Stability of the viscously spreading ring

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.

13 pages, 12 figures; A&A accepted

References in corpus (3)

• Mass Flow and Accretion through gaps in Accretion Discs
• Non-linear fluid dynamics of eccentric discs
• SPH Simulations of Accretion Disks and Narrow Rings

Cited by in corpus (10)

• Simulations of eccentric disks in close binary systems
• Interaction between massive planets on inclined orbits and circumstellar discs
• Simulations of planet-disc interactions using Smoothed Particle Hydrodynamics
• Spectral Methods for Time-Dependent Studies of Accretion Flows. I. Two-dimensional, Viscous, Hydrodynamic Disks
• Oscillations of the Inner Regions of Viscous Accretion Disks
• Measuring the Effects of Artificial Viscosity in SPH Simulations of Rotating Fluid Flows
• An approach for solving the boundary free edge difficulties in SPH modelling: application to a viscous accretion disc in close binaries
• An approach to the Riemann problem in the light of a reformulation of the state equation for SPH inviscid ideal flows: a highlight on spiral hydrodynamics in accretion discs
• How initial and boundary conditions affect protoplanetary migration in a turbulent sub-Keplerian accretion disc: 2D non viscous SPH simulations
• Measuring the Numerical Viscosity in Simulations of Protoplanetary Disks in Cartesian Grids -- The Viscously Spreading Ring Revisited