New Perspectives on Mean-Field Theories of Astrophysical Dynamos and Accretion Disks

Mean-field theories have become indispensable for studying astrophysical hydromagnetic flows which are otherwise hard to solve exactly. The proper modeling of turbulent velocity and magnetic fields, the validity of mean-field theories in astrophysical flows, and its accuracy and precision when compared to astronomical observations are the main focus of this thesis. In particular, the following studies on astrophysical dynamos and accretion disks are presented: (1) We construct a new model of galactic dynamos in which the turbulent kinetic energy and correlation time are coupled to the galactic differential rotation. We find that a strong differential rotation, while contributing to field amplification by line stretching, can ultimately reduce the overall saturated magnetic field strength compared to conventional models because it decreases the turbulent correlation time when its effect on turbulence is included. (2) We present an efficient, concise, physically grounded way of calculating turbulent transport coefficients through averaging the motion of a single fluid blob. The demonstrated configuration-space calculation gives the same result as much lengthier previously used Fourier-space methods. (3) We generalize dynamo quenching theory to anisotropic flows. Understanding how strong magnetic fields can become in astrophysical objects via dynamos is an active area of research, but quenching theories with predictive power so far have almost exclusively been restricted to systems in which turbulence is isotropic and homogenous. We generalize the isotropic dynamical quenching formulae to anisotropic α2 dynamos, where a new ``selective-damping-τ' closure is proposed that conserves magnetic helicity as required, reduces to previous results when the turbulence is isotropic, and includes the full Lorentz force backreaction of the magnetic field for anisotropic flows. (4) We study the consequences of finite scale separation on validity and precision of mean-field dynamo theories. The governing equations for mean field dynamos are newly derived to properly include terms in higher order of the scale ratio between mean and fluctuating fields, and the intrinsic and filtering errors as two types of precision are identified. The formalism is then applied to a galactic dynamo model and its Faraday rotation measure, in order to quantify the precision of theoretical predictions. (5) We generalize the technique and approach for mean field precision calculation that we first worked out for dynamos and apply it to a hydrodynamic accretion disk model. The fluctuations in the local black-body emission are carefully averaged to obtain a predicted 1 σ error bar in the observed spectrum. This produces a precision error of the theory that must be included when assessing agreement or disagreement between theories and observations