 [6] (CORSIKA v6.02) model are also
shown for comparison.

Figure 2: Red, blue and green lines show distributions of the numbers of electrons with SIBYLL,QGSJET-II and QGSJET01, respectively.
Figure 2 and 3 show distribution of the electron(Ek > 1 MeV) numbers and the muon (Ek >1 GeV) numbers at the altitude of observatory. Leftpanels are results from vertical incidence protonprimaries whose energies are 100 TeV and rightpanels are results from iron primaries in both fig-ures. QGSJET-II model is seen to be similar toSIBYLL for the electron results and similar toQGSJET01 for the muon results.
Henceforth, MC data were generated from Proton,Helium, N, Al and Fe primaries whose energies
followed power spectrum and whose incidence angles and core locations were determined randomlyto compare with observed data.
Though NKG approximation is used for theelectromagnetic component of EAS, differences
between this approximation and full-MC with
EGS4 [7] are considered including detector response [8]. Those generated EAS events were analyzed with the same manner as observed events.

EAS analysis
Various EAS parameters, size (Ne ), core location(X0 , Y0 ) and age (s) are estimated by fitting aNKG function to the lateral distribution, using themaximum likelihood algorithm with MINUIT [9].
The muon track reconstruction efficiency was measured and incorporated into simulations. Generating EAS events with MC, one can get the muon
multiplicity in the muon detectors. Since the number of muons in a detector is counted by individual
track of muon and not in terms of pulse height ofthe proportional counter, the accuracy in counting
is very good. Effect of geometrical track overlapping has been corrected through MC. All the EAS
are summed up with their size in intervals of 0.2
in log10 (Ne ). Then we get the distribution of total
number of detected muons for particular size bin.
Every one size bin contains PCRs of various nuclear groups covering a relatively broader range ofenergies. Each nuclear group has its own MMDs,

30 TH I NTERNATIONAL C OSMIC R AY C ONFERENCE

as can be seen in fig. 4. Fig. 4 (a) and (b) shows examples of the relative abundance of nuclear components for different nuclear groups in two size regions.

Normalized Number of Showers(a)(b)SumN

AlHeFeH

Detected Muon NumberFigure 4: Observed and simulated (SIBYLL) distribution of multiple muons for two size bins. (a)104.2 ≤ Ne < 104.4 , (b) 105.0 ≤ Ne < 105.2
Since different nuclei contribute different amountof muons, one has to adjust the contribution fromevery nuclear group to fit the observed MMDs. By
fitting the MC MMDs to the observed MMDs, relative abundance of each nuclear group can be estimated.
considering there is significant overlap between theMMDs for the Al and Fe groups, these two distributions are combined assuming an abundance ratio(Al/Fe) of 0.8 based on direct measurements.
Using this relative abundance data, the energyspectrum of PCRs can be obtained from size spectrum.

Energy spectra
The PCRs’ energy spectrum of each nuclear component can be estimated from the EAS’s size spectrum by utilizing MMDs.
Relation between average PCRs’ energy hE0 i andaverage size hNe i was calculated through MC. To
obtain this relation we applied the same conditions
as experimental one, triggering, core location etc.
Size is converted to energy in the following manner.

1. Generate showers through MC assuming
PCRs energy spectrum with intensity ofPCRs as dI/dE0 ∝ E0−2.7 .
2. Classify these EASs in their size interval of
0.2 in log10 (Ne ) and get MMD for each size
bin for each nuclear group.
3. Using least χ2 method, adjust the relative
abundance for four groups (Proton, He, Nand combination Al + Fe) by fitting the MC’s
MMDs to the observed MMD for each sizebin.
4. Multiply the amount of relative abundancewith intensity of particular size bin in size
spectrum.
5. Convert a size hNe i to energy of PCRs using
relation between hNe i and hE0 i.
Now, intensity of a nucleus with an energy is obtained. Thus we obtain the energy spectra for eachnuclear group. They are shown in fig. 5.
There are obvious difference between spectra ofQGSJET01 and others in spectrum of each nuclear
group. However, obtained spectra from QGSJET-II
are much closer to the spectra from SIBYLL. Theenergy spectra of protons based on SIBYLL andQGSJET-II models seems to well overlap with direct measurement like JACEE. But there is big discrepancy with QGSJET01’s especially for heavier
nuclei.

SummaryAn analysis of 6 × 108 EAS and their associated muon content in the GRAPES-3 experimentis used to study the muon multiplicity distribution
as a function of Ne . The observed data were compared with the results obtained by simulation, using three hadronic interaction models, QGSJET01,
SIBYLL and QGSJET-II. SIBYLL and QGSJETII seem to provide better description of particle interactions at energies ∼ 1014 − 1015 eV. One cansee good agreement between the GRAPES-3 results and direct measurements of various nuclear
groups.

I NFLUENCE OF HADRONIC INTERACTION MODELS ON THE MUON MULTIPLICITY DISTRIBUTION

References

Figure 5: Energy spectra of H (a), He (b), N(c), Al (d) and Fe (e) groups from GRAPES-3(• SIBYLL,  QGSJET-II, N QGSJET01) andcorresponding spectra from direct measurements,
NRyan [10], •SOKOL [11], JACEE [12][13] and RUNJOB [14].

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