Global Simulations of Accretion Disks I: Convergence and Comparisons with Local Models

TL;DR

This paper presents high-resolution global MHD simulations of accretion disks, demonstrating convergence and comparing results with local models, highlighting the importance of magnetic flux connectivity in disk physics.

Contribution

The study introduces a new orbital advection algorithm in Athena, achieving unprecedented resolution in global disk simulations and identifying magnetic field tilt as a key convergence diagnostic.

Findings

Convergence achieved at high resolutions with 32-64 zones per vertical scale height.

Magnetic field tilt angle is a reliable indicator of simulation convergence.

Global magnetic flux conservation differs from local models, emphasizing the importance of global physics.

Abstract

Grid-based magnetohydrodynamic (MHD) simulations have proven invaluable for the study of astrophysical accretion disks. However, the fact that angular momentum transport in disks is mediated by MHD turbulence (with structure down to very small scales) raises the concern that the properties of the modeled accretion disks are affected by the finite numerical resolution of the simulation. By implementing an orbital advection algorithm into the Athena code in cylindrical geometry, we have performed a set of global (but unstratified) Newtonian disk simulations extending up to resolutions previously unattained. We study the convergence of these models as a function of spatial resolution and initial magnetic field geometry. The usual viscosity parameter ($\alpha$) or the ratio of thermal-to-magnetic pressure ($\beta$) are found to be poor diagnostics of convergence, whereas the average tilt angle of the magnetic field in the $(r,\phi)$-plane is a very good diagnostic of convergence. We suggest that this is related to the saturation of the MHD turbulence via parasitic modes of the magnetorotational instability. Even in the case of zero-net magnetic flux, we conclude that our highest resolution simulations (with 32-zones and 64-zones per vertical scale height) have achieved convergence. Our global simulations reach resolutions comparable to those used in local, shearing box models of MHD disk turbulence. We find that the saturation predictors derived from local simulations correspond well to the instantaneous correlations between local flux and stress found in our global simulations. However, the conservation of magnetic flux implicit in local models is not realized in our global disks. Thus, the magnetic connectivity of an accretion disk represents physics that is truly global and cannot be captured in any ab-initio local model.