Dynamics of Thin Astrophysical Boundary Layers

Abstract

We study the modal structure and

angular momentum transport mechanisms of astrophysical boundary

layers. We focus

on the case where the accretion disk extends all the way to surface of

the star and the boundary layer is thin in comparison with

the stellar radius. Such a scenario is applicable, for example, to

weakly magnetized

neutron stars and white dwarfs, for which the strength of the magnetic

field outside the star is too small to disrupt the disk and funnel

matter to the poles.

Within the boundary layer, material rotating at the Keplerian velocity

within the disk slows down to the rotational

velocity inside the star. This generates intense velocity gradients and makes

the boundary layer susceptible to shear

instabilities. By performing a linear stability analysis for the

simplified case

of a plane-parallel, compressible shear layer, we argue that

astrophysical boundary layers are unstable to the sonic

instability. This instability is part of a more general class of

acoustic instabilities that includes the Papaloizou-Pringle instability.

We confirm the predictions of our linear stability analysis by running a suite

of simulations in 2D and 3D, with and without stratification, and

with and without magnetic field. In our numerical experiments, we find

that acoustic modes excited by the sonic instability persist even

in the nonlinear regime. We explain the morphological properties

and derive analytic formulas for the pattern speed of these acoustic modes.

Our work has significant implications for semianalytic models

describing the structure and spectral emission from boundary

layers. Typically, these models adopt a local, effective viscosity

prescription for the angular momentum transport. However, in our

simulations we find that angular momentum transport in the boundary

layer is facilitated by acoustic modes. In this scenario, accreting

material inside the

boundary layer loses angular momentum to sound waves that propagate

into both the star and the disk. Since transport of angular momentum by

waves is inherently

nonlocal, our work invites the construction of new phenomenological models of

the boundary layer in which angular momentum is transported by waves

rather than by an anomalous viscosity.