A simple approach to the evolution of twisted accretion discs

Abstract

A simple set of equations is introduced which governs the time evolution of a twisted accretion disc. The time evolution is governed by two ‘viscosities’, one governing shear within the plane of the disc and the other governing shear perpendicular to the disc (brought about by non-planarity of the disc). It is shown that these equations can be put in numerical difference form so that angular momentum is locally conserved. Numerical simulations are given for two simple cases, the evolution of a simple twist in a steady Keplerian accretion disc, and the effect of precession about an axis which is not aligned with the disc on the inner regions of the disc (the Bardeen–Petterson effect). It is emphasized that the methods presented here can be applied to more general rotation laws, and precession rates – for example, warped gaseous discs in galactic potentials.