Alignment and Precession of a Black Hole with a Warped Accretion Disc

TL;DR

This paper models the steady-state shape of warped accretion discs around black holes, analyzing how misalignment affects disc structure, precession, and alignment timescales, with implications for observational shadowing and disc evolution.

Contribution

It extends previous models by considering realistic surface density profiles and disc truncation effects on warp dynamics and precession timescales.

Findings

Alignment timescale remains relatively unchanged with different density profiles.

Precession timescale is sensitive to the surface density distribution.

Disc truncation impacts precession timescales less for steep density declines.

Abstract

We consider the shape of an accretion disc whose outer regions are misaligned with the spin axis of a central black hole and calculate the steady state form of the warped disc in the case where the viscosity and surface densities are power laws in the distance from the central black hole. We discuss the shape of the resulting disc in both the frame of the black hole and that of the outer disc. We note that some parts of the disc and also any companion star maybe shadowed from the central regions by the warp. We compute the torque on the black hole caused by the Lense-Thirring precession and hence compute the alignment and precession timescales. We generalise the case with viscosity and hence surface density independent of radius to more realistic density distributions for which the surface density is a decreasing function of radius. We find that the alignment timescale does not change greatly but the precession timescale is more sensitive. We also determine the effect on this timescale if we truncate the disc. For a given truncation radius, the the timescales are less affected for more sharply falling density distributions.