Non-variable cosmologically distant gamma-ray emitters as an imprint of propagation of ultra-high-energy protons

TL;DR

This paper explores how distant ultra-high-energy protons produce non-variable gamma-ray sources through secondary synchrotron radiation, offering a new method to trace cosmic ray acceleration sites at high redshifts.

Contribution

It introduces a model of secondary synchrotron gamma-ray emission from UHE protons propagating through the CMB, emphasizing its potential for detecting distant cosmic ray sources.

Findings

Secondary gamma-ray sources are nearly point-like and non-variable.

Energy transfer efficiency increases with redshift due to denser CMB.

Predicted gamma-ray spectra are detectable by Fermi LAT and Chandra.

Abstract

The acceleration cites of ultra-high-energy (UHE) protons can be traced by the footprint left by these particles propagating through cosmic microwave background (CMB) radiation. Secondary electrons produced in extended region of several tens of Mpc emit their energy via synchrotron radiation predominantly in the initial direction of the parent protons. It forms a non-variable and compact (almost point-like) source of high energy gamma rays. The importance of this effect is increased for cosmologically distant objects; because of severe energy losses, UHE protons cannot achieve us even in the case of extremely weak intergalactic magnetic fields. Moreover, at high redshifts the energy conversion from protons to secondary particles becomes significantly more effective due to the denser and more energetic CMB in the past. This increases the chances of UHE cosmic rays to be traced by the secondary synchrotron gamma radiation. We discuss the energy budget and the redshift dependence of the efficiency of energy transfer from UHE protons to synchrotron radiation. The angular and spectral distributions of radiation in the gamma- and X-ray energy bands are calculated and discussed in the context of their detectability by Fermi LAT and Chandra observatories.