Turbulence in Global Simulations of Magnetized Thin Accretion Disks

Abstract

We use a global magnetohydrodynamic simulation of a geometrically thin accretion disk to investigate the locality and detailed structure of turbulence driven by the magnetorotational instability (MRI). The model disk has an aspect ratio $H/R\simeq 0.07$, and is computed using a higher-order Godunov MHD scheme with accurate fluxes. We focus the analysis on late times after the system has lost direct memory of its initial magnetic flux state. The disk enters a saturated turbulent state in which the fastest growing modes of the MRI are well-resolved, with a relatively high efficiency of angular momentum transport $<<\alpha >>\approx 2.5\times 10^{-2}$. The accretion stress peaks at the disk midplane, above and below which exists a moderately magnetized corona with patches of superthermal field. By analyzing the spatial and temporal correlations of the turbulent fields, we find that the spatial structure of the magnetic and kinetic energy is moderately well-localized (with correlation lengths along the major axis of $2.5H$ and $1.5H$ respectively), and generally consistent with that expected from homogenous incompressible turbulence. The density field, conversely, exhibits both a longer correlation length and a long correlation time, results which we ascribe to the importance of spiral density waves within the flow. Consistent with prior results, we show that the mean local stress displays a well-defined correlation with the local vertical flux, and that this relation is apparently causal (in the sense of the flux stimulating the stress) during portions of a global dynamo cycle. We argue that the observed flux-stress relation supports dynamo models in which the structure of coronal magnetic fields plays a central role in determining the dynamics of thin-disk accretion.

24 pages and 25 figures. MNRAS in press. Version with high resolution figures available from http://jila.colorado.edu/~krb3u/Thin_Disk/thin_disk_turbulence.pdf

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