Inverse problem for extragalactic transport of ultra-high energy cosmic rays

TL;DR

This paper presents a numerical method to infer the original spectra of ultra-high energy cosmic rays at their sources from observed data, accounting for propagation effects in the universe.

Contribution

It introduces a novel inverse problem solution for cosmic-ray transport equations, enabling source spectra determination from Earth-based observations.

Findings

Injection spectra of protons and Iron nuclei are derived from observational data.

The method successfully reconstructs source spectra using Auger and Telescope Array + HiRes data.

The approach enhances understanding of cosmic-ray origins and acceleration mechanisms.

Abstract

The energy spectra and composition of ultra-high energy cosmic rays are changing in a course of propagation in the expanding Universe filled with background radiation. We developed a numerical code for solution of inverse problem for cosmic-ray transport equations that allows the determination of average source spectra of different nuclei from the cosmic ray spectra observed at the Earth. Employing this approach, the injection spectra of protons and Iron nuclei in extragalactic sources are found assuming that only these species are accelerated at the source. The data from the Auger experiment and the combined data from the Telescope Array + HiRes experiments are used to illustrate the method.