# 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 inmore »

- Authors:

- Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen Ø (Denmark)

- Publication Date:

- OSTI Identifier:
- 22525343

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 811; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; ASTROPHYSICS; AXIAL SYMMETRY; BOUNDARY CONDITIONS; DENSITY; EQUILIBRIUM; INSTABILITY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PERIODICITY; PLASMA; POTENTIALS; SHEAR

### Citation Formats

```
McNally, Colin P., and Pessah, Martin E., E-mail: cmcnally@nbi.dk, E-mail: mpessah@nbi.dk.
```*ON VERTICALLY GLOBAL, HORIZONTALLY LOCAL MODELS FOR ASTROPHYSICAL DISKS*. United States: N. p., 2015.
Web. doi:10.1088/0004-637X/811/2/121.

```
McNally, Colin P., & Pessah, Martin E., E-mail: cmcnally@nbi.dk, E-mail: mpessah@nbi.dk.
```*ON VERTICALLY GLOBAL, HORIZONTALLY LOCAL MODELS FOR ASTROPHYSICAL DISKS*. United States. doi:10.1088/0004-637X/811/2/121.

```
McNally, Colin P., and Pessah, Martin E., E-mail: cmcnally@nbi.dk, E-mail: mpessah@nbi.dk. Thu .
"ON VERTICALLY GLOBAL, HORIZONTALLY LOCAL MODELS FOR ASTROPHYSICAL DISKS". United States.
doi:10.1088/0004-637X/811/2/121.
```

```
@article{osti_22525343,
```

title = {ON VERTICALLY GLOBAL, HORIZONTALLY LOCAL MODELS FOR ASTROPHYSICAL DISKS},

author = {McNally, Colin P. and Pessah, Martin E., E-mail: cmcnally@nbi.dk, E-mail: mpessah@nbi.dk},

abstractNote = {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.},

doi = {10.1088/0004-637X/811/2/121},

journal = {Astrophysical Journal},

number = 2,

volume = 811,

place = {United States},

year = {Thu Oct 01 00:00:00 EDT 2015},

month = {Thu Oct 01 00:00:00 EDT 2015}

}