Pairing function of visual binary stars

Abstract

ABSTRACTAn all-sky sample of 1227 visual binaries based on Washington Double Star catalogue is constructed to infer the initial mass function (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) ∼ s−1.2 in 102–2 × 103 au range for 1–4.5 m⊙ primary stars. Several algorithms are explored as pairing functions. Random pairing is confidently rejected. Primary-constrained pairing (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 α ∼ 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) ∼ q−1 is preferred with a tiny twin fraction, models with f(q) ∼ 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) ∼ qβ + 0.7.