Causal Viscosity in Accretion Disc Boundary Layers

Abstract

The structure of the boundary layer region between the disc and a comparatively slowly rotating star is studied using a causal prescription for viscosity. The vertically integrated viscous stress relaxes towards its equilibrium value on a relaxation timescale $τ$, which naturally yields a finite speed of propagation for viscous information. For a standard alpha prescription with alpha in the range 0.1-0.01, and ratio of viscous speed to sound speed in the range 0.02-0.5, details in the boundary layer are strongly affected by the causality constraint. We study both steady state polytropic models and time dependent models, taking into account energy dissipation and transport. Steady state solutions are always subviscous with a variety of $Ω$ profiles which may exhibit near discontinuities. For alpha =0.01 and small viscous speeds, the boundary layer adjusted to a near steady state. A long wavelength oscillation generated by viscous overstability could be seen at times near the outer boundary. Being confined there, the boundary layer remained almost stationary. However, for alpha =0.1 and large viscous speeds, short wavelength disturbances were seen throughout which could significantly affect the power output in the boundary layer. This could be potentially important in producing time dependent behaviour in accreting systems such as CVs and protostars.