Systematic Differences Due to High Energy Hadronic Interaction Models

Systematic Differences due to High Energy Hadronic Interaction Models in Air Shower Simulations in the 100 GeV-100 TeV Range R.D. Parsons1, ∗ and H. Schoorlemmer1 1Max-Planck-Institut fürKernphysik P.O. Box 103980; D 69029 Heidelberg; Germany The predictions of hadronic interaction models for cosmic-ray induced air showers contain inherent uncertainties due to limitations of available accelerator data and theoretical understanding in the required energy and rapidity regime. Differences between models are typically evaluated in the range appropriate for cosmic-ray air shower arrays (1015- 1020 eV). However, accurate modelling of charged cosmic-ray measurements with ground based gamma-ray observatories is becoming more and more important. We assess the model predictions on the gross behaviour of measurable air shower parameters in the energy (0.1-100 TeV) and altitude ranges most appropriate for detection by ground-based gamma- ray observatories. We go on to investigate the particle distributions just after the first interaction point, to examine how differences in the micro-physics of the models may compound into differences in the gross air shower behaviour. Differences between the models above 1 TeV are typically less than 10%. However, we find the largest variation in particle densities at ground at the lowest energy tested (100 GeV), resulting from striking differences in the early stages of shower development. INTRODUCTION vations, as most pointedly seen in the measurement of the cosmic ray electron spectrum [8{11] where the back- Ground based gamma-ray astronomy uses the particle ground contamination must be estimated from compar- shower initiated when a very high energy (> 100 GeV) ison to Monte Carlo simulations, in which case the sys- gamma-ray interacts with an atom in the Earth's atmo- tematic uncertainties in the hadronic interactions quickly sphere, to detect and reconstruct the primary particles become the dominant form of uncertainty in the measure- of the primary gamma-rays. Such reconstruction is per- ment. Or in the case when these observatories are used to formed either by directly detecting the energetic particles perform measurement of the hadronic cosmic rays (for ex- formed in the shower at ground level (as in the HAWC ample [12]). Finally, hadron simulations are required to gamma-ray observatory [1]) or detecting the Cherenkov estimate the sensitivity of future gamma-ray observato- light emitted as the relativistic particles pass through the ries, such as the Cherenkov Telescope Array (CTA) [13], atmosphere using Imaging Atmospheric Cherekov Tele- the Southern Gamma-ray Survey Observatory (SGSO) scopes (IACTs), as in the H.E.S.S., MAGIC and VERI- [14], and the Large High Altitude Air Shower Obser- TAS experiments [2{4]. Event reconstruction in all these vatory (LHAASO) [15] which could be affected by the instruments is performed in combination with detailed choice of models. Monte Carlo simulations of the air shower development, The advent of LHC measurements has provided large which is typically very well understood for gamma-ray amounts of data at never before probed energies [16] and induced air showers. at extreme rapidities [17, 18]. This data glut promises Both experiment types also observe the flux from air improvements to hadronic interaction models by facili- showers induced from hadronic cosmic rays, which con- tating model tuning in energy ranges not before possible stitutes the major background for gamma-ray ray obser- and has resulted in the creation of a new generation of vations. Although they can be largely rejected, some air shower focused hadronic interaction models [19{21] cosmic-ray contamination will remain which must be es- tuned to this data set. timated. This can be problematic as lack of knowledge Although many detailed tests have been performed on of microscopic hadronic physics in the energy range of this model generation, most have concentrated on the 15 19 arXiv:1904.05135v3 [astro-ph.HE] 26 Jul 2019 interest, leads to significant variations in the air shower predictions in the energy range from 10 eV to 10 eV predictions. In most observations of gamma-ray sources [22], where measurements such as the primary particle this uncertainty can be negated by instead using posi- mass can be critically dependent on the model used. Such tions within the instrument field of view which contain studies lie far beyond the energy range of interest for no gamma-ray emission to estimate the background con- gamma-ray instruments from 1011 eV to 1014 eV. In order tamination (e.g. [5]). However, in the case of extremely to investigate