Differential velocity cumulative distribution (DVCD): an efficient statistical method for binary-star analysis in large stellar catalogues using radial velocities

ABSTRACT Binary stars are fundamental to astrophysics, offering crucial insights into stellar evolution, galactic dynamics, and fundamental physics. Nevertheless, the high dimensionality of orbital parameters and observational constraints poses significant challenges for statistically characterizing their properties. In this study, we present a novel algorithm called the differential velocity cumulative distribution (DVCD) for analysing binary-star systems using radial velocity data. The DVCD method exhibits superior accuracy and computational efficiency compared to existing approaches, achieving computation time reductions of $10^{-4}$ to $10^{-5}$ under equivalent conditions. We applied the DVCD algorithm to red giant samples from APOGEE DR16, dividing the data set into 16 subsets based on $\log g$ and M/H. Our findings reveal that the intrinsic binary fraction decreases with decreasing surface gravity and increasing metallicity, offering valuable constraints on the evolutionary processes of binary stars. This study underscores the potential of the DVCD method for large-scale statistical analyses of binary systems.