Plummer model

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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.

Properties[edit]

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

Applications[edit]

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]

References[edit]