Saturation of the Magneto-rotational Instability in Strongly Radiation-dominated Accretion Disks

The saturation level of the magneto-rotational instability (MRI) in a strongly radiation-dominated accretion disk is studied using a new Godunov radiation MHD code in the unstratified shearing box approximation. Since vertical gravity is neglected in this work, our focus is on how the MRI saturates in the optically thick mid-plane of the disk. We confirm that turbulence generated by the MRI is very compressible in the radiation-dominated regime, as found by previous calculations using the flux-limited diffusion approximation. We also find little difference in the saturation properties in calculations that use a larger horizontal domain (up to four times the vertical scale height in the radial direction). However, in strongly radiation pressure dominated disks (one in which the radiation energy density reaches ~1% of the rest mass energy density of the gas), we find that Maxwell stress from the MRI turbulence is larger than the value produced when radiation pressure is replaced with the same amount of gas pressure. At the same time, the ratio between Maxwell stress and Reynolds stress is increased by almost a factor of eight compared with the gas pressure dominated case. We suggest that this effect is caused by radiation drag, which acts like bulk viscosity and changes the effective magnetic Prandtl number of the fluid. Radiation viscosity significantly exceeds both the microscopic plasma viscosity and resistivity, ensuring that radiation-dominated systems occupy the high magnetic Prandtl number regime. Nevertheless, we find that radiative shear viscosity is negligible compared to the Maxwell stress and Reynolds stress in the flow. This may have important implications for the structure of radiation-dominated accretion disks.