$X_{max}^{\mu}$ vs. $N^{\mu}$ from Extensive Air Showers as estimator for the mass of primary UHECR's. Application for the Pierre Auger Observatory

TL;DR

This paper proposes a Bayesian method combining $X_{max}^{}$ and $N^{}$ measurements to improve primary mass estimation of UHECRs, validated with simulated data for the Pierre Auger Observatory.

Contribution

It introduces a 2D probability function approach that enhances mass reconstruction accuracy over traditional methods using only $X_{max}^{}$.

Findings

Improved accuracy in primary mass estimation using combined $X_{max}^{}$ and $N^{}$ data.

Bayesian approach effectively distinguishes between proton and iron primaries.

Validation with simulated data shows better performance than single-variable methods.

Abstract

We study the possibility of primary mass estimation for Ultra High Energy Cosmic Rays (UHECR's) using the $X_{max}^{\mu}$ (the height where the number of muons produced on the core of Extensive Air Showers (EAS) is maximum) and the number $N^{\mu}$ of muons detected on ground. We use the 2D distribution - $X_{max}^{\mu}$ against $N^{\mu}$ in order to find its sensitivity to the mass of the primary particle. For that, we construct a 2D Probability Function $Prob(p,Fe \ | \ X_{max}^{\mu},N^{\mu})$ which estimates the probability that a certain point from the plane $(X_{max}^{\mu}$, $N^{\mu})$ corresponds to a shower induced by a proton, respectively an iron nucleus. To test the procedure, we analyze a set of simulated EAS induced by protons and iron nuclei at energies of $10^{19} eV$ and $20^{\circ}$ zenith angle with CORSIKA. Using the Bayesian approach and taking into account the geometry of the infill detectors from the Pierre Auger Observatory, we observe an improvement in the accuracy of the primary mass reconstruction in comparison with the results obtained using only the $X_{max}^{\mu}$ distributions.