It is currently believed that angular momentum transport in accretion disks is mediated by magnetohydrodynamic (MHD) turbulence driven by the magnetorotational instability (MRI). More than 15 years after its discovery, an accretion disk model that incorporates the MRI as the mechanism driving the MHD turbulence is still lacking. This dissertation constitutes the first in a series of steps towards establishing the formalism and methodology needed to move beyond the standard accretion disk model and incorporating the MRI as the mechanism enabling the accretion process. I begin by presenting a local linear stability analysis of a compressible, differentially rotating flow and addressing the evolution of the MRI beyond the weak-field limit when magnetic tension forces due to strong toroidal fields are considered. Then, I derive the first formal analytical proof showing that, during the exponential growth of the instability, the mean total stress produced by correlated MHD fluctuations is positive and leads to a net outward flux of angular momentum. I also show that some characteristics of the MHD stresses that are determined during this initial phase are roughly preserved in the turbulent saturated state observed in local numerical simulations. Motivated by these results, I present the first mean-field MHD model for angular momentum transport driven by the MRI that is able to account for a number of correlations among stresses found in local numerical simulations. I point out the relevance of a new type of correlation that couples the dynamical evolution of the Reynolds and Maxwell stresses and plays a key role in developing and sustaining the MHD turbulence. Finally, I address how the turbulent transport of angular momentum depends on the magnitude of the local shear. I show that turbulent MHD stresses in accretion disks cannot be described in terms of shear-viscosity.

A companion to earlier volumes (497, 536, 596, 617 and 631) of the Annals, this entry in the nonlinear astronomy series has contributions by most of the acknowledged experts in the field. They write on many topics, all of current interest. As several hold strong opposing views, this is a lively, important and timely publication.

Magnetized turbulent systems such as accretion disks can be numerically evolved for long times much more cheaply if axisymmetry is assumed. However, the field in such 2D simulations unphysically decays unless dynamo terms, representing the underlying nonaxisymmetry, are explicitly added to the induction equation. Thus far, such simulations have commonly assumed an isotropic, diagonal forms of the dynamo coefficient tensors. While this does yield magnetic fields that do not die off, it is unclear that it is necessarily correct. We test this assumption by azimuthally averaging data from a 3D black hole accretion simulation carried out by the IllinoisGRMHD code. Multiple local models, in which the dynamo electromotive force is a linear function of the local azimuthally averaged magnetic field and current, are tested, but no statistically reliable model could be attained. However, we do find that most of the turbulent kinetic and magnetic energy in the disk is not in the azimuthal mean, but in the RMS deviation, although the jet is mostly axisymmetric. As such, we conclude by discussing more general models that incorporate turbulent energy, dynamo electromotive force and momentum transport.

Accretion disks in compact stellar systems containing white dwarfs, neutron stars or black holes are the principal laboratory for understanding the role of accretion disks in a wide variety of environments from proto-stars to quasars. Recent work on disk instabilities and dynamics has given a new theoretical framework with which to study accretion disks. Modeling of time-dependent phenomena provides new insight into the causes and interpretation of photometric and spectroscopic variability and new constraints on the fundamental physical problem — the origin of viscosity in accretion disks. This book contains expert reviews on the nature of limit cycle thermal instabilities and a variety of closely related topics from the theory of angular momentum transport to eclipse mapping of the disk structure. The result is a comprehensive contemporary survey of the structure and evolution of accretion disks in compact binary systems.

Accretion disks in astrophysics represent the characteristic flow by which compact bodies accrete mass from their environment. Their intrinsically high luminosity, and recent progress in observational accessibility at all wavelength bands, have led to rapidly growing awareness of their importance and made them the object of intense research on widely different scales, ranging from binary stars to young stellar objects and active galactic nuclei. This book contains the proceedings of the NATO Advanced Workshop on `Theory of Accretion Disks 2' for which some of the most active researchers in the different fields came together at the Max-Planck-Institut for Astrophysics in Garching in March, 1993. Its reviews and contributions give an up-to-date account of the present status of our understanding and provide a stimulating challenge in discussions of open questions in a rapidly developing field.

This volume extends the ISSI series on magnetic fields in the Universe into the domain of what are by far the strongest fields in the Universe, and stronger than any field that could be produced on Earth. The chapters describe the magnetic fields in non-degenerate strongly magnetized stars, in degenerate stars (such as white dwarfs and neutron stars), exotic members called magnetars, and in their environments, as well as magnetic fields in the environments of black holes. These strong fields have a profound effect on the behavior of matter, visible in particular in highly variable processes like radiation in all known wavelengths, including Gamma-Ray bursts. The generation and structure of such strong magnetic fields and effects on the environment are also described.