Adiabatic Index in Fluid Models of Collisionless Black Hole Accretion

TL;DR

This paper investigates the appropriate adiabatic index for single fluid models of collisionless black hole accretion, finding it should be slightly less than 5/3 for low luminosity conditions, and discusses implications for electron temperature fluctuations.

Contribution

It clarifies the suitable adiabatic index in collisionless plasma models of black hole accretion and introduces a simple equilibrium model relating dissipation and temperature ratios.

Findings

Optimal adiabatic index is slightly less than 5/3 for low luminosity accretion.

Different gamma values lead to significantly different model outcomes.

Implications for electron temperature fluctuations in EHT sources.

Abstract

Models of highly sub-Eddington accretion onto black holes commonly use a single fluid model for the collisionless, near-horizon plasma. These models must specify an equation of state. It is common to use an ideal gas with $p = (\gamma - 1) u$ and $\gamma = 4/3, 13/9,$ or $5/3$, but these produce significantly different outcomes. We discuss the origins of this discrepancy and the assumptions underlying the single fluid model. The main result of this investigation is that under conditions relevant to low luminosity black hole accretion the best choice of single fluid adiabatic index is close to but slightly less than $5/3$. Along the way we provide a simple equilibrium model for the relation between the ion-to-electron dissipation ratio and the ion to electron temperature ratio and explore the implications for electron temperature fluctuations in Event Horizon Telescope sources.