Simulations of accretion flows crossing the last stable orbit

We use three-dimensional magnetohydrodynamic simulations, in a pseudo-Newtonian potential, to study geometrically thin accretion disk flows crossing r(ms), the marginally stable circular orbit around black holes. We concentrate on vertically unstratified and isothermal disk models but also consider a model that includes stratification. In all cases we find that the sonic point lies just inside r(ms), with a modest increase in the importance of magnetic field energy, relative to the thermal energy, observed inside the last stable orbit. The time-averaged gradient of the specific angular momentum of the flow, (dl/dr), is close to zero within r(ms) despite the presence of large fluctuations and continuing magnetic stress in the plunging region. The result that the speciDc angular momentum is constant within r(ms) is in general agreement with traditional disk models computed using a zero-torque boundary condition at the last stable orbit.