Testing the distance scale of the Gaia TGAS catalogue by kinematic method

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We have studied the simultaneous and separate solutions of the basic kinematic equations obtained using the stellar velocities calculated on the basis of data from the Gaia TGAS and RAVE5 catalogues. By comparing the values of Omega₀' found by separately analyzing only the line-of-sight velocities of stars and only their proper motions, we have determined the distance scale correction factor p to be close to unity, 0.97+/-0.04. Based on the proper motions of stars from the Gaia TGAS catalogue with relative trigonometric parallax errors less than 10% (they are at a mean distance of 226 pc), we have found the components of the group velocity vector for the sample stars relative to the Sun (U,V,W)o=(9.28,20.35,7.36)+/-(0.05,0.07,0.05) km s⁻¹, the angular velocity of Galactic rotation Omega0=27.24+/-0.30 km s⁻¹ kpc⁻¹, and its first derivative Omega₀'=-3.77+/-0.06 km s⁻¹ kpc⁻²; here, the circular rotation velocity of the Sun around the Galactic center is V₀=218+/-6 km s⁻¹ kpc (for the adopted distance R₀=8.0+/-0.2 kpc), while the Oort constants are A=15.07+/-0.25 km s⁻¹ kpc⁻¹ and B=-12.17+/-0.39 km s⁻¹ kpc⁻¹, p=0.98+/-0.08. The kinematics of Gaia TGAS stars with parallax errors more than 10% has been studied by invoking the distances from a paper by Astraatmadja and Bailer-Jones that were corrected for the Lutz-Kelker bias. We show that the second derivative of the angular velocity of Galactic rotation Omega₀"=0.864+/-0.021 km s⁻¹ kpc⁻³ is well determined from stars at a mean distance of 537 pc. On the whole, we have found that the distances of stars from the Gaia TGAS catalogue calculated using their trigonometric parallaxes do not require any additional correction factor.