Contribution of Binary Stars to the Velocity Dispersion inside OB Associations with Gaia DR2 Data

Abstract

We estimated the contribution of binary systems to the velocity dispersion inside OB-associations derived from Gaia DR2 proper motions. The maximum contribution to the velocity dispersion is given by the systems with the period of revolution of $P = 5.9$ yr whose components shift by a distance of about the diameter of the system during the base-line time of Gaia DR2 observations. We employed two methods to study the motion of the photocenter of the binary system: the first one uses the total displacement between the initial and final visibility periods and the second one is based on solving a system of $n$ equations defining the displacements at the times ${{t}_{n}}$. The first and second methods yield very similar ${{\sigma }_{{bn}}}$ values of 0.90 and 0.87 km/s, respectively. Taking into account the fact that orbits are elliptical slightly decreases the inferred ${{\sigma }_{{bn}}}$. We estimated the eccentricity-averaged $\overline {{{\sigma }_{{bn}}}}$ value to be $\overline {{{\sigma }_{{bn}}}} = 0.81$ km/s assuming that the orbital eccentricities of massive binary systems are distributed uniformly in the $e \in [0,0.9]$ interval. The choice of the exponent $\gamma$ in the power-law distribution, ${{p}_{q}} \sim {{q}^{\gamma }}$, of the component-mass ratios $q = {{M}_{2}}{\text{/}}{{M}_{1}}$ of binary systems appears to have little effect on ${{\sigma }_{{bn}}}$. A change of $\gamma$ from 0 (flat distribution) to $-$2.0 (preponderance of systems with low-mass components) changes ${{\sigma }_{{bn}}}$ from 0.90 to 1.07 km/s. The paper is based on a presentation made at the conference “Astrometry yesterday, today, tomorrow” (SAI MSU, Oct. 14–16, 2019).