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

¹ Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
e-mail: anton.prosekin@mpi-hd.mpg.de
² Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland

Received: 10 May 2011
Accepted: 20 September 2011

Abstract

The acceleration sites of ultra-high-energy (UHE) protons can be traced by the footprint left by these particles when they propagate through cosmic microwave background (CMB) radiation. Secondary electrons produced in the extended region of several tens of Mpc emit their energy via synchrotron radiation predominantly in the initial direction of the parent protons. This 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 reach 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 because of 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 energy transfer efficiency 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 the Fermi LAT and Chandra observatories.