# Shock acceleration efficiency in radio relics

## TL;DR

This study investigates the efficiency of shock acceleration in radio relics of galaxy clusters, revealing that standard diffusive shock acceleration often cannot account for observed luminosities, implying alternative mechanisms are needed.

## Contribution

The paper provides the first systematic analysis of electron acceleration efficiency in multiple radio relics, challenging the adequacy of standard DSA in explaining relic luminosities.

## Key findings

- Standard DSA requires >10% efficiency to explain relic luminosities.
- Re-acceleration or modified DSA mechanisms are likely necessary.
- Most relics cannot be explained by thermal electron acceleration alone.

## Abstract

Radio relics in galaxy clusters are giant diffuse synchrotron sources powered in cluster outskirts by merger shocks. Although the relic-shock connection has been consolidated in recent years by a number of observations, the details of the mechanisms leading to the formation of relativistic particles in this environment are still not well understood. The diffusive shock acceleration (DSA) theory is a commonly adopted scenario to explain the origin of cosmic rays at astrophysical shocks, including those in radio relics in galaxy clusters. However, in a few specific cases it has been shown that the energy dissipated by cluster shocks is not enough to reproduce the luminosity of the relics via DSA of thermal particles. Studies based on samples of radio relics are required to further address this limitation of the mechanism. In this paper, we focus on ten well-studied radio relics with underlying shocks observed in the X-rays and calculate the electron acceleration efficiency of these shocks that is necessary to reproduce the observed radio luminosity of the relics. We find that in general the standard DSA cannot explain the origin of the relics if electrons are accelerated from the thermal pool with an efficiency significantly smaller than 10%. Our results show that other mechanisms, such as shock re-acceleration of supra-thermal seed electrons or a modification of standard DSA, are required to explain the formation of radio relics.