Abstract
We present local shearing box simulations with the Athena code in order to study angular momentum transport in magnetized accretion disks via the magnetorotational instability (MRI). Parameterizing dissipation in the form of shear viscosity, <i>ν</i>, Ohmic resistivity, η, and the magnetic Prandtl number, Pm = ν/η, we examine the role of these parameters in setting the MRI-turbulent angular momentum transport rate. Through a series of simulations without physical dissipation or vertical gravity, we characterize numerical dissipation as a function of length scale and resolution, quantified in terms of effective ν, η, and Pm. The resulting effective Pm ∼ 2, independent of resolution and initial field geometry, and we find that MRI simulations with effective ν, η, and Pm determined by numerical dissipation are not equivalent to those where these numbers are set by actual physical dissipation. We also determine that energy injected into turbulent fluctuations from differential rotation dissipates on a timescale of much less than an orbital time; turbulent stress and disk heating are locally correlated.
We then study the effect of physical dissipation on the MRI, but without vertical gravity. In agreement with a previous study performed with the ZEUS code, we find that turbulence dies out for values of Pm ≾1 if there is no net magnetic flux through the domain. With a net toroidal magnetic flux, however, turbulence can be sustained even when Pm < 1; only a sufficiently large resistivity can quench the turbulence. In both cases, volume-averaged stress levels increase with Pm when turbulence is sustained.
Finally, we examine the Pm effect with vertical gravity. Again, increasing Pm leads to enhanced turbulence, but with a shallower dependence on Pm and with considerably more temporal variability in the turbulent stress levels. Resistivity is again the critical parameter; if η is sufficiently large, the turbulence decays, leaving a remnant weak radial field. This radial field then shears into toroidal field that eventually reaches sufficient strength to reactivate the MRI. The result is episodic outbursts of turbulence occurring on timescales ranging from tens to hundreds of orbits.
