Kinetic Effects on Turbulence Driven by the Magnetorotational Instability in Black Hole Accretion

Magnetorotational Instability (MRI), the instability causing turbulent transport in accretion disks, is studied in the kinetic regime. Radiatively Inefficient Accretion Flows (RIAFs), like the one around the supermassive black hole in the center of our Galaxy, are believed to be collisionless. Kinetic MHD formalism, based on the moments of the Vlasov equation, is used for linear analysis and nonlinear simulations. ZEUS MHD code is modified to include key kinetic MHD terms: anisotropic pressure tensor and anisotropic thermal conduction. Simulations use the local shearing box approximation. Pressure anisotropy is created, because of the adiabatic invariance ($\mu=p_\perp/B$), as magnetic field is amplified by the MRI. Larmor radius scale instabilities--mirror, ion-cyclotron, and firehose--are excited at large pressure anisotropy. Pressure isotropization due to pitch angle scattering by these instabilities is included as a subgrid model. A key result of the kinetic MHD simulations is that the anisotropic (viscous) stress can be as large as the Maxwell stress. A new numerical method to simulate anisotropic thermal conduction with large temperature gradients is suggested. Simple tests show that the centered differencing of anisotropic thermal conduction can result in heat flowing from lower to higher temperatures, giving rise to negative temperatures. Limiting of transverse temperature gradients does not accentuate temperature extrema