Electron Thermodynamics in GRMHD Simulations of Low-Luminosity Black Hole Accretion

TL;DR

This paper develops a self-consistent electron thermodynamics model for GRMHD simulations of low-luminosity black hole accretion, improving the realism of predicted electron temperature distributions and thermal conduction effects.

Contribution

It introduces a new model evolving electron entropy with spatially varying heating and conduction, applicable to low accretion rate systems, enhancing simulation accuracy.

Findings

Electron temperatures differ significantly from previous assumptions.

Electron thermal conduction affects inner accretion flow temperatures.

Higher electron temperatures are concentrated in the corona region.

Abstract

Simple assumptions made regarding electron thermodynamics often limit the extent to which general relativistic magnetohydrodynamic (GRMHD) simulations can be applied to observations of low-luminosity accreting black holes. We present, implement, and test a model that self-consistently evolves an electron entropy equation and takes into account the effects of spatially varying electron heating and relativistic anisotropic thermal conduction along magnetic field lines. We neglect the back-reaction of electron pressure on the dynamics of the accretion flow. Our model is appropriate for systems accreting at $\ll 10^{-5}$ of the Eddington rate, so radiative cooling by electrons can be neglected. It can be extended to higher accretion rates in the future by including electron cooling and proton-electron Coulomb collisions. We present a suite of tests showing that our method recovers the correct solution for electron heating under a range of circumstances, including strong shocks and driven turbulence. Our initial applications to axisymmetric simulations of accreting black holes show that (1)~physically-motivated electron heating rates yield electron temperature distributions significantly different from the constant electron to proton temperature ratios assumed in previous work, with higher electron temperatures concentrated in the coronal region between the disc and the jet; (2)~electron thermal conduction significantly modifies the electron temperature in the inner regions of black hole accretion flows if the effective electron mean free path is larger than the local scale-height of the disc (at least for the initial conditions and magnetic field configurations we study). The methods developed in this work are important for producing more realistic predictions for the emission from accreting black holes such as Sagittarius A* and M87; these applications will be explored in future work.