Data-driven analysis for understanding ultrahigh energy cosmic ray source spectra

TL;DR

This paper investigates the source spectra of ultrahigh energy cosmic rays by analyzing observational data to understand how energy losses and interactions influence their emission characteristics, challenging the simple Peters cycle assumption.

Contribution

It introduces a data-driven method to explore the source emission spectra of UHECRs considering energy losses and composition, moving beyond traditional assumptions.

Findings

Data favors complex source spectra over simple Peters cycle.

Energy losses significantly alter the expected source spectra.

Systematic uncertainties impact the interpretation of composition data.

Abstract

One of the most challenging open questions regarding the origin of ultrahigh energy cosmic rays (UHECRs) deals with the shape of the source emission spectra. A commonly-used simplifying assumption is that the source spectra of the highest energy cosmic rays trace a Peters cycle, in which the maximum cosmic-ray energy scales linearly with $Z$, i.e., with the charge of the UHECR in units of the proton charge. However, this would only be a natural assumption for models in which UHECRs escape the acceleration region without suffering significant energy losses. In most cases, however, UHECRs interact in the acceleration region and/or in the source environment changing the shape of the source emission spectra. Energy losses are typically parameterized in terms of $Z$ and the UHECR baryon number $A$, and therefore one would expect the source emission spectra to be a function of both $Z$ and $A$. Taking a pragmatic approach, we investigate whether existing data favor any region of the $(Z,A)$ parameter space. Using data from the Pierre Auger Observatory, we carry out a maximum likelihood analysis of the observed spectrum and nuclear composition to shape the source emission spectra for the various particle species. We also study the impact of possible systematic uncertainties driven by hadronic models describing interactions in the atmosphere.