The Spectral Shape and Photon Fraction as Signatures of the GZK-Cutoff

TL;DR

This paper explores how the spectral shape and photon fraction of ultra high energy cosmic rays can reveal information about their sources and the GZK cutoff, using an analytic model and considering magnetic field effects.

Contribution

It introduces an analytic framework to relate the GZK cutoff shape and photon fraction to the local UHECR source distribution and maximum proton energies.

Findings

Photon fraction curve varies with source distribution and maximum energy.

Spectral shape near the cutoff indicates the origin of the GZK feature.

Magnetic fields influence proton propagation and observed flux.

Abstract

With the prospect of measuring the fraction of arriving secondary photons, produced through photo-pion energy loss interactions of ultra high energy cosmic ray (UHECR) protons with the microwave background during propagation, we investigate how information about the local UHECR source distribution can be inferred from the primary (proton) to secondary (photon) ratio. As an aid to achieve this, we develop an analytic description for both particle populations as a function of propagation time. Through a consideration of the shape of the GZK cut-off and the corresponding photon fraction curve, we investigate the different results expected for both different maximum proton energies injected by the sources, as well as a change in the local source distribution following a perturbative deformation away from a homogeneous description. At the end of the paper, consideration is made as to how these results are modified through extra-galactic magnetic field effects on proton propagation. The paper aims to demonstrate how the shape of the cosmic ray flux in the cut-off region, along with the photon fraction, are useful indicators of the cutoff origin as well as the local UHECR source distribution.