Evolution of rotating star clusters at the inelastic-collision stage. I. Contraction of the stellar component

The evolution of a dense, rotating star cluster is considered at the stage when inelastic two-body collisions have come into play. Colliding stars are assumed to lose kinetic energy much more efficiently than mass, so that the gas they throw off will not affect the contraction of the stellar component of the cluster. A solution for the time dependence of the flattening epsilon-c = 1-c/a and other cluster parameters is obtained in the Maclaurin-spheroid approximation. Analysis of the terminal evolution and luminosity indicates that a sufficiently dense cluster with small angular momentum will collapse into a ''superstar,'' a massive black hole, or several such objects. The dissipative contact collisions will release enough energy to sustain a cluster of 109--1010 stars for t> or approx. =107--108 yr only at luminosities L> or approx. =1044 erg/sec