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 amongst the main-sequence , giant and blue straggler 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 - 0.9 M _ { \odot } ) , and extends to a projected radius of 17 pc ( \sim 13 core radii ) .
Our detectable binaries have periods ranging from a few days to of order 10 ^ { 4 } days , and thus are hard binaries that dynamically power the cluster .
The main-sequence solar-type hard binaries in NGC 188 are nearly indistinguishable from similar binaries in the Galactic field .
We observe a global solar-type main-sequence hard-binary frequency in NGC 188 of 23 \pm 2 % , which when corrected for incompleteness results in a frequency of 29 \pm 3 % for binaries with periods less than 10 ^ { 4 } days .
For main-sequence hard binaries in the cluster we observe a log-period distribution that rises towards 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 towards lower-mass companions .
Importantly , the NGC 188 blue straggler binaries show significantly different characteristics than the solar-type main-sequence binaries in NGC 188 .
We observe a blue straggler hard-binary frequency of 76 \pm 19 % , three times that of the main sequence .
The excess of this binary frequency over the normal main-sequence binary frequency is valid at the > 99 % confidence level .
Furthermore , the blue straggler binary eccentricity - log period distribution is distinct from that of the main-sequence at the 99 % confidence level , with the majority of the blue straggler binaries having periods of order 1000 days and lower eccentricities .
The secondary-mass distribution for these long-period blue straggler binaries is narrow and peaked with a mean value of about 0.5 M _ { \odot } .
Predictions for mass-transfer products are most closely consistent with the binary properties of these NGC 188 blue stragglers , which comprise two-thirds of the blue straggler population .
Additionally we compare the NGC 188 binaries to those evolved within the sophisticated N -body open cluster simulation .
The main-sequence hard-binary population predicted by the simulation is significantly different from the main-sequence 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 .