Global MHD Simulations of Accretion Disks in Cataclysmic Variables (CVs). II. The Relative Importance of MRI and Spiral Shocks

We perform global three-dimensional MHD simulations of unstratified accretion disks in cataclysmic variables (CVs). By including mass inflow via an accretion stream, we are able to evolve the disk to a steady state. We investigate the relative importance of spiral shocks and the magnetorotational instability (MRI) in driving angular momentum transport and how each depend on the geometry and strength of the seed magnetic field and the Mach number of the disk (where Mach number is the ratio of the azimuthal velocity and the sound speed of gas). We use a locally isothermal equation of state and adopt temperature profiles that are consistent with CV disk observations. Our results indicate that the relative importance of spiral shocks and MRI in driving angular momentum transport is controlled by the gas Mach number and the seed magnetic field strength. MRI and spiral shocks provide comparable efficiency of angular momentum transport when the disk Mach number is around 10 and the seed magnetic field has plasma $\beta =400$ (where β is the ratio of gas pressure and magnetic pressure). The MRI dominates whenever the seed field strength, or the disk Mach number, is increased. Among all of our simulations, the effective viscosity parameter ${\alpha }_{eff}\sim 0.016\text{--}0.1$ after MRI saturates and the disk reaches steady state. Larger values of ${\alpha }_{eff}$ are favored when the seed magnetic field has vertical components or the flow has stronger magnetization ($1/\beta$). Our models all indicate that the role of MRI in driving angular momentum transport thus mass accretion in CV disks is indispensable, especially in cool disks with weak spiral shocks.