Numerical Simulations of Driven Supersonic Relativistic MHD Turbulence

TL;DR

This paper presents high-resolution 3D numerical simulations of relativistic MHD turbulence relevant to GRB outflows, revealing magnetic field amplification, spectral properties, and rapid decay of turbulence, challenging sustained turbulence models for GRB variability.

Contribution

The study provides the first detailed analysis of relativistic MHD turbulence spectra, magnetic energy amplification, and decay timescales in conditions relevant to astrophysical phenomena like GRBs.

Findings

Magnetic energy reaches a few percent of total energy density.

Relativistic turbulence decays on a sound crossing time of an eddy.

Relativistic effects couple spectral components uniquely.

Abstract

Models for GRB outflows invoke turbulence in relativistically hot magnetized fluids. In order to investigate these conditions we have performed high-resolution three-dimensional numerical simulations of relativistic magneto-hydrodynamical (RMHD) turbulence. We find that magnetic energy is amplified to several percent of the total energy density by turbulent twisting and folding of magnetic field lines. Values of epsilon_B near 1% are thus naturally expected. We study the dependence of saturated magnetic field energy fraction as a function of Mach number and relativistic temperature. We then present power spectra of the turbulent kinetic and magnetic energies. We also present solenoidal (curl-like) and dilatational (divergence-like) power spectra of kinetic energy. We propose that relativistic effects introduce novel couplings between these spectral components. The case we explore in most detail is for equal amounts of thermal and rest mass energy, corresponding to conditions after collisions of shells with relative Lorentz factors of several. These conditions are relevant in models for internal shocks, for the late afterglow phase, for cocoon material along the edge of a relativistic jet as it propagates through a star, as well neutron stars merging with each other and with black hole companions. We find that relativistic turbulence decays extremely quickly, on a sound crossing time of an eddy. Models invoking sustained relativistic turbulence to explain variability in GRB prompt emission are thus strongly disfavored unless a persistant driving of the turbulence is maintained for the duration of the prompt emission.