Bayesian Characterization of Main-sequence Binaries in the Old Open Cluster NGC 188

The binary fractions of open and globular clusters yield powerful constraints on their dynamical state and evolutionary history. We apply publicly available Bayesian analysis tools to a UBV RIJHK _S photometric catalog of the open cluster NGC 188 to detect and characterize photometric binaries along the cluster main sequence. This technique has the advantage of self-consistently handling photometric errors, missing data in various bandpasses, and star-by-star prior constraints on cluster membership. Simulations are used to verify uncertainties and quantify selection biases in our analysis, illustrating that among binaries with mass ratios >0.5, we recover the binary fraction to better than 7% in the mean, with no significant dependence on binary fraction and a mild dependence on assumed mass-ratio distribution. Using our photometric catalog, we recover the majority (65% ± 11%) of spectroscopically identified main-sequence binaries, including eight of the nine with spectroscopically measured mass ratios. Accounting for incompleteness and systematics, we derive a mass-ratio distribution that rises toward lower mass ratios (within our q > 0.5 analysis domain). We observe a raw binary fraction for solar-type main-sequence stars with mass ratios q > 0.5 of 42% ± 4%, independent of the assumed mass-ratio distribution to within its uncertainties, consistent with literature values for old open clusters but significantly higher than the field solar-type binary fraction. We confirm that the binaries identified by our method are more concentrated than single stars, in agreement with previous studies, and we demonstrate that the binary nature of those candidates that remain unidentified spectroscopically is strongly supported by photometry from Gaia DR2.