Equipartition and the Formation of Compact Nuclei in Spherical Stellar Systems

In a spherical system composed of stars of two masses, m1 and m2, with fli2 greater than m1, the heavier stars will lose kinetic energy with a time constant about twice the equipartition time, teq, and wi]1 gravi- tate toward the center. It is shown that if M2, the total mass of the heavier stars, exceeds a certain critical value, the self-attraction of these stars requires such a large rms velocity dispersion that equipartition with the lighter stars becomes impossible. This critical value equals fl(mi/m2)3I2Mi, where M1 is the cor- responding total mass of the lighter stars and i~ is a numerical constant less than unity that equals 0.16 when m2/mi is large. When M2 exceeds this value, the subsystem of heavy stars continues to contract with a time constant about equal to teq, forming a dense nucleus within the core of the system. Application of this criterion to the mass distribution for newly created stars suggests that equipartition is impossible initially for all young systems. The formation and continuing contraction of a dense nucleus of heavy stars is likely to be important in the dynamical evolution of galactic and globular clusters and of galactic nuclei. I. INTRODUCTIO