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 code to a $UBVRIJHK_{S}$ photometric catalog of the old 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.
