Turbulent Cosmic-Ray Reacceleration and the Curved Radio Spectrum of the Radio Relic in the Sausage Cluster

TL;DR

This paper proposes that turbulence-driven reacceleration of cosmic-ray electrons downstream of shocks explains the curved radio spectrum of the Sausage Cluster's relic, challenging the traditional shock acceleration model.

Contribution

It introduces a turbulence reacceleration model for cosmic-ray electrons that accounts for spectral curvature and hard electron spectra observed in the relic.

Findings

Reacceleration occurs with mean free paths shorter than Coulomb mean free paths.

Turbulent eddies must be smaller than the relic width.

Predicted hard X-ray spectra from inverse Compton scattering.

Abstract

It has often been thought that the northern radio relic in the galaxy cluster CIZA J2242.8+5301 (the "Sausage" Cluster) is associated with cosmic ray (CR) electrons that are accelerated at a shock through the diffusive shock acceleration (DSA) mechanism. However, recent radio observations have shown that the radio spectrum is curved, which is inconsistent with the prediction of a simple DSA model. Moreover, the CR electron spectrum before being affected by radiative cooling seems to be too hard for DSA. In this study, we show that these facts are natural consequences if the electrons are reaccelerated in turbulence downstream of the shock. In this model, DSA is not the main mechanism for generating high-energy electrons. We find that the mean free path of the electrons should be much shorter than the Coulomb mean free path for efficient reacceleration. The scale of the turbulent eddies must be smaller than the width of the relic. We also predict hard X-ray spectra of inverse Compton scattering of photons.