SPH simulations of accretion disks and narrow rings

We model a massless viscous disk using smoothed particle hydrodynamics (SPH) and note that it evolves according to the Lynden-Bell & Pringle (1974) theory until a non-axisymmetric instability develops at the inner edge of the disk. This instability may have the same origin as the instability of initially axisymmetric viscous disks discussed by Lyubarskij et al. (1994). To clarify the evolution we evolved single and double rings of particles. It is actually inconsistent with the SPH scheme to set up a single ring as an initial condition because SPH assumes a smoothed initial state. As would be expected from an SPH simulation, the ring rapidly breaks up into a band. We analyse the stability of the ring and show that the predictions are confirmed by the simulation.