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 height-independent 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 shearing-periodic boundary conditions. We refer to the resulting framework as the vertically global shearing box (VGSB). These models can be non-axisymmetric 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 shearing-periodic boundary conditions to allow for a height-dependent angular frequency and shear rate. We also discuss the limitations that result from the radial approximations that are needed in order to impose height-dependent 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.

24 pages, 8 figures, updated to match published version

References in corpus (8)

• Turbulent Structure of a Stratified Supernova-Driven Interstellar Medium
• Semi-global simulations of the magneto-rotational instability in core collapse supernovae
• Direct simulations of a supernova-driven galactic dynamo
• Vertical shear instability in accretion disc models with radiation transport
• MHD Simulations of Global Accretion Disks with Vertical Magnetic Fields
• On the vertical-shear instability in astrophysical discs
• High accretion rates in magnetised Keplerian discs mediated by a Parker instability driven dynamo
• Shearing box simulations of accretion disk winds

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• Vortices and the saturation of the vertical shear instability in protoplanetary disks
• Global Simulations of the Vertical Shear Instability with Non-ideal Magnetohydrodynamical Effects
• Local models of astrophysical discs
• Polydisperse Streaming Instability III. Dust evolution encourages fast instability
• Stratified and vertically-shearing streaming instabilities in protoplanetary disks
• Linear analysis of the vertical shear instability: outstanding issues and improved solutions (Research Note)
• Motivation and challenge to capture both large scale and local transport in next generation accretion theory
• Magnetohydrodynamics in a Cylindrical Shearing Box
• A minimal model for vertical shear instability in protoplanetary accretion disks
• Analytic construction of baroclinic tori by non-linear summation