Electron thermodynamics in GRMHD simulations of low-luminosity black hole accretion

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 entropy equation for the electrons 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 ≪ 10 −5 of the Eddington accretion 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 that depend on the local magnetic field strength 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.

Radiative, two-temperature simulations of low-luminosity black hole accretion flows in general relativity

“…Only recently has this method been improved. Ressler et al (2015) introduced an independent second fluid, electrons, and they used a prescription for the heating of electrons and ions according to a physically motivated sub-grid model (Howes 2010). This approach leads to the ability to determine electron temperatures with fewer ad hoc prescriptions.…”

“…The fraction of heating going into electrons depends on the microscopic properties of a collisionless plasma. In this work we follow Ressler et al (2015) and use the fitting formula of Howes (2010) for the fraction, δ e , of the total heating that goes into electrons,…”

“…We start with a one-dimensional high Mach number shock test problem as described in detail in Ressler et al (2015). Two fluids move in opposite directions with |v| = 10 −3 c and collide at x = 0.…”

“…Two fluids move in opposite directions with |v| = 10 −3 c and collide at x = 0. The gas adiabatic index is fixed to γ = 5/3, while the electron adiabatic index is γ e = 4/3 (Ressler et al 2015 also considered the trivial case γ e = 5/3, but we focus here on the more difficult problem). The temperature of the gas is set up to give a Mach number of M = 49.…”

Modeling Polarized Emission from Black Hole Jets: Application to M87 Core Jet

“…Inspired by early models for radio cores in quasars [1] and the Solar corona plasma models [19,29,30], we have developed a simple parametric description for electron thermodynamics in the simulation of accretion flows. In combination with radiative transfer model, this finally makes our numerical simulations of accretion flows resemble observations of underluminous accreting black holes [13,14,16,18,31].…”