Steady critical accretion onto black holes: selfgravity and sonic point characteristics

TL;DR

This paper investigates how selfgravity affects steady accretion flows onto black holes, extending previous models to a broader class of equations of state and identifying conditions where selfgravity influences sonic point characteristics.

Contribution

It generalizes earlier findings by analyzing a wider range of polytropic indices and establishes boundary conditions under which selfgravity impacts sonic points.

Findings

Selfgravity does not influence sonic point characteristics under certain conditions.

Numerical examples show limits of analytic criteria for selfgravity effects.

Implications for black hole lifetime estimates within stellar objects.

Abstract

The spherically symmetric steady accretion of polytropic perfect fluids onto a black hole is the simplest flow model that can demonstrate effects of backreaction (selfgravity). It has been discovered 16 years ago that backreaction does not influence some ("intensive") characteristics of sonic points, under suitable conditions. Herein we consider a wider class of equations of state, with polytropic indices in the range (1,2], and establish detailed boundary conditions that allow one to prove this fact. We find also numerical examples showing limits of our analytic criteria - if suitable analytic conditions are not satisfied, then selfgravity influences all characteristics of sonic points. That fact constrains the applicability of the recent proposal of Baumgarte and Shapiro to estimate the lifetime of black holes within compact stellar objects.