On Vertically Global, Horizontally Local Models for Astrophysical Disks
Abstract
Disks with a barotropic equilibrium structure, for which the pressure is only a function of the density, rotate on cylinders in the presence of a gravitational potential, so that the angular frequency of such a disk is independent of height. Such disks with barotropic equilibria can be approximately modeled using the shearing box framework, representing a small disk volume with heightindependent angular frequency. If the disk is in baroclinic equilibrium, the angular frequency does generally depend on height, and it is thus necessary to go beyond the standard shearing box approach. In this paper, we show that given a global disk model, it is possible to develop approximate models that are local in horizontal planes without an expansion in height with shearingperiodic boundary conditions. We refer to the resulting framework as the vertically global shearing box (VGSB). These models can be nonaxisymmetric for globally barotropic equilibria but should be axisymmetric for globally baroclinic equilibria. We provide explicit equations for this VGSB which can be implemented in standard magnetohydrodynamic codes by generalizing the shearingperiodic boundary conditions to allow for a heightdependent angular frequency and shear rate. We also discuss the limitations that result from the radial approximations that are needed in order to impose heightdependent shearing periodic boundary conditions. We illustrate the potential of this framework by studying a vertical shear instability and examining the modes associated with the magnetorotational instability.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 2015
 DOI:
 10.1088/0004637X/811/2/121
 arXiv:
 arXiv:1406.4864
 Bibcode:
 2015ApJ...811..121M
 Keywords:

 accretion;
 accretion disks;
 instabilities;
 ISM: structure;
 magnetic fields;
 magnetohydrodynamics: MHD;
 plasmas;
 Astrophysics  Earth and Planetary Astrophysics;
 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 24 pages, 8 figures, updated to match published version