Re-acceleration Model for Radio Relics with Spectral Curvature

TL;DR

This paper proposes a re-acceleration model for radio relics involving shock waves passing through fossil electron clouds, explaining observed spectral steepening and matching radio observations with specific shock parameters.

Contribution

It introduces a model where shock re-acceleration in finite fossil electron clouds explains spectral curvature, extending previous DSA models to account for steep spectra.

Findings

The model fits the Sausage relic's radio spectrum and brightness profile.

Shock speed and Mach number are constrained to match observations.

Steep spectra can be explained by fossil electron re-acceleration and cloud configuration.

Abstract

Most of the observed features of radio {\it gischt} relics such as spectral steepening across the relic width and power-law-like integrated spectrum can be adequately explained by diffusive shock acceleration (DSA) model, in which relativistic electrons are (re-)accelerated at shock waves induced in the intracluster medium. However, the steep spectral curvature in the integrated spectrum above $\sim 2$ GHz detected in some radio relics such as the Sausage relic in cluster CIZA J2242.8+5301 may not be interpreted by simple radiative cooling of postshock electrons. In order to understand such steepening, we here consider a model in which a spherical shock sweeps through and then exits out of a finite-size cloud with fossil relativistic electrons. The ensuing integrated radio spectrum is expected to steepen much more than predicted for aging postshock electrons, since the re-acceleration stops after the cloud-crossing time. Using DSA simulations that are intended to reproduce radio observations of the Sausage relic, we show that both the integrated radio spectrum and the surface brightness profile can be fitted reasonably well, if a shock of speed, $u_s \sim 2.5-2.8\times 10^3 \kms$, and sonic Mach number, $M_s \sim 2.7-3.0$, traverses a fossil cloud for $\sim 45$ Myr and the postshock electrons cool further for another $\sim 10$ Myr. This attempt illustrates that steep curved spectra of some radio gischt relics could be modeled by adjusting the shape of the fossil electron spectrum and adopting the specific configuration of the fossil cloud.