Pairing function of visual binary stars

TL;DR

This study analyzes a large sample of visual binary stars to determine their pairing functions, mass ratio distributions, and separation patterns, using Gaia and Hipparcos data to validate models and explore different pairing scenarios.

Contribution

It introduces a comprehensive population synthesis model to infer pairing functions and mass ratio distributions in visual binaries, rejecting random pairing and favoring primary-constrained pairing with a specific mass ratio distribution.

Findings

Projected separation follows $f(s) \\sim s^{-1.2}$ in 100-2000 AU range.

Primary-constrained pairing with $f(q) \\sim q^{-1}$ is preferred.

A small twin excess is favored in the mass ratio distribution.

Abstract

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