Black hole spin-down by truncated disc emission

TL;DR

This paper investigates how radiation from truncated accretion discs influences black hole spin-down, revealing that certain disc models can significantly reduce the equilibrium spin parameter below the canonical value.

Contribution

It introduces a detailed analysis of radiation capture effects in truncated and optically thin discs, showing their impact on black hole spin evolution and equilibrium spin values.

Findings

Radiation capture effects are negligible for radiatively inefficient discs.

Optically thin discs can lead to a lower equilibrium spin parameter (~0.996-0.997).

Deviations from Keplerian motion near the last stable orbit can dominate over radiation effects.

Abstract

The influence of disc radiation capture upon black hole rotational evolution is negligible for radiatively inefficient discs. For the standard thin disc model it is a slight but potentially important effect leading to the equilibrium spin parameter value of about 0.998. For optically thin discs, the fraction of disc radiation captured by the black hole is however about two times larger. In some disc radiation models, inner parts of the accretion flow are optically thin, advection-dominated flows, and the thin disc ends at some transition radius R_{tr}. The thermal energy of the disc stored in trapped radiation is released at this radius. Angular distribution of the radiation released at this radial photosphere facilitates its capture by the black hole. For accretion rates close to critical and disc truncation radius of (2..4) GM/c^2, radiation capture is most efficient in spinning the black hole down that may lead to a_{eq} ~ 0.996..0.997 or less depending on the mass accretion rate. For an accretion flow radiating some constant fraction \epsilon of dissipated energy, the equilibrium Kerr parameter is shown to obey the relation 1-a_{eq} \propto \epsilon^{3/2} as long as 1-a_{eq} << 1. Deviations from Keplerian law near the last stable orbit dominate over the radiation capture effect if they exceed 1..2%.