Angular momentum transport by magnetohydrodynamic turbulence in accretion disks: Gas pressure dependence of the saturation level of the magnetorotational instability

The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard alpha disk model. From our numerical experiments we find that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength and is unaffected by ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly isothermal calculations, where pressure varies little with time. Over the entire region of parameter space explored, turbulence driven by the MRI has many characteristic ratios such as that of the Maxwell stress to the magnetic pressure. We also find that the amplitudes of the spatial fluctuations in density and the time variability in the stress are characterized by the ratio of magnetic pressure to gas pressure in the nonlinear regime. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure-stress relation, however, may require advances in the theoretical understanding of nonsteady magnetic reconnection.