Plummer model

From Wikipedia, the free encyclopedia
Jump to: navigation, search

The Plummer model or Plummer sphere is a density law that was first used by H. C. Plummer to fit observations of globular clusters.[1] It is now often used as toy model in N-body simulations of stellar systems.

Description of the model[edit]

The density law of a Plummer model

The Plummer 3-dimensional density profile is given by

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

where G is Newton's gravitational constant.


The mass enclosed within radius is given by


Many other properties of the Plummer model are described in Herwig Dejonghe's comprehensive paper.[2]

Core radius , where the surface density drops to half its central value, is at .

Half-mass radius is

Virial radius is


The Plummer model comes closest to representing the observed density profiles of star clusters, although the rapid falloff of the density at large radii () is not a good description of these systems.

The behavior of the density near the center does not match observations of elliptical galaxies, which typically exhibit a diverging central density.

The ease with which the Plummer sphere can be realized as a Monte-Carlo model has made it a favorite choice of N-body experimenters, in spite of the model's lack of realism.[3]