Chemistry - Plummer model

The Plummer model or Plummer's model is a density profile and potential pair that is used to describe the distribution of positions and velocities of particles in dynamical systems. It was first used by H.C. Plummer (1911) to fit the observations of globular clusters, and so is associated with his name.

Contents

1 Description of the model

2 Properties

3 References

3.1 General resources
3.2 Books
3.3 Articles

Description of the model

The density profile for Plummer model is given by

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

where M is the total mass of the cluster, and b is the Plummer radius. The corresponding potential is then

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

where G is Newton's gravitational constant.

Properties

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. NASA ADS (This article has an appendix on how to create a Plummer model)