Turbulence in global simulations of magnetized thin accretion discs

We use a global magnetohydrodynamic simulation of a geometrically thin accretion disc to investigate the locality and detailed structure of turbulence driven by the magnetorotational instability (MRI). The model disc has an aspect ratio H/R≃ 0.07, and is computed using a higher order Godunov magnetohydrodynamics (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 disc 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 〈〈α〉〉≈ 2.5 × 10^-2. The accretion stress peaks at the disc mid-plane, above and below which exists a moderately magnetized corona with patches of superthermal field. By analysing 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 of homogeneous incompressible turbulence. The density field, conversely, exhibits both a longer correlation length and a long correlation time, results that 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-disc accretion.