An Extended Magnetohydrodynamics Model for Relativistic Weakly Collisional Plasmas

TL;DR

This paper develops a phenomenological, extended magnetohydrodynamics model for relativistic, weakly collisional plasmas in RIAFs, incorporating anisotropic pressure and thermal conduction, applicable to black hole accretion flows like Sgr A* and M87.

Contribution

It introduces a novel MHD model based on Israel-Stewart theory, adapted for magnetized, relativistic, weakly collisional plasmas, bridging non-relativistic and relativistic regimes.

Findings

Model reduces to Braginskii theory in non-relativistic limit.

Describes linear plasma behavior and parameter interpretations.

Outlines limits for saturated conduction and pressure anisotropy.

Abstract

Black holes that accrete far below the Eddington limit are believed to accrete through a geometrically thick, optically thin, rotationally supported plasma that we will refer to as a radiatively inefficient accretion flow (RIAF). RIAFs are typically collisionless in the sense that the Coulomb mean free path is large compared to $GM/c^2$, and relativistically hot near the event horizon. In this paper we develop a phenomenological model for the plasma in RIAFs, motivated by the application to sources such as Sgr A* and M87. The model is derived using Israel-Stewart theory, which considers deviations up to second order from thermal equilibrium, but modified for a magnetized plasma. This leads to thermal conduction along magnetic field lines and a difference in pressure, parallel and perpendicular to the field lines (which is equivalent to anisotrotropic viscosity). In the non-relativistic limit, our model reduces to the widely used Braginskii theory of magnetized, weakly collisional plasmas. We compare our model to the existing literature on dissipative relativistic fluids, describe the linear theory of the plasma, and elucidate the physical meaning of the free parameters in the model. We also describe limits of the model when the conduction is saturated and when the viscosity implies a large pressure anisotropy. In future work, the formalism developed in this paper will be used in numerical models of RIAFs to assess the importance of non-ideal processes for the dynamics and radiative properties of slowly accreting black holes.