Magnetorotational instability with smoothed particle hydrodynamics

TL;DR

This study demonstrates that smoothed particle magnetohydrodynamics (SPMHD) can successfully simulate the magnetorotational instability (MRI) with sustained turbulence, aligning with grid-based results, and explores the influence of numerical parameters on MRI behavior.

Contribution

First successful simulation of MRI with sustained turbulence using SPMHD, including detailed analysis of turbulence dependence on numerical Prandtl number and mean-field effects.

Findings

MRI with turbulence can be simulated with SPH, matching grid-based results.

Turbulence is sustained only with Prandtl number >~2.5 in SPH.

Magnetic energy and stresses are resolution-independent at fixed Prandtl number.

Abstract

We present a thorough numerical study on the MRI using the smoothed particle magnetohydrodynamics method (SPMHD) with the geometric density average force expression (GDSPH). We perform 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 SPH, with results consistent with prior work with grid-based codes. 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 mesh-less methods. We investigated the dependency of MRI turbulence on the numerical Prandtl number in SPH, focusing on the unstratified, zero net-flux case. We found that turbulence can only be sustained with a Prandtl number larger than $\sim$2.5, similar to the critical values of 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 $\alpha$-effect in the unstratified cases, but an active $\alpha\Omega$ 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.