Weak Alfv\'{e}nic turbulence in relativistic plasmas. Part 1. Dynamical equations and basic dynamics of interacting resonant triads

TL;DR

This paper develops relativistic MHD equations to study weak Alfvénic turbulence in high-energy astrophysical plasmas, revealing similarities and key differences from non-relativistic turbulence, especially regarding compressible mode coupling and energy escape mechanisms.

Contribution

It derives and analyzes reduced relativistic MHD equations for weak Alfvénic turbulence, highlighting the role of fast mode coupling and differences from non-relativistic turbulence.

Findings

Many non-relativistic turbulence features are retained in relativistic systems.

Finite coupling to compressible fast modes exists regardless of magnetic field strength.

Fast-Alfvén coupling diminishes with oblique wave propagation.

Abstract

Alfv\'{e}n wave collisions are the primary building blocks of the non-relativistic turbulence that permeates the heliosphere and low-to-moderate energy astrophysical systems. However, many astrophysical systems such as gamma-ray bursts, pulsar and magnetar magnetospheres, and active galactic nuclei have relativistic flows or energy densities. To better understand these high energy systems, we derive reduced relativistic MHD equations and employ them to examine weak Alfv\'{e}nic turbulence, dominated by three-wave interactions, in reduced relativistic magnetohydrodynamics, including the force-free, infinitely magnetized limit. We compare both numerical and analytical solutions to demonstrate that many of the findings from non-relativistic weak turbulence are retained in the relativistic system. But, an important distinction in the relativistic limit is the inapplicability of a formally incompressible limit, i.e, there exists finite coupling to the compressible fast mode regardless of the strength of the magnetic field. Since fast modes can propagate across field lines, this mechanism provides a route for energy to escape strongly magnetized systems, e.g., magnetar magnetospheres. However, we find that the fast-Alfv\'{e}n coupling is diminished in the limit of oblique propagation.