# On the connection between turbulent motions and particle acceleration in galaxy clusters

## TL;DR

This study links turbulent motions in galaxy clusters to the presence of giant radio halos, showing that higher turbulence correlates with increased radio emission, supporting the turbulent re-acceleration model.

## Contribution

It introduces a novel method using density fluctuations to estimate turbulent velocities and confirms their correlation with radio halo power in galaxy clusters.

## Key findings

- Radio halo clusters have higher turbulent velocities than radio quiet clusters.
- Radio power correlates with turbulent velocity as P_radio ∝ σ_v^{3.3±0.7}.
- Results support the turbulent re-acceleration model for radio halo origin.

## Abstract

Giant radio halos are Mpc-scale diffuse radio sources associated with the central regions of galaxy clusters. The most promising scenario to explain the origin of these sources is that of turbulent re-acceleration, in which MeV electrons injected throughout the formation history of galaxy clusters are accelerated to higher energies by turbulent motions mostly induced by cluster mergers. In this Letter, we use the amplitude of density fluctuations in the intracluster medium as a proxy for the turbulent velocity and apply this technique to a sample of 51 clusters with available radio data. Our results indicate a segregation in the turbulent velocity of radio halo and radio quiet clusters, with the turbulent velocity of the former being on average higher by about a factor of two. The velocity dispersion recovered with this technique correlates with the measured radio power through the relation $P_{\rm radio}\propto\sigma_v^{3.3\pm0.7}$, which implies that the radio power is nearly proportional to the turbulent energy rate. Our results provide an observational confirmation of a key prediction of the turbulent re-acceleration model and possibly shed light on the origin of radio halos.