Empirical isochrones for single and binary stars in open clusters

We compose systems of empirical isochrones for single and binary stars with various components' mass ratio $q=M_{2}/M_{1}$ ($M_{2}$ – mass of the secondary component, $M_{1}$ – mass of the primary component) in order to search for unresolved binaries and multiple stars in open star clusters. We fit an empirical isochrone for single stars across the main sequence (MS) elements assigned using the HDBSCAN algorithm. Isochrones for binaries are obtained by shifting this empirical isochrone to values determined using PARSEC theoretical isochrones. We determine the parameter q for each source that lies within the corresponding intervals between the binary isochrones. We then plot a probability density distribution of the component mass ratio q and estimate the fraction of binaries in the cluster. This work is focuses on the study of close open star clusters with heliocentric distances less than 200 pc. We consider the color-magnitude diagrams (CMDs) in the Gaia photometric system and the two-index diagrams (TIDs) composed of bands in the visible and infrared wavelengths.