Magnetorotational instability with smoothed particle hydrodynamics

Abstract

The magnetorotational instability (MRI) is an important process in driving turbulence in sufficiently ionized accretion disks. It has been extensively studied using simulations with Eulerian grid codes, but remains fairly unexplored for meshless codes. Here, we present a thorough numerical study on the MRI using the smoothed particle magnetohydrodynamics method with the geometric density average force expression. We performed 37 shearing box simulations with different initial setups and a wide range of resolution and dissipation parameters. We show, for the first time, that MRI with sustained turbulence can be simulated successfully with smoothed-particle hydrodynamics (SPH), with results consistent with prior work with grid-based codes, including saturation properties such as magnetic and kinetic energies and their respective stresses. In particular, for the stratified boxes, our simulations reproduce the characteristic “butterfly” diagram of the MRI dynamo with saturated turbulence for at least 100 orbits. On the contrary, traditional SPH simulations suffer from runaway growth and develop unphysically large azimuthal fields, similar to the results from a recent study with meshless methods. We investigated the dependency of MRI turbulence on the numerical Prandtl number (Pm) in SPH, focusing on the unstratified, zero net-flux case. We found that turbulence can only be sustained with a Prandtl number larger than ∼2.5, similar to the critical values for the physical Prandtl number found in grid-code simulations. However, unlike grid-based codes, the numerical Prandtl number in SPH increases with resolution, and for a fixed Prandtl number, the resulting magnetic energy and stresses are independent of resolution. Mean-field analyses were performed on all simulations, and the resulting transport coefficients indicate no α-effect in the unstratified cases, but an active αω dynamo and a diamagnetic pumping effect in the stratified medium, which are generally in agreement with previous studies. There is no clear indication of a shear-current dynamo in our simulation, which is likely to be responsible for a weaker mean-field growth in the tall, unstratified, zero net-flux simulation.