Stability of the viscously spreading ring

¹ University of Leicester, Department of Physics and Astronomy, Leicester LE1 7RH, UK
² Universität Tübingen, Institut für Astronomie und Astrophysik, Abt. Computational Physics, Auf der Mor gen stelle 10, 72076 Tübingen, Germany e-mail: kley@tat.physik.uni-tuebingen.de

Corresponding author: R. Speith, ros@star.le.ac.uk

Received: 26 July 2002
Accepted: 2 December 2002

Abstract

We study analytically and numerically the stability of the pressure-less, viscously spreading accretion ring. We show that the ring is unstable to small non-axisymmetric perturbations. To perform the perturbation analysis of the ring we use a stretching transformation of the time coordinate. We find that to 1st order, one-armed spiral structures, and to 2nd order additionally two-armed spiral features may appear. Furthermore, we identify a dispersion relation determining the instability of the ring. The theoretical results are confirmed in several simulations, using two different numerical methods. These computations prove independently the existence of a secular spiral instability driven by viscosity, which evolves into persisting leading and trailing spiral waves. Our results settle the question whether the spiral structures found in earlier simulations of the spreading ring are numerical artifacts or genuine instabilities.