Impact of the finite life-time of UHECR sources

TL;DR

This paper proposes that the finite lifetime of ultrahigh energy cosmic ray sources, combined with magnetic field effects, can explain the observed hard spectra and composition of UHECRs at Earth.

Contribution

It introduces a model linking source lifetime and magnetic field effects to the spectral features of UHECRs, providing conditions for dominant sources to shape observed spectra.

Findings

Hard spectra can result from finite source lifetimes and magnetic deflections.

Conditions for source dominance depend on magnetic field strength, source distance, and coherence length.

Proposed scenarios match observed spectral steepening at Earth.

Abstract

The observational data on ultrahigh energy cosmic rays (UHECR), in particular their mass composition, show strong indications for extremely hard spectra of individual mass groups of CR nuclei at Earth. In this work, we show that such hard spectra can be the result of the finite life-time of UHECR sources, if a few individual sources dominate the UHECR flux at the highest energies. In this case, time delays induced by deflections in the turbulent extragalactic magnetic field as well as from the diffusive or advective escape from the source environment can suppress low-energy CRs, leading to a steepening of the observed spectrum. Considering radio galaxies as the main source of UHECRs, we discuss the necessary conditions that few individual sources dominate over the total contribution from the bulk of sources that have been active in the past. We provide two proof-of-principle scenarios showing that for a turbulent extragalactic magnetic field with a strength $B$ and a coherence length $l_{\rm coh}$, the life-time of a source at a distance $d_{\rm src}$ should satisfy ${t_{\rm act} \sim \left( B/1\,\text{nG} \right)^2\,\left( d_{\rm src}/10\,\text{Mpc} \right)^2\,\left( l_{\rm coh}/1\,\text{Mpc} \right)\,\text{Myr}}$ to obtain the necessary hardening of the CR spectrum at Earth.