Kinematic study of the association Cyg OB3 with Gaia DR2

We study the stellar kinematic properties and spatial distribution of the association Cyg OB3 using precise astrometric data from Gaia DR2. All known O- and B-type stars in Cyg OB3 region with positions, parallaxes and proper motions available are included, comprising a total of 41 stars. The majority of stars are found to be concentrated at a heliocentric distance of 2.0 +/- 0.3 kpc. The mean peculiar velocity of the sample after removing Galactic rotation and solar motion is ~22 km/s, dominated by the velocity component towards the Galactic center. The relative position and velocity of the black hole X-ray binary Cyg X-1 with respect to the association suggest that Cyg OB3 is most likely its parent association. The peculiar kinematic properties of some of the stars are revealed and are suggestive of past stellar encounters. The sample includes a previously known runaway star HD 227018, and its high peculiar velocity of ~50 km/s is confirmed with Gaia. We estimated the velocities of stars relative to the association and the star HD 225577 exhibits peculiar velocity smaller than its velocity relative to the association. The star has lower value of proper motion than the rest of the sample. The results suggest a slowly expanding nature of the association, which is supported by the small relative speeds