WIYN OPEN CLUSTER STUDY. XLVIII. THE HARD-BINARY POPULATION OF NGC 188

We present an in-depth study of the hard-binary population of the old (7 Gyr) open cluster NGC 188. Utilizing 85 spectroscopic binary orbits out of a complete sample of 129 detected binary members, we study the cluster binary frequency and the distributions of binary orbital elements among the main-sequence (MS), giant, and blue straggler (BS) populations. The results are derived from our ongoing radial velocity survey of the cluster, which spans in magnitude from the brightest stars in the cluster to V = 16.5 (about 1.1-0.9M(circle dot)), and extends to a projected radius of 17 pc (similar to 13 core radii). Our detectable binaries have periods ranging from a few days to of order 104 days, and thus are hard binaries that dynamically power the cluster. The MS solar-type hard binaries in NGC 188 are nearly indistinguishable from similar binaries in the Galactic field. We observe a global solar-type MS hard-binary frequency in NGC 188 of 23% +/- 2%, which when corrected for incompleteness results in a frequency of 29% +/- 3% for binaries with periods less than 104 days. For MS hard binaries in the cluster, we observe a log-period distribution that rises toward our detection limit, a roughly Gaussian eccentricity distribution centered on e = 0.35 (for binaries with periods longer than the circularization period), and a secondary-mass distribution that rises toward lower-mass companions. Importantly, the NGC 188 BS binaries show significantly different characteristics than the solar-type MS binaries in NGC 188. We observe a BS hard-binary frequency of 76% +/- 19%, three times that of the MS. The excess of this binary frequency over the normal MS binary frequency is valid at the > 99% confidence level. Furthermore, the BS binary eccentricity-log-period distribution is distinct from that of the MS at the 99% confidence level, with the majority of the BS binaries having periods of order 1000 days and lower eccentricities. The secondary-mass distribution for these long-period BS binaries is narrow and peaked with a mean value of about 0.5 M-circle dot. Predictions for mass-transfer products are most closely consistent with the binary properties of these NGC 188 BSs, which comprise two-thirds of the BS population. Additionally, we compare the NGC 188 binaries to those evolved within the sophisticated Hurley et al. (2005) N-body open cluster simulation. The MS hard-binary population predicted by the simulation is significantly different from the MS hard-binary population observed in NGC 188, in frequency and distributions of period and eccentricity. Many of these differences result from the adopted initial binary population, while others reflect on the physics used in the simulation (e. g., tidal circularization). Additional simulations with initial conditions that are better motivated by observations are necessary to properly investigate the dynamical evolution of a rich binary population in open clusters like NGC 188.