Re-acceleration model for the "Toothbrush" Radio Relic

TL;DR

This paper proposes a re-acceleration model involving a weak shock and fossil relativistic electrons to explain the radio emission of the Toothbrush relic, reconciling radio and X-ray observations.

Contribution

It introduces a re-acceleration scenario with specific electron spectra that better match observed radio profiles and spectra of the Toothbrush relic.

Findings

Re-acceleration model reproduces radio flux profiles.

Model aligns with observed radio spectrum.

Confirms link between fossil plasma and radio relics.

Abstract

The Toothbrush radio relic associated the merging cluster 1RXS J060303.3 is presumed to be produced by relativistic electrons accelerated at merger-driven shocks. Since the shock Mach number inferred from the observed radio spectral index, $M_{radio}\approx 2.8$, is larger than that estimated from X-ray observations, $M_{X-ray}\lesssim 1.5$, we consider the re-acceleration model in which a weak shock of $M_s\approx 1.2-1.5$ sweeps through the intracluster plasma with a preshock population of relativistic electrons. We find the models with a power-law momentum spectrum with the slope, $s\approx 4.6$, and the cutoff Lorentz factor, $\gamma_{e,c}\approx 7-8\times 10^4$ can reproduce reasonably well the observed profiles of radio fluxes and integrated radio spectrum of the head portion of the Toothbrush relic. This study confirms the strong connection between the ubiquitous presence of fossil relativistic plasma originated from AGNs and the shock-acceleration model of radio relics in the intracluster medium.