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Supersonic Shear Instabilities in Astrophysical Boundary Layers

Disk accretion onto weakly magnetized astrophysical objects often proceeds via a boundary layer that forms near the object's surface, in which the rotation speed of the accreted gas changes rapidly. Here we study the initial stages of formation for such a boundary layer around a white dwarf or a young star by examining the hydrodynamical shear instabilities that may initiate mixing and momentum transport between the two fluids of different densities moving supersonically with respect to each other. We find that an initially laminar boundary layer is unstable to two different kinds of instabilities. One is an instability of a supersonic vortex sheet (implying a discontinuous initial profile of the angular speed of the gas) in the presence of gravity, which we find to have a growth rate of order (but less than) the orbital frequency. The other is a sonic instability of a finite width, supersonic shear layer, which is similar to the Papaloizou-Pringle instability. It has a growth rate proportional to the shear inside the transition layer, which is of order the orbital frequency times the ratio of stellar radius to the boundary layer thickness. For a boundary layer that is thin compared to the radius of the star, the shear rate is much larger than the orbital frequency. Thus, we conclude that sonic instabilities play a dominant role in the initial stages of nonmagnetic boundary layer formation and give rise to very fast mixing between disk gas and stellar fluid in the supersonic regime.