Star clusters with primordial binaries - II. Dynamical evolution of models in a tidal field

We extend our analysis of the dynamical evolution of simple star cluster models, in order to provide comparison standards that will aid in interpreting the results of more complex realistic simulations. We augment our previous primordial-binary simulations by introducing a tidal field, and starting with King models of different central concentrations. We present the results of N-body calculations of the evolution of equal-mass models, starting with primordial binary fractions of 0-100 per cent, and N values from 512 to 16384. We also attempt to extrapolate some of our results to the larger number of particles that are necessary to model globular clusters. We characterize the steady-state 'deuterium main-sequence' phase in which primordial binaries are depleted in the core in the process of 'gravitationally burning'. In this phase, we find that the ratio of the core to half-mass radius, r(c)/r(h), is similar to that measured for isolated systems. In addition to the generation of energy due to hardening and depletion of the primordial binary population, the overall evolution of the star clusters is driven by a competing process: the tidal dissolution of the system. If the primordial binary fraction is greater than 5 per cent and the total number of particles N >= 8192, we find that primordial binaries are not fully depleted before tidal dissolution, in systems initially described by a King model with a self-consistent tidal field. We compare our findings, obtained by means of direct N-body simulations but scaled, where possible, to larger N, with similar studies carried out by means of Monte Carlo methods. We find significant qualitative and quantitative differences with the results in the earlier paper. Some of these differences are explicable by the different treatment of the tidal field in the two studies. Others, however, confirm the conclusion of Fregeau et al. that the efficiency of binary burning in the earlier Monte Carlo runs was too high. There remain unexplained differences, however. In particular, the binary population appears to be depleted too quickly, even in the most recent Monte Carlo results.