Pairing function of visual binary stars

An all-sky sample of 1227 visual binaries based on Washington Double Star catalogue is constructed to infer the IMF, mass ratio, and projected distance distribution with a dedicated population synthesis model. Parallaxes from Gaia DR2 and Hipparcos are used to verify the distance distribution. The model is validated on the single-star Tycho-2 sample and successfully reproduces the observed magnitudes and angular separations. The projected separation distribution follows $f(s)\sim s^{-1.2}$ in $10^2 - 2\cdot10^3$ AU range for 1--4.5 $m_{\odot}$ primary stars. Several algorithms are explored as pairing functions. Random pairing is confidently rejected. Primary-constrained (PCP) and split-core pairing (SCP), the scenarios adopting primary component's or total system's mass as fundamental, are considered. The preferred IMF slope is $\alpha \sim 2.8$ either way. A simple power-law mass ratio distribution is unlikely, but the introduction of a twin excess provides a favourable result. PCP with $f(q) \sim q^{-1}$ is preferred with a tiny twin fraction, models with $f(q) \sim q^{-1.5}$ are acceptable when a larger twin excess is allowed. SCP is similar to PCP when a larger slope of the power law is adopted: $f(q)\sim q^{\beta+0.7}$.