Stability of the viscously spreading ring
Roland Speith & Wilhelm Kley
Astronomy & Astrophysics, 399, 395 (2003)
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-fold spiral
structures, and to 2nd order additionally two-fold 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.
A&A: March 2003