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.

1 Description of the model
2 Properties
3 References

[edit] Description of the model

The density law of a Plummer model

The density profile for Plummer model is given by

$\rho_P(r) = \bigg(\frac{3M}{4\pi a^3}\bigg)\bigg(1+\frac{r^2}{a^2}\bigg)^{-\frac{5}{2}}\,,$

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

$\Phi_P = -\frac{G M}{\sqrt{r^2+a^2}}\,,$

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

$M = \int 4\pi r^2 \rho_P(r) dr$

is finite. It is decrescent at large distances from the center, $ρ P ˜ r - 5$ ( $r \gg a$ ), and is constant near the center, $\rho_P \sim \mathrm{constant}$ ( $r \ll a$ ).

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)