How many radio relics await discovery?
S. E. Nuza (1), M. Hoeft (2), R. J. van Weeren (3), S. Gottloeber (1),, G. Yepes (4) ((1) AIP-Potsdam, (2) TLS-Tautenburg, (3) Leiden Observatory,, (4) UAM-Madrid)

TL;DR
This paper models the expected abundance of radio relics in galaxy clusters and predicts that future low-frequency radio surveys like LOFAR and WSRT could discover thousands of new relics, depending on cluster catalog completeness.
Contribution
It introduces a statistical framework linking galaxy cluster properties with radio relic counts and estimates relic discoveries for upcoming surveys.
Findings
Model reproduces observed relic fraction increase with X-ray luminosity and redshift.
Faint relics are likely in clusters with low X-ray flux.
LOFAR and WSRT surveys could discover thousands of relics.
Abstract
Upcoming radio telescopes will allow to study the radio sky at low frequencies with unprecedent sensitivity and resolution. New surveys are expected to discover a large number of new radio sources. Here we investigate the abundance of radio relics, i.e. steep-spectrum diffuse radio emission coming from the periphery of galaxy clusters, which are believed to trace shock waves induced by cluster mergers. With the advent of comprehensive relic samples a framework is needed to analyze statistically the relic abundance. To this end, we introduce the probability to find a relic located in a galaxy cluster with given mass and redshift allowing us to relate the halo mass function of the Universe with the radio relic number counts. Up to date about 45 relics have been reported and we compile the resulting counts, N(>S_1.4). In principle, the parameters of the distribution could be determined…
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