Unified Mean-Field Theory for Turbulent Accretion Disks: Magnetorotational Turbulence and Dynamos

Magnetorotational instability (MRI)-driven turbulence and dynamo phenomena are analyzed using direct statistical simulations. Our approach begins by developing a unified mean-field model that combines the traditionally decoupled problems of the large-scale dynamo and angular-momentum transport in accretion disks. The model consists of a hierarchical set of equations, capturing up to the second-order correlators while employing a statistical closure approximation for third-order correlators. We highlight the web of interactions that connect different components of stress tensors---Maxwell, Reynolds, and Faraday---through shear, rotation, mean fields, and nonlinear terms. We determine the dominant interactions crucial for the development and sustenance of MRI turbulence. Our unified mean-field model allows for a self-consistent construction of the electromotive force, accounting for inhomogeneities and anisotropies. Regarding the large-scale magnetic field dynamo, we identify two key mechanisms: the rotation-shear-current effect and the rotation-shear-vorticity effect, responsible for generating the radial and vertical magnetic fields respectively. We provide explicit expressions for the transport coefficients associated with each of these dynamo effects. Notably, both mechanisms rely on the intrinsic presence of a large-scale vorticity dynamo within MRI turbulence. Finally, I will delve into the fundamental processes associated with the dynamo cycle patterns.