Plummer model

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The Plummer model or Plummer's model is a density profile and
potential pair. It was first used by H.C. Plummer (1911) to fit the observations of globular clusters. It
is now often used as a stellar distribution model in simulations.

Contents

1 Description of the
model

2 Properties

3 References

3.1 General
resources

3.2 Books

3.3 Articles

[edit]
Description of the model

The density law of a Plummer model

The density profile for Plummer model is given by

where M is the total mass of the cluster, and a is the
Plummer radius, a scale parameter which sets the density of the cluster.
The corresponding potential is then

where G is Newton's gravitational
constant.

[edit]
Properties

The Plummer density distribution can be used as an analytical toy model
either for globular clusters or galaxies. The total mass of the model, given
by

is finite. It is decrescent at large distances from the center,
(),
and is constant near the center,
().

The behaviour near the center does not match observations of elliptical
galaxies, which show a density divergence all the way to the Hubble Space
Telescope resolution. This makes the Plummer density law a rather poor
description of them.

[edit]
References

[edit]
General resources

NASA Astrophysics Data System (http://adswww.harvard.edu/) has a
collection of past articles, from all major astrophysics journals and many
conference proceedings.

[edit]
Books

Binney, James; Tremaine, Scott (1987). Galactic Dynamics, Princeton
University Press, Princeton, New Jersey.

Heggie, Douglas; Hut, Piet (2003). The Gravitational Million-Body
Problem: A Multidisciplinary Approach to Star Cluster Dynamics, Cambridge
University Press.

[edit]
Articles

Aarseth, S. J.; Henon, M.; Wielen, R. (1974). A comparison of numerical
methods for the study of star cluster dynamics. Astronomy and
Astrophysics 37 183. NASA
ADS (This article has an appendix on how to create a Plummer model)

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This page was last modified 10:33, 23 September 2006.

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