The Plummer 3-dimensional density profile is given by ρ ρ P ( r ) = 3 M 0 4 π π a 3 ( 1 + r 2 a 2 ) − − 5 / 2 , where M 0 is the total mass of the cluster, and a is the Plummer radius, a scale parameter that sets the size of the cluster core. The corresponding potential is Φ Φ P ( r ) = − − G M 0 r 2 + a 2 , where G is Newton 's gravitational constant. The velocity dispersion is σ σ P 2 ( r ) = G M 0 6 r 2 + a 2 .