Random Gravitational Encounters and the Evolution of Spherical Systems. V. Gravitational Shocks

Numerical calculations of dynamical evolution have been extended to spherical systems in which the stars gain kinetic energy by transient external gravitational perturbations, or "gravitational shocks." Most models were computed for compressive shocks, produced when a cluster crosses the galactic plane; some calculations were made for tidal shocks, produced by passing interstellar clouds or other massive objects. In all models the quasi-static tidal field o the Galaxy was assumed to produce a cutoff in the cluster at the escape radius, r6. It was that all stars have the same mass and that the density distribution is spherical. Because of the strong central condensation, the shock heating required to avert the collapse of the central core is substantially greater than previously realized, requiring that t8,L be less than about Strh, where 4a is the reference relaxation time at the mean density within the median radius, , and tsh is a parameter which measures the rate of shock heating at the radius . It is doubtful whether shock heating is this strong in any clusters. In the range where ts is between Strh and about 1O04a, shock heating can make a dominant contribution to the rate at which stars escape from the system, with an increase in the evaporation probability per star per unit time equal to about 2/t . For open clusters this effect becomes large if r exceeds about 2 pc. Tidal shocks seem to produce about the same effects as compressive shocks. While the computations do not yet include the simultaneous effects both of shock heating and of dynamical relaxation with stars of different masses, the latter process drives the lighter stars out to somewhat greater radii, where the former process should greatly accelerate their escape from the system. Subject headings: globular clusters - stellar dynamics