Dr. Tushar Mondal

Accretion is a fundamental cosmic process involved in phenomena ranging from planet formation to X-ray binaries and the generation of jets from protostars and black holes. Evidence suggests magnetorotational instability (MRI) drives the turbulence that transports angular momentum outwards, allowing gas to spiral inwards in a disk. MRI-induced turbulence depends on coherent magnetic fields, which are susceptible to dissipation unless maintained by a dynamo. The fundamental processes sustaining MRI turbulence and dynamos remain elusive due to the historical separation of mean-field dynamo and angular momentum transport problems. We investigate MRI turbulence and dynamo phenomena using direct statistical simulations in a zero net-flux, unstratified shearing box. Our approach begins with the development of a unified mean-field model that integrates the traditionally decoupled problems of large-scale dynamo action and angular momentum transport in accretion disks. The model includes a hierarchical set of equations, capturing up to second-order correlators, with a statistical closure approximation used for third-order correlators. We emphasize the complex web of interactions connecting various components of the stress tensors—Maxwell, Reynolds, and Faraday—through shear, rotation, correlators associated with mean fields, and nonlinear terms. By identifying the dominant interactions, we pinpoint the key mechanisms essential for the generation and maintenance of MRI turbulence. Our general mean-field model for MRI turbulence allows for a self-consistent formulation of the electromotive force, accounting for both inhomogeneities and anisotropies. In the context of large-scale magnetic field generation, we identify two critical mechanisms: the rotation-shear-current effect, which generates radial magnetic fields, and the rotation-shear-vorticity effect, responsible for vertical magnetic fields. We provide explicit, non-perturbative expressions for the transport coefficients associated with these dynamo effects. Importantly, both mechanisms rely on the inherent presence of large-scale vorticity dynamo within MRI turbulence. Lastly, I will discuss the associated helicities in such unstratified turbulent disks.