Acceleration of Cosmic-Ray Electrons at Weak Shocks in Galaxy Clusters

Abstract

According to structure formation simulations, weak shocks with typical Mach number, M< 3, are expected to form in merging galaxy clusters. The presence of such shocks have been indicated by X-ray and radio observations of many merging clusters. In particular, diffuse radio sources known as radio relics could be explained by synchrotron-emitting electrons accelerated via diffusive shock acceleration at quasi-perpendicular shocks. Here we explore a puzzling discrepancy that for some radio relics, the shock Mach number inferred from the radio spectral index is substantially larger than that estimated from X-ray observations. We suggest that shock surfaces associated with radio relics could consist of multiple shocks with different strengths, so X-ray observations pick up the part of shocks with lower Mach numbers, while radio emissions come preferentially from the part with higher Mach numbers. Then relativistic electrons accelerated by the stronger shocks can reproduce the observed radio spectrum.