The Frequency and Mass-Ratio Distribution of Binaries in Clusters I: Description of the method and application to M67

We present a new method for probabilistic generative modelling of stellar colour-magnitude diagrams (CMDs) to infer the frequency of binary stars and their mass-ratio distribution. The method invokes a mixture model to account for overlapping populations of single stars, binaries and outliers in the CMD. We apply the model to Gaia observations of the old open cluster, M67, and find a frequency $f_B(q>0.5)=0.258\pm 0.019$ for binary stars with mass ratio greater than 0.5. The form of the mass-ratio distribution function rises towards higher mass ratios for $q>0.3$.