Global Magnetohydrodynamic Simulations of Cylindrical Keplerian Disks

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Abstract
This paper presents a series of global three-dimensional accretion disk simulations carried out in the cylindrical limit in which the vertical component of the gravitational field is neglected. The simulations use a cylindrical pseudo-Newtonian potential, ∝1/(R - Rg), to model the main dynamical properties of the Schwarzschild metric. The radial grid domain runs out to 60Rg to minimize the influence of the outer boundary on the inner disk evolution. The disks are initially constant density with a Keplerian angular momentum distribution and contain a weak toroidal or vertical field that serves as the seed for the magnetorotational instability. These simulations reaffirm many of the conclusions of previous local simulations. The magnetorotational instability (MRI) grows rapidly and produces MHD turbulence with a significant Maxwell stress that drives accretion. Tightly wrapped low-m spiral waves are prominent. In some simulations radial variations in Maxwell stress concentrate gas into rings, creating substantial spatial inhomogeneities. As in previous global simulations, there is a nonzero stress at the marginally stable orbit. The stress is smaller than seen in stratified torus simulations but nevertheless produces a small decline in specific angular momentum inside the last stable orbit. Detailed comparisons between simulations are used to examine the effects of various choices in computational setup. Because the driving instability is local, a reduction in the azimuthal computational domain to some fraction of 2π does not create large qualitative differences. Similarly, the choice of either an isothermal or adiabatic equation of state has little impact on the initial evolution. Simulations that begin with vertical fields have greater field amplification and higher ratios of stress to magnetic pressure compared with those beginning with toroidal fields. In contrast to MHD, hydrodynamics alone neither creates nor sustains turbulence.
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