# CONSTRAINTS ON VELOCITY ANISOTROPY OF SPHERICAL SYSTEMS WITH SEPARABLE AUGMENTED DENSITIES

## Abstract

If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable into functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy parameter alone, also fixes the anisotropic ratios of every higher order velocity moment. It is inferred from this that the non-negativity of the distribution function necessarily limits the allowed behaviors of the radial function. This restriction is translated into the constraints on the behavior of the anisotropy parameter. We find that not all radial variations of the anisotropy parameter satisfy these constraints and thus anisotropy profiles exist that are not consistent with any separable augmented density.

- Authors:

- National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing 100012 (China)

- Publication Date:

- OSTI Identifier:
- 21578220

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 736; Journal Issue: 2; Other Information: DOI: 10.1088/0004-637X/736/2/151; Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; COSMIC RADIO SOURCES; DENSITY; DISTRIBUTION FUNCTIONS; FUNCTIONS; PHYSICAL PROPERTIES

### Citation Formats

```
An, Jin H., E-mail: jinan@nao.cas.cn.
```*CONSTRAINTS ON VELOCITY ANISOTROPY OF SPHERICAL SYSTEMS WITH SEPARABLE AUGMENTED DENSITIES*. United States: N. p., 2011.
Web. doi:10.1088/0004-637X/736/2/151.

```
An, Jin H., E-mail: jinan@nao.cas.cn.
```*CONSTRAINTS ON VELOCITY ANISOTROPY OF SPHERICAL SYSTEMS WITH SEPARABLE AUGMENTED DENSITIES*. United States. doi:10.1088/0004-637X/736/2/151.

```
An, Jin H., E-mail: jinan@nao.cas.cn. Mon .
"CONSTRAINTS ON VELOCITY ANISOTROPY OF SPHERICAL SYSTEMS WITH SEPARABLE AUGMENTED DENSITIES". United States. doi:10.1088/0004-637X/736/2/151.
```

```
@article{osti_21578220,
```

title = {CONSTRAINTS ON VELOCITY ANISOTROPY OF SPHERICAL SYSTEMS WITH SEPARABLE AUGMENTED DENSITIES},

author = {An, Jin H., E-mail: jinan@nao.cas.cn},

abstractNote = {If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable into functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy parameter alone, also fixes the anisotropic ratios of every higher order velocity moment. It is inferred from this that the non-negativity of the distribution function necessarily limits the allowed behaviors of the radial function. This restriction is translated into the constraints on the behavior of the anisotropy parameter. We find that not all radial variations of the anisotropy parameter satisfy these constraints and thus anisotropy profiles exist that are not consistent with any separable augmented density.},

doi = {10.1088/0004-637X/736/2/151},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 2,

volume = 736,

place = {United States},

year = {2011},

month = {8}

}