Viscous overstability and eccentricity evolution in three-dimensional gaseous discs

Abstract

We investigate the growth or decay rate of the fundamental mode of even symmetry in a viscous accretion disc. This mode occurs in eccentric discs and is known to be potentially overstable. We determine the vertical structure of the disc and its modes, treating radiative energy transport in the diffusion approximation. In the limit of very long radial wavelength, an analytical criterion for viscous overstability is obtained, which involves the effective shear and bulk viscosity, the adiabatic exponent and the opacity law of the disc. This differs from the prediction of a two-dimensional model. On shorter wavelengths (a few times the disc thickness), the criterion for overstability is more difficult to satisfy because of the different vertical structure of the mode. In a low-viscosity disc a third regime of intermediate wavelengths appears, in which the overstability is suppressed as the horizontal velocity perturbations develop significant vertical shear. We suggest that this effect determines the damping rate of eccentricity in protoplanetary discs, for which the long-wavelength analysis is inapplicable and overstability is unlikely to occur on any scale. In thinner accretion discs and in decretion discs around Be stars overstability may occur only on the longest wavelengths, leading to the preferential excitation of global eccentric modes.

11 pages, 8 figures

References in corpus (7)

• Non-linear fluid dynamics of eccentric discs
• Three-dimensional waves generated at Lindblad resonances in thermally stratified disks
• On the dynamics of magnetorotational turbulent stresses
• The Excitation, Propagation and Dissipation of Waves in Accretion Discs: The Non-linear Axisymmetric Case
• Waves and instabilities in a differentially rotating disc containing a poloidal magnetic field
• The effect of an isothermal atmosphere on the propagation of three-dimensional waves in a thermally stratified accretion disk
• The linear stability of dilute particulate rings

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