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: $f(q)\sim
q^{\beta+0.7}$.