the model behaviour in this energy regime, large or truly diffuse sources, no such signal free region we have therefore studied the effects of the most com- exists and the background contamination may need to monly used hadronic interaction model versions included be estimated from simulated data (like for example the in the air shower simulation package CORSIKA [23], con- Fermi-Bubbles [6] and the Halo around Geminga [7] in centrating on model predictions relevant to ground-based the case of IACTs). gamma-ray astronomy with both atmospheric Cherenkov This is even more apparent in non gamma-ray obser- telescopes and particle detectors at observation levels ap- 2 3 ) 10 2 N E − d d 0.1 TeV m ( 2 × 10 4 1 TeV y y 10 t i g 10 TeV s r n 1 e e 10 n 100 TeV E D 3 10 e l 0 c i 10 t r a 2 P 10 10-1 10-2 101 10-3 100 10-4 10-1 10-5 10-2 10-6 10-7 10-3 0 100 200 300 400 500 600 10-2 10-1 100 101 102 103 Core Distance (m) Energy (GeV) FIG. 1. Lateral distribution functions in number density for the EM component (solid) and muon component(dashed) [left] and spectral density [right] at ground (4100 m) for vertical simulated showers with EPOS-LHC hadronic interaction model. Cuts are placed on the particle energy of 0.3 MeV on electrons and gammas and 300 MeV on muons. propriate to these detector types. Energy Particle Cherenkov First In this publication we concentrate on understanding Distributions Distributions Interaction the gross behaviour of the shower, in terms of the par- 100 GeV 106 106 106 ticles or Cherenkov light arriving at ground level. We 1 TeV 105 105 106 compare the spread of predictions in this energy range, 10 TeV 104 104 106 quantifying the level of systematic uncertainties in mea- 100 TeV 103 103 106 surements due to the use of hadronic interaction models and testing the hypothesis that the tuning of models to TABLE I. Number of events simulated at different energies a wider range of data will inevitably lead to a conver- for the studies presented. gence of model predictions. We then go on to compare the particle production of the first interaction to understand how the differences in air shower development stem energy in CORSIKA). Each of the above mentioned high from differences in the interaction characteristics of indi- energy hadronic interaction models was combined with vidual particles. It should be noted that the average dis- the UrQMD [24] low energy hadronic interaction model tributions presented here do not necessarily correspond with the cross over energy set at 80 GeV. The electromag- directly to measurables at gamma-ray observatories and netic shower component was simulated with the EGS4 biases in observations might expose different systematic [25] model. Energy cuts were placed on both electrons differences between the model predictions. and muons of 0.3 and 300 MeV respectively within the CORSIKA simulations. Finally to better understand the transition between high end low energy interaction mod- AIR SHOWER SIMULATIONS els, showers were also simulated using only the UrQMD model in the lowest energy bands tested. To best calcu- To test the prediction of the models in gamma-ray ob- late the relevant parameters for the two types of gamma- servatories a series of simulation sets were created using ray observatories currently operating the ground level of CORSIKA with the Cherenkov light option activated. the simulations were set to 4100 m (which corresponds Protons showers were simulated at zenith, with COR- the elevation of the HAWC gamma-ray observatory) and SIKA v7.64 using (at the time of writing) the latest 1800 m (corresponding to the elevation of the H.E.S.S. versions of the high energy hadronic interaction models experiment). Protons make up the dominant source of EPOS-LHC, QGSJet-II-04 and SIBYLL 2.3c (assumed background in these experiments, hence no simulations to be valid at energies >80 GeV, the default transition were performed with heavier nuclei. Vertical showers 3 1.5 1.5 100 GeV Proton EPOS-LHC 1.4 1.4 QGSJetII-04 1.3 1.3 SIBYLL 2.3c UrQMD 1.2 1.2 Rel. EM Deposit 1.1 1.1 1.0 Rel. Muon Number 1.0 0.9 0.9 0.8 0.8 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Core Distance (m) Core Distance (m) 1.5 1.5 1 TeV Proton 1.4 1.4 1.3 1.3 1.2 1.2 Rel. EM Deposit 1.1 1.1 1.0 Rel. Muon Number 1.0 0.9 0.9 0.8 0.8 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Core Distance (m) Core Distance (m) 1.5 1.5 10 TeV Proton 1.4 1.4 1.3 1.3 1.2 1.2 Rel. EM Deposit 1.1 1.1 1.0 Rel. Muon Number 1.0 0.9 0.9 0.8 0.8 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Core Distance (m) Core Distance (m) 1.5 1.5 100 TeV Proton 1.4 1.4 1.3 1.3 1.2 1.2 Rel.

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