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While it is widely accepted that disk accretion onto compact objects powers a diverse group of objects, from cataclysmic variables to the central engines of active galaxies, there is little consensus on the detailed properties of accretion disks. The reason that no specific model has gained ascendency is not mysterious: accretion physics is complex. It involves multidimensional, time-dependent gas flows in which such processes as radiation transport and magnetohydrodynamics play significant roles. An important tool for investigating this complexity is computer simulation. In this talk I will focus on recent simulations that have helped to clarify some central issues for accretion disks, namely the origin of turbulence and angular momentum transport.
The standard model for angular momentum transport assumes turbulence within the disk; the resulting stress is usually parameterized by the Shakura-Sunyaev ``alpha'' value. The origin of disk turbulence had been a long standing problem, since no compelling dynamical explanation for why a Keplerian disk should be destabilized was forthcoming. The identification of a powerful linear instability in differentially rotating disks (Balbus and Hawley 1991, ApJ, 376, 241) may be the key to understanding the origin of turbulence in these systems. Triggered by a weak (subthermal) magnetic field, the instability has a characteristic growth rate on order the rotation frequency, independent of the strength and geometry of the field. The instability grows because magnetic tension causes low angular momentum orbits to lose yet more angular momentum to higher angular momentum orbits; the flow of angular momentum is not a gentle transfer but an explosive runaway. Only a weak magnetic field and an outwardly decreasing angular velocity are required for the instability to proceed.
This generality of the instability suggests that magnetic fields are fundamental to the evolution and structure of accretion disks. However, the character of the saturated nonlinear instability is not easily obtained by analytic means. Fortunately, both the wavelength and timescale of the instability make it suitable to study by direct numerical simulation. Recent two- and three-dimensional magnetohydrodynamical simulations of a rotationally-supported shearing system, both with and without vertical stratification, demonstrate that the instability produces field amplification and angular momentum transport.
