Angular Momentum Transport in Accretion Disks: Scaling Laws in MRI-driven Turbulence

Abstract

We present a scaling law that predicts the values of the stresses obtained in numerical simulations of saturated MRI-driven turbulence in non-stratified shearing boxes. It relates the turbulent stresses to the strength of the vertical magnetic field, the sound speed, the vertical size of the box, and the numerical resolution and predicts accurately the results of 35 numerical simulations performed for a wide variety of physical conditions. We use our result to show that the saturated stresses in simulations with zero net magnetic flux depend linearly on the numerical resolution and would become negligible if the resolution were set equal to the natural dissipation scale in astrophysical disks. We conclude that, in order for MRI-driven turbulent angular momentum transport to be able to account for the large value of the effective alpha viscosity inferred observationally, the disk must be threaded by a significant vertical magnetic field and the turbulent magnetic energy must be in near equipartition with the thermal energy. This result has important implications for the spectra of accretion disks and their stability.

Accepted for publication in ApJ Letters. Two color figures. References added

References in corpus (4)

• Accretion disc viscosity: how big is alpha?
• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. I. The issue of convergence
• The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs
• A Local Model for Angular Momentum Transport in Accretion Disks Driven by the Magnetorotational Instability

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