Plummer model

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

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 ${\displaystyle r}$ is given by

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

Core radius ${\displaystyle r_{c}}$, where the surface density drops to half its central value, is at ${\displaystyle r_{c}=a{\sqrt {{\sqrt {2}}-1}}\approx 0.64a}$.

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