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

The evolution of a dense, rotating cluster with colliding stars is examined theoretically. The colliding stars are assumed to lose kinetic energy much more efficiently than mass so that the gas they expel will not affect the contraction of the stellar component of the cluster. A solution is obtained for the time dependence of cluster flattening by means of the Maclaurin spheroid approximation. An analysis of the terminal evolution and luminosity shows that a sufficiently dense cluster with small angular momentum will collapse into a single rotating body of stellar density (a superstar), or a massive black hole. It is shown that the dissipative contact collisions between the stars will release enough energy to sustain a cluster of 10 to the 9th to 10 to the 10th stars for more than about 10 to the 7th to 10 to the 8th years at luminosities of less than about 10 to the 44th erg/sec.