Investigation of the Kinematics of Stars from the Gaia Data Release 2 with Radial Velocities Catalogue Using Scalar and
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stigation of the Kinematics of Stars from the Gaia Data Release 2 with Radial Velocities Catalogue Using Scalar and Vector Spherical Harmonics A. S. Tsvetkov1* , F. A. Amosov1** , D. A. Trofmiov1 , and S. D. Petrov1 1
St. Petersburg State University, Bibliotechnaya pl. 2, St. Petersburg, 198504 Russia Received May 15, 2019; revised September 4, 2019; accepted September 16, 2019
Abstract—This paper is a continuation of our work. The proper motions and radial velocities of stars from the Gaia DR2 with RV catalogue have been decomposed. We have confirmed that the Ogorodnikov–Milne model is consistent with the observational data and found the kinematic components that are not described by this model. The beyond-the-model harmonics have been partially identified with the nonlinear terms of the extended Oort model and the parameters of the second-order kinematic model. DOI: 10.1134/S1063773719110070 Keywords: Gaia, stellar kinematics, spherical harmonics.
INTRODUCTION
scalar spherical harmonic decomposition coefficients are presented in Vityazev and Tsvetkov (2014). For the convenience of readers, in this paper we present only the tables of relations between the kinematic parameters and decomposition coefficients. The standard notation for the kinematic parameters is adopted in Tables 1 and 2: U, V, W are the components of the translational velocity vector of the Sun V0 among the stars, r is the mean distance of the group of stars under consideration; ω1 , ω2 , ω3 are the components of the angular velocity vector Ω; + + + , M22 , M33 are the parameters of the deforM11 mation tensor describing the contraction–expansion along the principal axes of the Galactic coordinate system; + + + , M13 , M23 are the parameters of the tensor M12 + M describing the velocity field deformation in the principal plane and two perpendicular planes. The inverse relations, which we will not provide here, are also presented in Vityazev and Tsvetkov (2009).
A kinematic analysis of the proper motions and radial velocities of 6 million stars from the Gaia DR2 with RV catalogue was performed by Tsvetkov and Amosov (2019). The parameters of the linear threedimensional Ogorodnikov–Milne model (Ogorodnikov 1965) were determined from separate and simultaneous solutions. However, the traditional approach, which consists in solving the conditional equations by the least-squares method, has wellknown shortcomings, because it does not allow the systematic components in the observational data that initially were not included in the model equations to be revealed. Using the apparatus of vector (when analyzing the proper motions) and scalar (when analyzing the radial velocities) spherical harmonics allows one not only to detect the disregarded systematic effects, but also to check whether the model is consistent with the observations. This technique was apparently first described by Vityazev and Tsvetkov (1989) and applied by Vityazev and Tsvetkov (1990) based data from the FK4 and earlier catalogues. The complete form and the algorithm of calculating the vector
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