Comparison of CORSIKA and COSMOS simulations
Soonyoung Roh, Jihee Kim, Katsuaki Kasahara, Eiji Kido, Akimichi Taketa, Dongsu Ryu, Hyesung Kang
aa r X i v : . [ a s t r o - ph . H E ] A p r Comparison of CORSIKA and COSMOS simulations
Soonyoung Roh ∗ , Jihee Kim ∗ , Katsuaki Kasahara † , Eiji Kido † , Akimichi Taketa ∗∗ ,Dongsu Ryu ∗ and Hyesung Kang ‡ ∗ Department of Astronomy and Space Science, Chungnam National University, Daejeon 305-764, Korea † Institute for Cosmic Ray Research, University of Tokyo, Chiba 277-8582, Japan ∗∗ Center for High Energy geophysics Research, Earthquake Research Institute, University of Tokyo, Chiba277-8582, Japan ‡ Department of Earth Sciences, Pusan National University, Pusan 609-735, Korea
Abstract.
Ultra-high-energy cosmic rays (UHECRs) refer to cosmic rays with energy above 10 eV. UHECR experimentsutilize simulations of extensive air shower to estimate the properties of UHECRs. The Telescope Array (TA) experimentemploys the Monte Carlo codes of CORSIKA and COSMOS to obtain EAS simulations. In this paper, we compare the resultsof the simulations obtained from CORSIKA and COSMOS and report differences between them in terms of the longitudinaldistribution, Xmax-value, calorimetric energy, and energy spectrum at ground. Keywords:
Ultra high energy cosmic rays — Air shower simulation: CORSIKA, COSMOS, FLUKA, QGSJET-II, PHITS, JAM
PACS:
I. INTRODUCTION
Ultra-high-energy cosmic rays (UHECRs) with energygreater than 10 eV arrive at Earth from space. Exper-iments to detect UHECRs utilize extensive air shower(EAS) to estimate their energy, composition and arrivaldirection. In an EAS, the cascade of interactions, inducedby a UHECR in the upper atmosphere, results in a verylarge number of secondary particles: of order 10 parti-cles for a primary particle with energy 10 eV.Monte Carlo codes have been used to simulate EAS.The codes reproduce cascades of particles initiated by theinteraction between primary UHECRs and atmosphericnuclei. EAS simulations give the spatial, temporal, en-ergy, and angular distributions of secondary, air showerparticles. To extract the information of primary particlesin experiments, that is, the energy, composition and ar-rival direction, the measured quantities of EAS need to becompared with those from simulations. Hence, the accu-rate reproduction of EAS is an essential part of UHECRexperiments.CORSIKA [1] and COSMOS [2] are among the MonteCarlo codes. Most experiments including the recent oneat the Pierre Auger Cosmic Ray Observatory have re-lied simulations from CORSIKA. On the other hand, theTelescope Array (TA) experiment [3] has employed bothCORSIKA and COSMOS, to cross-check the simula-tions from the codes. In this paper, we compare COR-SIKA and COSMOS simulations by examining the dif-ferences in the quantities such as the longitudinal dis-tribution, Xmax-value, calorimetric energy, and energyspectrum at ground in EAS. II. SIMULATIONS
We employed the most recent versions of codes: Ver-sion 7.54 for COSMOS and Version 6960 for CORSIKA.Each code has an option to set interaction models; dif-ferent interaction models result in somewhat differentresults. We chose the following interaction models: 1)for CORSIKA, QGSJETII-03 [4] for high-energy (above80 GeV) hadronic interactions, FLUKA (v.2008.3c) forlow-energy (below 80 GeV) hadronic interactions, andEGS4 for electromagnetic interactions, 2) for COSMOS,QGSJETII-03 for high-energy (above 80 GeV) hadronicinteractions, PHITS [5] and JAM [6] for low-energy (be-low 80 GeV) hadronic interactions, and Tasi’s and Nel-son’s formula for electromagnetic interactions. Pleasesee references for CORSIKA and COSMOS for details.The above interaction models are the default, so most-widely used models. In this paper, we intend to comparethe results of most-commonly employed CORSIKA andCOSMOS simulations. We note that even with the sameinteraction models, the results of CORSIKA and COS-MOS simulations could be different, because of the dif-ferences in handling the development of EAS. Compar-isons of CORSIKA and COSMOS simulations with dif-ferent interaction models will be reported in an upcomingjournal paper.We adopted exactly same parameters for CORSIKAand COSMOS simulations. For thinning parameter, 10 − was used (Hillas thinning algorithm) [7]. The groundlevel was located at 875 g/cm (1430 m), and the atmo-spheric depth and the Earth magnetic field suitable forthe TA site were applied. CORSIKACOSMOSPhoton 02•10 Electron 0 2•10 Muon0 200 400 600 800Vertical Atmospheric Depth [g/cm -2 ]0 1.0•10 Hadron
FIGURE 1.
Longitudinal development of proton EAS withthe primary energy 10 eV and the zenith angle 0 degree.Panels show the numbers of photons, electrons, muons, andhadrons as a function of atmospheric depth. Black lines are theCORSIKA results, while blue lines are the COSMOS results.The lines are averages of 50 shower events. We generated air shower events with cosine of thezenith angle of 1, 0.95, 0.9, · · · , 0.7 and primary energyof 10 . , 10 . , 10 , · · · , 10 . eV for proton and ironprimaries. Altogether, about 10,000 showers were gener-ated with each of CORSIKA and COSMOS. The resultsbelow are based on some of the shower simulations. III. COMPARISONS
1. LONGITUDINAL DISTRIBUTION
Figure 1 shows a typical longitudinal development ofair showers obtained with CORSIKA and COSMOS.Overall, the numbers of secondary particles are predictedto be larger with CORSIKA than with COSMOS. Thereare noticeable differences. For instance, the maximumdifference in the photon number reaches up to ∼ ∼
5% orless. Energy [GeV]650700750800850 S l a n t A t m o s ph er i c D e p t h [ g / c m - ] ProtonIronVertical shower CORSIKACOSMOS
FIGURE 2.
