Plummer model

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.

Description of the 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

:$Phi\_P\; =\; -frac\{G\; M\}\{sqrt\{r^2+a^2,,$

where "G" is Newton's gravitational constant.

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 :$M\; =\; int\; 4pi\; r^2\; ho\_P(r)\; dr$is finite. It is decrescent at large distances from the center, $ho\_P\; sim\; r^\{-5\}$ ($r\; gg\; a$), and is constant near the center, $ho\_P\; sim\; mathrm\{constant\}$ ($r\; ll\; a$).

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.

References

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.

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.

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. [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1974A%26A....37..183A NASA ADS] (This article has an appendix on how to create a Plummer model)