Effect of binary stars on the dynamical evolution of stellar clusters. II - Analytic evolutionary models

Analytical models are used to compute the evolution of the core of a stellar system due simultaneously to stellar evaporation, which causes the system (core) to contract, and to its binaries, which cause it to expand by progressively decreasing its binding energy. The evolution of the system is determined by two parameters: the initial number of stars in the system and the fraction of its stars which are binaries. For a fixed binary fraction, stellar evaporation initially dominates the dynamical evolution if the initial number is sufficiently large, due to the fact that the rate of evaporation is determined chiefly by long-range encounters which increase in importance as the number of stars in the system increases. If stellar evaporation initially dominates, the system first contracts, but as the number of remaining stars in the system decreases by evaporation, the system reaches a minimum radius and a maximum density, and then it expands monotonically as the number of remaining stars decreases further. Open clusters expand monotonically from the beginning if they have anything approaching average Population I binary frequencies. Globular clusters are highly deficient in binaries in order to have formed and retained the high-density stellar cores observed in most of them. The binary fraction for these systems is estimated to be no more than 0.15.