Xmax as a function of the primary energy. Theresults shown are for vertical showers with zenith angle 0degree. The upper part is for proton primaries, and the lowerpart is for iron primaries. Black dots are the CORSIKA results,while blue dots are the COSMOS results. Those are averagesof 50 shower events. Lines are least chi-square fits of points.
2. Xmax
Xmax is the atmospheric depth of the shower maxi-mum, specifically the maximum of the electron distribu-tion. It is one of most important quantities in UHECRexperiments; it is mainly used to determine the com-position. We employed the Geisser-Hillas function [8]to determine the longitudinal development and Xmax,which has been widely employed in other studies. Fig-ure 2 shows Xmax for both proton and iron primariesfrom COSMOS and the CORISKA simulations. In gen-eral, iron-initiated air showers penetrate less than proton-initiated air showers, so Xmax for iron primaries is lessthan that for proton primaries. And Xmax increases withthe energy of primaries. The agreement in COSMOS andthe CORSIKA simulations is reasonably good; the differ-ence in Xmax is only a few percent at most.
3. CALORIMETRIC ENERGY
As EASs develops, a part of the energy of primaryparticles ( E ) is deposited into air molecules and even-tually radiated as fluorescence lights. But a fraction ofthe energy is carried away by secondary particles, notcontributing to fluorescence lights. A correction for theso-called missing energy must be applied to the mea-surement of the calorimetric energy ( E cal ), in order tocorrectly determine the primary energy, E , from obser-vation of fluorescence lights. Here, we calculated themissing energy by following the prescription described Energy [GeV]0.900.920.940.960.981.00 E c a l/ E Vertical shower CORSIKACOSMOS
FIGURE 3.
Calorimetric energy as a function of the primaryenergy for proton primaries. The results shown are for verticalshowers with zenith angle 0 degree. Black dots are the COR-SIKA results, while blue dots are the COSMOS results. Thoseare averages of 50 shower events. Lines are least chi-square fitsof points. by [9], and so the calorimetric energy. Figure 3 showsthe resulting E cal for proton primaries from CORSIKAand COSMOS simulations. Our result indicates that E cal from COSMOS is ∼
2% larger than that from COR-SIKA. This implies that the primary energy estimatedwith fluorescence detector would be ∼
2% smaller whenCOSMOS simulations are used.
4. ENERGY DISTRIBUTION AT THE GROUND
As a consequence of EAS, a number of secondary par-ticles arrive at ground. In experiments, those particles areregistered by surface detectors and used to estimate theenergy and arrival direction of the primary particles. InFigures 4, 5, and 6, we compare the energy (rest-mass en-ergy no included) distribution of photons, electrons, andmuons reached at ground from CORSIKA and COSMOSsimulations. Particles in the core are included. The figureindicates a good agreement between the CORSIKA andCOSMOS results; the typical difference is ∼
3% or so.Although not shown here, the difference in the distribu-tion of hadrons is much larger. But again, the number andenergy of hadrons are much smaller than those of otherparticles.
IV. DISCUSSION
Monte Carlo codes of CORSIKA and COSMOS are cur-rently used to analyze the data of the TA experiment. In N u m be r o f pa r t i c l e s log Energy [GeV]Gamma COSMOS 7.54 P 1.0 19eVCORSIKA Fluka P 1.0 19eV
FIGURE 4.
Energy (rest-mass energy no included) distribu-tion of photons at ground over the entire ground for proton EASwith the primary energy 10 eV and the zenith angle 0 degree.Black lines are the CORSIKA results, while blue lines are theCOSMOS results. The lines are averages of 50 shower events. N u m be r o f pa r t i c l e s log Energy [GeV]Electron COSMOS 7.54 P 1.0 19eVCORSIKA Fluka P 1.0 19eV
FIGURE 5.
Energy (rest-mass energy no included) distribu-tion of electrons at ground over the entire ground for protonEAS with the primary energy 10 eV and the zenith angle 0degree. Black lines are the CORSIKA results, while blue linesare the COSMOS results. The lines are averages of 50 showerevents. this paper, we compared simulations of EAS using COR-SIKA and COSMOS codes and quantified the differencesin the simulations. For the longitudinal distribution ofphotons, electrons, and muons, we found the maximumdifference of ∼ N u m be r o f pa r t i c l e s log Energy [GeV]Muon COSMOS 7.54 P 1.0 19eVCORSIKA Fluka P 1.0 19eV
FIGURE 6.
Energy (rest-mass energy no included) distribu-tion of muons at ground over the entire ground for proton EASwith the primary energy 10 eV and the zenith angle 0 degree.Black lines are the CORSIKA results, while blue lines are theCOSMOS results. The lines are averages of 50 shower events. large difference in the production of secondary hadronsin the CORSIKA and COSMOS codes. We found that theproduction is rather sensitive to the low-energy (below 80GeV) hadronic interaction model. This may indicate thatlow-energy hadronic interaction models in Monte Carlocodes for EAS need to be further investigated. ACKNOWLEDGMENTS
The work was supported by the National Research Foun-dation of Korea through grant 2007-0093860 and Grant-in-Aid for Scientific Research on Priority Areas (HighestCosmic Rays: 15077205) of MEXT, Japan.
REFERENCES ∼∼