Dependence of the saturation level of magnetorotational instability on gas pressure and magnetic Prandtl number

A large set of numerical simulations of magnetohydrodynamic (MHD) turbulence induced by the magnetorotational instability (MRI) is presented. Revisiting the previous survey conducted by Sano et al. (2004), we investigate the gas pressure dependence of the saturation level. In ideal MHD simulations, the gas pressure dependence is found to be very sensitive to the choice of a numerical scheme. This is because the numerical magnetic Prandtl number varies according to the scheme as well as the pressure, which considerably affects the results. The saturation level is more sensitive to the numerical magnetic Prandtl number than the pressure. In MHD simulations with explicit viscosity and resistivity, the saturation level increases with the physical magnetic Prandtl number, and it is almost independent of the gas pressure when the magnetic Prandtl number is constant. This is indicative of the incompressible turbulence saturated by the secondary tearing instability.