The Shape of an Accretion Disc in a Misaligned Black Hole Binary

TL;DR

This paper models the shape of a misaligned accretion disc around a spinning black hole, considering the competing effects of tidal torques and Lense-Thirring precession, providing both numerical and analytical solutions.

Contribution

It offers the first comprehensive numerical and analytical models of accretion disc shapes in misaligned black hole binaries, accounting for complex precession effects.

Findings

Analytical solutions are accurate for large misalignments.

Numerical solutions provide detailed disc shape configurations.

Analytical approximations are computationally efficient.

Abstract

We model the overall shape of an accretion disc in a semi-detached binary system in which mass is transfered on to a spinning black hole the spin axis of which is misaligned with the orbital rotation axis. We assume the disc is in a steady state. Its outer regions are subject to differential precession caused by tidal torques of the companion star. These tend to align the outer parts of the disc with the orbital plane. Its inner regions are subject to differential precession caused by the Lense-Thirring effect. These tend to align the inner parts of the disc with the spin of the black hole. We give full numerical solutions for the shape of the disc for some particular disc parameters. We then show how an analytic approximation to these solutions can be obtained for the case when the disc surface density varies as a power law with radius. These analytic solutions for the shape of the disc are reasonably accurate even for large misalignments and can be simply applied for general disc parameters. They are particularly useful when the numerical solutions would be slow.