On the inverse problem for extragalactic cosmic ray nuclei with energies $10^{18}$ to $10^{20}$ eV

TL;DR

This paper addresses the inverse problem of cosmic ray transport at ultra-high energies, using Auger data to infer source spectrum characteristics and discussing regularization methods for the ill-posed problem.

Contribution

It introduces a method to analyze the source spectrum of ultra-high energy cosmic rays through inverse problem techniques and regularization, based on Auger data.

Findings

Source spectrum shape inferred from Auger data

Regularization approach for ill-posed inverse problem

Constraints on cosmic ray composition and origin

Abstract

The inverse problem of cosmic ray transport of ultra-high energy cosmic rays is considered. The analysis of Auger data on energy spectrum, energy dependence of mean logarithm of atomic mass number and its variance allows definite conclusions on the shape of the source spectrum in the frameworks of the inverse problem approach. The discussion on regularization procedure for considered ill-posed problem is presented.