A Simulation Study on the Cosmic Ray Energy Spectra of Elemental Mass Groups using the Tibet Air Shower and Muon Detector Arrays through the Bayesian Unfolding Method

Abstract

We study the analysis method to determine the cosmic-ray energy spectra of different mass groups assuming the use of the Tibet AS$\gamma$ experiment, which consists of the high-density Tibet air-shower array (Tibet-AS) and the underground muon detector (MD) array. These arrays measure the sampling air shower size $\Sigma\rho$ and the total muon number $\Sigma N_{\mu}$ of each air shower event. These parameters are known to contain information on the energy and mass of the primary particle. To reconstruct the energy spectra of individual cosmic-ray mass groups, we apply a multidimensional unfolding method based on Bayes' theorem to the two-dimensional distribution of $\Sigma\rho$ and $\Sigma N_{\mu}$ produced by Monte Carlo simulation. Simulated datasets with combinations of the EPOS-LHC, SIBYLL-2.3c, and QGSJET~II-04 high-energy hadronic interaction models and a helium-dominant composition model are analyzed while using a response matrix produced by EPOS-LHC. The unfolded spectra of the EPOS + helium-dominant composition model dataset show a deviation from the input flux within $\pm$10\% except for a few bins, meaning that the uncertainty of the technique itself and the composition model dependence is at that level. It is also shown that the deviation in the all-particle spectrum is within $\pm$10\% even when using different hadronic interaction models in the dataset and the response matrix. On the other hand, the unfolded spectra of individual mass groups have a clear dependence on the hadronic interaction model. The model dependence of the proton and helium spectra amounts to \pm25% below 10$^{6.5}$ GeV. The dependence in the carbon group is at a \pm25% level below 10$^{6}$ GeV, and for the iron spectrum, it amounts to +55% and -30% in the energy range of 10$^{5.1}$ GeV to 10$^{6.7}$ GeV.