Global MHD Simulation of the Inner Accretion Disk in a Pseudo-Newtonian Potential

We present a detailed three dimensional magnetohydrodynamic (MHD) simulation describing the inner region of a disk accreting onto a black hole. To avoid the technical complications of general relativity, the dynamics are treated in Newtonian fashion using the pseudo-Newtonian Pacz\'ynski-Wiita potential. The disk evolves due to angular momentum transport which is produced naturally from MHD turbulence generated by the magnetorotational instability. We find that the resulting stress is continuous across the marginally stable orbit, in contradiction with the widely-held assumption that the stress should go to zero there. As a consequence, the specific angular momentum of the matter accreted into the hole is smaller than the specific angular momentum at the marginally stable orbit. The disk exhibits large fluctuations in almost every quantity, both spatially and temporally. In particular, the ratio of stress to pressure (the local analog of the Shakura-Sunyaev $\alpha$ parameter) exhibits both systematic gradients and large fluctuations; from $\sim 10^{-2}$ in the disk midplane at large radius, it rises to $\sim 10$ both at a few gas density scaleheights above the plane at large radius, and near the midplane well inside the plunging region. Driven in part by large-amplitude waves excited near the marginally stable orbit, both the mass accretion rate and the integrated stress exhibit large fluctuations whose Fourier power spectra are smooth "red" power-laws stretching over several orders of magnitude in timescale.