Plummer model - Alchetron, The Free Social Encyclopedia

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.

Description of the model

The Plummer 3-dimensional density profile is given by

ρ P ( r ) = ( 3 M 4 π a 3 ) ( 1 + r 2 a 2 ) − 5 2 ,

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

Φ P ( r ) = − G M r 2 + a 2 ,

where G is Newton's gravitational constant.

Properties

The mass enclosed within radius r is given by

M ( < r ) = 4 π ∫ 0 r r 2 ρ P ( r ) d r = M r 3 ( r 2 + a 2 ) 3 / 2 .

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

Core radius r c , where the surface density drops to half its central value, is at r c = a 2 − 1 ≈ 0.64 a .

Half-mass radius is r h ≈ 1.3 a

Virial radius is r V = 16 3 π a ≈ 1.7 a

Applications

The Plummer model comes closest to representing the observed density profiles of star clusters, although the rapid falloff of the density at large radii ( ρ → r − 5 ) 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.

References

Plummer model Wikipedia

(Text) CC BY-SA

Contents

Description of the model

Properties

Applications

References