Viscous accretion and ejection from tori around black holes in general relativity

TL;DR

This study uses long-term simulations to analyze viscous accretion and ejection processes around black holes, revealing how angular momentum influences mass infall and ejection, with implications for supermassive black hole growth.

Contribution

It provides a systematic analysis of viscous hydrodynamics in black hole tori, deriving a formula for spin-dependent mass infall, highlighting the role of angular momentum in black hole growth.

Findings

Mass infall fraction is proportional to $j^{-1}$.

Majority of matter is ejected at a few percent of light speed.

Mass ejection occurs outside approximately 2 $r_ ext{ISCO}$.

Abstract

We systematically perform long-term (millions of Schwarzschild time) axisymmetric viscous hydrodynamics simulations for tori around black holes in general relativity supposing the super Eddington accretion flow. The initial condition for the tori is modeled simply by the Fishbone-Moncrief torus with a constant specific angular momentum $j$ but with a wide variety of $j$. We find that for a given density profile, the fraction of the mass infall onto the black hole is approximately proportional to $j^{-1}$, indicating that only a minor fraction of the matter in the torus formed far from the black hole falls into the black hole while the majority is ejected with the typical average velocity of a few percent of the speed of light. We also find that the mass ejection is driven only outside $\approx 2\,r_\mathrm{ISCO}$ where $r_\mathrm{ISCO}$ is the areal radius of the innermost stable circular orbit around black holes, which depends strongly on the black hole spin. We derive an approximate fitting formula for the spin-dependence on the mass infall fraction as $\propto r_\mathrm{ISCO}^{0.7}$, which suggests that the rapid growth of supermassive black holes proceeded primarily by the accretion of the matter with the angular momentum counter-rotating with the black hole spin.