Global simulations of magnetorotational turbulence I: convergence and the quasi-steady state

TL;DR

This study uses global 3D MHD simulations to analyze magnetorotational turbulence in accretion disks, demonstrating convergence of turbulent stresses and emphasizing the role of boundary conditions and magnetic energy dynamics.

Contribution

It provides the first detailed analysis of convergence properties and magnetic energy processes in global accretion disk simulations, highlighting differences from shearing-box models.

Findings

Convergence in stress-to-gas-pressure ratio at ~0.04 for specific resolutions.

Magnetic energy mainly produced by Maxwell stresses and mean rotation.

Boundary conditions significantly influence magnetic energy transfer and turbulence behavior.

Abstract

Magnetorotational turbulence provides a viable mechanism for angular momentum transport in accretion disks. We present global, three dimensional (3D), MHD accretion disk simulations that investigate the dependence of the turbulent stresses on resolution. Convergence in the time-and-volume-averaged stress-to-gas-pressure ratio, at a value of $\sim0.04$, is found for a model with radial, vertical, and azimuthal resolution of 12-51, 27, and 12.5 cells per scale-height (the simulation mesh is such that cells per scale-height varies in the radial direction). A control volume analysis is performed on the main body of the disk (|z|<2H) to examine the production and removal of magnetic energy. Maxwell stresses in combination with the mean disk rotation are mainly responsible for magnetic energy production, whereas turbulent dissipation (facilitated by numerical resistivity) predominantly removes magnetic energy from the disk. Re-casting the magnetic energy equation in terms of the power injected by Maxwell stresses on the boundaries of, and by Lorentz forces within, the control volume highlights the importance of the boundary conditions (of the control volume). The different convergence properties of shearing-box and global accretion disk simulations can be readily understood on the basis of choice of boundary conditions and the magnetic field configuration. Periodic boundary conditions restrict the establishment of large-scale gradients in the magnetic field, limiting the power that can be delivered to the disk by Lorentz forces and by stresses at the surfaces. The factor of three lower resolution required for convergence in turbulent stresses for our global disk models compared to stratified shearing-boxes is explained by this finding. (Abridged)