Inverse cascade of non-helical magnetic turbulence in a relativistic fluid

Abstract

The free decay of non-helical relativistic magnetohydrodynamic turbulence is studied numerically, and found to exhibit cascading of magnetic energy toward large scales. Evolution of the magnetic energy spectrum $P_M(k,t)$ is self-similar in time and well modeled by a broken power law with sub-inertial and inertial range indices very close to $7/2$ and $-2$ respectively. The magnetic coherence scale is found to grow in time as $t^{2/5}$, much too slow to account for optical polarization of gamma-ray burst afterglow emission if magnetic energy is to be supplied only at microphysical length scales. No bursty or explosive energy loss is observed in relativistic MHD turbulence having modest magnetization, which constrains magnetic reconnection models for rapid time variability of GRB prompt emission, blazars and the Crab nebula.