Steady state solution of warped accretion discs

TL;DR

This paper derives and compares analytical and numerical solutions for the steady-state shape of warped accretion discs influenced by the Bardeen-Petterson effect, accounting for radially varying viscosities.

Contribution

It introduces a more accurate analytical solution for warped discs with power-law viscosity profiles, improving upon previous models.

Findings

Analytical solutions match numerical results for moderate warps.

Previous models overestimated outer disc inclination changes.

Numerical solutions are necessary for highly misaligned discs.

Abstract

We consider a thin accretion disc warped due to the Bardeen-Petterson effect, presenting both analytical and numerical solutions for the situation that the two viscosity coefficients vary with radius as power law, with the two power law indices not necessarily equal. The analytical solutions are compared with numerical ones, showing that our new analytical solution is more accurate than previous one, which overestimates the inclination changing in the outer disc. Our new analytical solution is appropriate for moderately warped discs, while for extremely misaligned disc, only numerical solution is appropriate.