Inefficient angular momentum transport in accretion disc boundary layers: angular momentum belt in the boundary layer

We present unstratified 3D magnetohydrodynamical (MHD) simulations of an accretion disc with a boundary layer (BL) that have a duration of similar to 1000 orbital periods at the inner radius of the accretion disc. 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 disc to the star. This is in spite of the fact that magnetic fields are advected into the BL from the disc and supersonic shear instabilities in the BL excite acoustic waves. In our simulations, these waves carry only a small fraction (similar to 10 per cent) 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 disc to the viscosity in the BL. Our MHD simulations have a dimensionless viscosity (alpha) in the BL that is at least a factor of similar to 100 smaller than that in the disc. We discuss the implications of these results for BL dynamics and emission.