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Contribution of binary stars to the velocity dispersion inside OB associations with Gaia DR2 data

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-1, respectively. Taking into account the fact that orbits are elliptical slightly decreases the inferred sigma_bn. We estimated the eccentricity-averaged sigma_bn value to be sigma_bn=0.81 km s-1 assuming that the orbital eccentricities of massive binary systems are distributed uniformly in the [0, 0.9] interval. The choice of the exponent gamma in the power-law distribution, p_q ~ q^gamma, of the component-mass ratios q=M_2/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-1.