Inefficient Angular Momentum Transport in Accretion Disk Boundary Layers: Angular Momentum Belt in the Boundary Layer

Abstract

We present unstratified 3D MHD simulations of an accretion disk with a boundary layer (BL) that have a duration $\sim 1000$ orbital periods at the inner radius of the accretion disk. We find the surprising result that angular momentum piles up in the boundary layer, which results in a rapidly rotating belt of accreted material at the surface of the star. The angular momentum stored in this belt increases monotonically in time, which implies that angular momentum transport mechanisms in the BL are inefficient and do not couple the accretion disk to the star. This is in spite of the fact that magnetic fields are advected into the BL from the disk and supersonic shear instabilities in the BL excite acoustic waves. In our simulations, these waves only carry a small fraction ($\sim 10 \%$) of the angular momentum required for steady state accretion. Using analytical theory and 2D viscous simulations in the $R-\phi$ plane, we derive an analytical criterion for belt formation to occur in the BL in terms of the ratio of the viscosity in the accretion disk to the viscosity in the BL. Our MHD simulations have a dimensionless viscosity ($\alpha$) in the BL that is at least a factor of $\sim 100$ smaller than that in the disk. We discuss the implications of these results for BL dynamics and emission.