Maximum entropy analysis of cosmic ray composition

TL;DR

This paper introduces a maximum entropy method to analyze the composition of ultra-high-energy cosmic rays using the depth of shower maximum data, providing insights with limited knowledge of underlying physics.

Contribution

It develops a maximum entropy framework combined with a superposition model to infer cosmic ray composition trends from limited observational data.

Findings

The method can identify composition trends consistent with observed shower data.

It demonstrates how primary composition varies with energy using two example scenarios.

The approach highlights the potential and limitations of maximum entropy analysis in cosmic ray studies.

Abstract

We focus on the primary composition of cosmic rays with the highest energies that cause extensive air showers in the Earth's atmosphere. A way of examining the two lowest order moments of the sample distribution of the depth of shower maximum is presented. The aim is to show that useful information about the composition of the primary beam can be inferred with limited knowledge we have about processes underlying these observations. In order to describe how the moments of the depth of shower maximum depend on the type of primary particles and their energies, we utilize a superposition model. Using the principle of maximum entropy, we are able to determine what trends in the primary composition are consistent with the input data, while relying on a limited amount of information from shower physics. Some capabilities and limitations of the proposed method are discussed. In order to achieve a realistic description of the primary mass composition, we pay special attention to the choice of the parameters of the superposition model. We present two examples that demonstrate what consequences can be drawn for energy dependent changes in the primary composition.