Estimate per-star binary mass fraction

[Gabriel-p]

I think this is rather simple to implement using Bayesian inference:

• The free parameters are the primary mass (M1) and the binary fraction (f), to estimate the secondary mass
• A theoretical isochrone with the cluster's (z, a) is required, affected by the appropriate E(B-V), dm

1. Select an observed binary system and generate a 2D Gaussian in the CMD, from its magnitude and color (and uncertainties)
2. Sample (M1, f)
3. Find the points in the (interpolated) isochrone with the closest masses to M1 and M2(=f*M1)
4. Combine the magnitudes of both stars to generate the binary system's CMD position
5. Evaluate the CMD position of this binary system in the 2D Gaussian generated in step 1
6. Steps 1 to 5 are the Bayesian inference loop. Repeat for all binary systems

Related articles:

• Mass distribution of binary stars using an iterative inversion technique
• A method to deconvolve mass ratio distribution of binary stars
• Study of the mass-ratio distribution of spectroscopic binaries - I. A novel algorithm