DYNAMIC EFFECTS OF PRIMORDIAL BINARIES IN STAR-CLUSTERS .1. EQUAL MASSES

We describe the evolution of an idealized star cluster in which all stars have the same mass and initially a modest fraction of the stars form hard binaries. The treatment ranges from simple theory based on considerations of time-scales and energetics, through continuum models which include the effects of segregation of binaries (as they have twice the mass of the single stars), to N-body simulations of systems with a few thousand stars. Particular consideration is given to the circumstances at the close of core collapse and its immediate aftermath. Simple theory implies that core collapse is arrested by two mechanisms: segregation of binaries, which increases their proportion in the core, and the slow-down of core collapse (in terms of the central relaxation time) caused by the deepening of the potential well. These considerations apply, however, only if enough of the binaries are not too hard, otherwise energy is released on too long a time-scale to be effective. Continuum models show that core collapse can be halted only when segregation has proceeded considerably further than is suggested by simple theory, and imply that destruction of binaries in binary-binary interactions is substantial. This is confirmed by direct N-body models, which also show that the energetics of core collapse and re-expansion are complicated by the escape of energetic binaries and single stars. Even so, the simplified and continuum models provide a remarkably good fit to the overall evolution, well into the regime of post-collapse evolution. The size of the core in post-collapse evolution is also in good accord with simple theory. We also consider, more briefly, how various aspects of the evolution depend on the initial distribution of the primordial binaries, and on the presence of a tidal field.