Curved Radio Spectra of Weak Cluster Shocks

TL;DR

This study models radio relics in galaxy clusters using diffusive shock acceleration, explaining observed features like surface brightness and curved spectra, and suggests additional processes influence high-frequency electron spectra.

Contribution

It introduces detailed DSA simulations for spherical shocks interacting with fossil electrons, reproducing observed relic features and spectra, and highlights the need for additional physics at high energies.

Findings

Shocks with ~3000 km/s explain relic width and spectra.

Radio spectra steepen gradually over 0.1-10 GHz with a ~1 GHz break.

Additional processes are needed to explain spectral index jumps above 1.5 GHz.

Abstract

In order to understand certain observed features of arc-like giant radio relics such as the rareness, uniform surface brightness, and curved integrated spectra, we explore a diffusive shock acceleration (DSA) model for radio relics in which a spherical shock impinges on a magnetized cloud containing fossil relativistic electrons. Toward this end, we perform DSA simulations of spherical shocks with the parameters relevant for the Sausage radio relic in cluster CIZA J2242.8+5301, and calculate the ensuing radio synchrotron emission from re-accelerated electrons. Three types of fossil electron populations are considered: a delta-function like population with the shock injection momentum, a power-law distribution, and a power-law with an exponential cutoff. The surface brightness profile of radio-emitting postshock region and the volume-integrated radio spectrum are calculated and compared with observations. We find that the observed width of the Sausage relic can be explained reasonably well by shocks with speed $u_s \sim 3\times 10^3 \kms$ and sonic Mach number $M_s \sim 3$. These shocks produce curved radio spectra that steepen gradually over $(0.1-10) \nu_{\rm br}$ with break frequency $ \nu_{\rm br}\sim 1$ GHz, if the duration of electron acceleration is $\sim 60 - 80$ Myr. However, the abrupt increase of spectral index above $\sim 1.5$ GHz observed in the Sausage relic seems to indicate that additional physical processes, other than radiative losses, operate for electrons with $\gamma_e \gtrsim 10^4$.