On the Evolution of Galactic Nuclei. II

The evolution of a very compact stellar system, under the influence first of evaporation of stars and next of direct collisions between stars, is followed to a later stage than that analyzed by Spitzer and Saslaw, to how the luminosity varies with time. On the assumption that the angular momentum per unit mass is constant, the contraction is limited by the initial angular momentum. If , the ratio of the system's rotational velocity to the random stellar velocity, is between 0 1 and 0 01 when collisions begin to dominate over evaporation (state 1), the total energy release is between 5 >c 1058 and 5 X 1060 ergs The detailed rate of energy liberation depends on the exchange of random kinetic energy between the old stars, which collide and liberate gas, and the new stars that form from the gas after this has fallen to the galactic center This exchange, which takes place through distant gravitational encounters, leads to a contraction of the system of old stars, increases the collision rate, accelerates the contraction and enhances the luminosity If this exchange is ignored in the later stages of evolution, then in a system of mass tO8 Mo the peak luminosity is 2 X 10 or 2 X 10 ergs/sec, for e equal to 0.1 or 0.01, respectively, and is prolonged over a period of more than 108 years. In a model which considers the maximum possible rate of energy exchange the peak luminosity is increased by more than an order of magnitude but its duration becomes less than 10 years. The optical thickness of the infalling gas for electron scattering rises to a value of between 5 and 50, for 6 equal to 001, and for the highest luminosities most of the photons emitted will tend to originate in the freely falling gas rather than from the disk of gas and stars at the galactic center.