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 UBVRIJHK _ { 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 that it self-consistently handles 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 % \pm 11 % ) of spectroscopically identified main sequence binaries , including 8 of the 9 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 % \pm 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 which remain unidentified spectroscopically is strongly supported by photometry from Gaia DR2 .