DIRECT N-BODY MODELING OF THE OLD OPEN CLUSTER NGC 188: A DETAILED COMPARISON OF THEORETICAL AND OBSERVED BINARY STAR AND BLUE STRAGGLER POPULATIONS

Following on from a recently completed radial-velocity survey of the old (7 Gyr) open cluster NGC 188 in which we studied in detail the solar-type hard binaries and blue stragglers of the cluster, here we investigate the dynamical evolution of NGC 188 through a sophisticated N-body model. Importantly, we employ the observed binary properties of the young (180 Myr) open cluster M35, where possible, to guide our choices for parameters of the initial binary population. We apply pre-main-sequence tidal circularization and a substantial increase to the main-sequence tidal circularization rate, both of which are necessary to match the observed tidal circularization periods in the literature, including that of NGC 188. At 7 Gyr the main-sequence solar-type hard-binary population in the model matches that of NGC 188 in both binary frequency and distributions of orbital parameters. This agreement between the model and observations is in a large part due to the similarities between the NGC 188 and M35 solar-type binaries. Indeed, among the 7 Gyr main-sequence binaries in the model, only those with P greater than or similar to 1000 days begin to show potentially observable evidence for modifications by dynamical encounters, even after 7 Gyr of evolution within the star cluster. This emphasizes the importance of defining accurate initial conditions for star cluster models, which we propose is best accomplished through comparisons with observations of young open clusters like M35. Furthermore, this finding suggests that observations of the present-day binaries in even old open clusters can provide valuable information on their primordial binary populations. However, despite the model's success at matching the observed solar-type main-sequence population, the model underproduces blue stragglers and produces an overabundance of long-period circular main-sequence-white-dwarf binaries as compared with the true cluster. We explore several potential solutions to the paucity of blue stragglers and conclude that the model dramatically underproduces blue stragglers through mass-transfer processes. We suggest that common-envelope evolution may have been incorrectly imposed on the progenitors of the spurious long-period circular main-sequence-white-dwarf binaries, which perhaps instead should have gone through stable mass transfer to create blue stragglers, thereby bringing both the number and binary frequency of the blue straggler population in the model into agreement with the true blue stragglers in NGC 188. Thus, improvements in the physics of mass transfer and common-envelope evolution employed in the model may in fact solve both discrepancies with the observations. This project highlights the unique accessibility of open clusters to both comprehensive observational surveys and full-scale N-body simulations, both of which have only recently matured sufficiently to enable such a project, and underscores the importance of open clusters to the study of star cluster dynamics.