The GZK horizon and constraints on the cosmic ray source spectrum from observations in the GZK regime

TL;DR

This paper introduces a method to constrain the injection spectrum of ultrahigh energy cosmic rays using GZK regime observations, even with limited event data, to distinguish different spectral indices.

Contribution

The paper presents a novel statistical method to determine the cosmic ray source spectrum from sparse observational data in the GZK regime.

Findings

A dataset of 100 events can distinguish spectral indices with high confidence.

The method effectively constrains the injection spectrum even with few observed events.

It demonstrates the potential to identify source characteristics from limited data.

Abstract

We discuss the GZK horizon of protons and present a method to constrain the injection spectrum of ultrahigh energy cosmic rays (UHECRs) from supposedly identified extragalactic sources. This method can be applied even when only one or two events per source are observed and is based on the analysis of the probability for a given source to populate different energy bins, depending on the actual CR injection spectral index. In particular, we show that for a typical source density of $4\times 10^{-5} Mpc^{-3}$, a data set of 100 events above $6\times 10^{19}$ eV allows one in 97% of all cases to distinguish a source spectrum $dN/dE\propto E^{-1.1}$ from one with $E^{-2.7}$ at 95% confidence level.