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

Understand

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.