High $\beta$ Effects on Cosmic Ray Streaming in Galaxy Clusters

Diffuse, extended radio emission in galaxy clusters, commonly referred to as radio halos, indicate the presence of high energy cosmic ray (CR) electrons and cluster-wide magnetic fields. We can predict from theory the expected surface brightness of a radio halo, given magnetic field and CR density profiles. Previous studies have shown that the nature of CR transport can radically effect the expected radio halo emission from clusters (Wiener et al. 2013). Reasonable levels of magnetohydrodynamic (MHD) wave damping can lead to significant CR streaming speeds. But a careful treatment of MHD waves in a high $\beta$ plasma, as expected in cluster environments, reveals damping rates may be enhanced by a factor of $\beta^{1/2}$. This leads to faster CR streaming and lower surface brightnesses than without this effect. In this work we re-examine the simplified, 1D Coma cluster simulations (with radial magnetic fields) of Wiener et al. (2013) and discuss observable consequences of this high $\beta$ damping. Future work is required to study this effect in more realistic simulations.