Equilibrium disks, MRI mode excitation, and steady state turbulence in global accretion disk simulations

TL;DR

This paper presents global 3D MHD simulations of accretion disks starting from equilibrium, analyzing MRI mode growth, turbulence saturation, and the influence of resolution and numerical methods on the results.

Contribution

It demonstrates that the saturated turbulence state is independent of initial MRI modes and explores the effects of resolution and algorithms on simulation convergence.

Findings

Saturated turbulence is independent of initial MRI mode.

Time-averaged stress normalized to gas pressure is approximately 0.034.

Convergence during MRI growth occurs with 23-35 cells per scaleheight.

Abstract

Global three dimensional magnetohydrodynamic (MHD) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied. The local linear theory of the magnetorotational instability (MRI) is used as a predictor of the growth of magnetic field perturbations in the global simulations. The linear growth estimates and global simulations diverge when non-linear motions - perhaps triggered by the onset of turbulence - upset the velocity perturbations used to excite the MRI. The saturated state is found to be independent of the initially excited MRI mode, showing that once the disk has expelled the initially net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of converged turbulence, such as the ratio of magnetic energies, are found to be in agreement with previous works. In particular, the globally averaged stress normalized to the gas pressure, <\alpha_{\rm P}> = 0.034, with notably higher values achieved for simulations with higher azimuthal resolution. Supplementary tests are performed using different numerical algorithms and resolutions. Convergence with resolution during the initial linear MRI growth phase is found for 23-35 cells per scaleheight (in the vertical direction).