Magnetorotational Turbulence and Dynamo in Accretion Disks: a Unified Mean-Field Theory

Accretion governs diverse astrophysical systems—from planet formation to X-ray binaries and jet-launching black holes. Magnetorotational instability (MRI) is widely accepted as the driver of disk turbulence and angular momentum transport. Yet, the persistence of MRI turbulence requires coherent magnetic fields maintained by a dynamo, whose underlying mechanism remains unresolved due to the traditional divide between mean-field dynamo theory and transport studies.

We present a unified mean-field framework for MRI turbulence using direct statistical simulations (DSS) in a zero–net-flux, unstratified shearing box. The model couples large-scale dynamo action and angular momentum transport through a hierarchy of equations up to second-order correlators, closed statistically at third order. This formulation captures the nonlinear couplings among Maxwell, Reynolds, and Faraday stresses mediated by shear and rotation. From this analysis, we identify two key dynamo mechanisms: the rotation–shear–current effect, generating radial magnetic fields, and the rotation–shear–vorticity effect, producing vertical fields—both rooted in large-scale vorticity within MRI turbulence. These results establish a self-consistent mean-field description that unifies turbulence, stress generation, and dynamo action in accretion disks.