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The systematic differences between the trigonometric parallaxes of the Hipparcos and TGAS catalogues have been investigated using spherical harmonics. The most significant harmonics in the expansion have been determined. The distribution of the parallax difference dispersion in various regions of the celestial sphere has also been studied. The distribution of the rms deviation has the simplest form in the ecliptic coordinate system. [ABSTRACT FROM AUTHOR]

Based on the Gaia DR1 TGAS parallaxes and photometry from the Tycho-2, Gaia, 2MASS, andWISE catalogues, we have produced a sample of ~100 000 clump red giants within ~800 pc of the Sun. The systematic variations of the mode of their absolute magnitude as a function of the distance, magnitude, and other parameters have been analyzed. We show that these variations reach 0.7 mag and cannot be explained by variations in the interstellar extinction or intrinsic properties of stars and by selection. The only explanation seems to be a systematic error of the Gaia DR1 TGAS parallax dependent on the square of the observed distance in kpc: 0.18 R mas. Allowance for this error reduces significantly the systematic dependences of the absolute magnitude mode on all parameters. This error reaches 0.1 mas within 800 pc of the Sun and allows an upper limit for the accuracy of the TGAS parallaxes to be estimated as 0.2 mas. A careful allowance for such errors is needed to use clump red giants as 'standard candles.' This eliminates all discrepancies between the theoretical and empirical estimates of the characteristics of these stars and allows us to obtain the first estimates of the modes of their absolute magnitudes from the Gaia parallaxes: mode( M ) = −1.49 ± 0.04, mode( M ) = −1.63 ± 0.03, mode( M ) = −1.67 ± 0.05 mode( M ) = −1.67 ± 0.05, mode( M ) = −1.66 ± 0.02, mode( M ) = −1.73 ± 0.03, as well as the corresponding estimates of their de-reddened colors. [ABSTRACT FROM AUTHOR]

A method for a kinematic analysis of stellar radial velocities using spherical harmonics is proposed. This approach does not depend on the specific kinematic model and allows both low-frequency and high-frequency kinematic radial velocity components to be analyzed. The possible systematic variations of distances with coordinates on the celestial sphere that, in turn, are modeled by a linear combination of spherical harmonics are taken into account. Theoretical relations showing how the coefficients of the decomposition of distances affect the coefficients of the decomposition of the radial velocities themselves have been derived. It is shown that the larger the mean distance to the sample of stars being analyzed, the greater the shift in the solar apex coordinates, while the shifts in the Oort parameter A are determined mainly by the ratio of the second zonal harmonic coefficient to the mean distance to the stars, i.e., by the degree of flattening of the spatial distribution of stars toward the Galactic plane. The distances to the stars for which radial velocity estimates are available in the CRVAD-2 catalog have been decomposed into spherical harmonics, and the existing variations of distances with coordinates are shown to exert no noticeable influence on both the solar motion components and the estimates of the Oort parameter A, because the stars from this catalog are comparatively close to the Sun (no farther than 500 pc). In addition, a kinematic component that has no explanation in terms of the three-dimensional Ogorodnikov-Milne model is shown to be detected in the stellar radial velocities, as in the case of stellar proper motions. [ABSTRACT FROM AUTHOR]

A method for determining the velocity field parameters free from the distortions due to the systematic variations of stellar parallaxes over the celestial sphere is proposed. The method is based on the approximation of parallaxes as a function of coordinates on the sphere using spherical harmonics and can be applied in those cases where the solar motion cannot be eliminated from the stellar proper motions. Numerical experiments have shown that our method is able to obtain accurate coordinates of the solar apex and to calculate the kinematic parameters of the Ogorodnikov-Milne model to within three coefficients of the decomposition of parallaxes into first-order spherical harmonics. Examples of applying the method to the stellar proper motions of the Hipparcos catalogue, which admits checking the results using trigonometric parallaxes, are provided. Such a check has been found to yield a positive result only for nearby stars at heliocentric distances that do not exceed 400 pc and for which the parallaxes were determined with a relative error of at least 30%. An interesting feature of this method is the possibility to construct the shape of the figure which is formed by the deviations of the parallaxes from the sphere corresponding to the average parallaxes of the stars under consideration. It should be specially emphasized that all of this is done in the complete absence of information about the stellar parallaxes. The 'solar terms' of the stellar proper motions that are formed by the products of the parallaxes by the solar motion components relative to the centroid of stars are the main source of information about the parallaxes here. [ABSTRACT FROM AUTHOR]

We investigate the relative motion of three stars, ADS 7446, 9346, and 9701, based on long-term observations with the Pulkovo 26-inch refractor. The relative motion of all three stars shows a perturbation that could be produced by the gravitational influence of an invisible companion. For ADS 7446, we have determined the orbit of the photocenter with a period of 7.9 yr; the mass of the companion is more than 0.4 M⊙. For ADS 9346, we have determined the radial velocities of the components: −14.60 km s−1 for A and −13.94 km s−1 for B. For ADS 9346 and 9701, we have determined the dynamical parallaxes, 24 and 20 mas, respectively, which are larger than those in the Hipparcos catalog by 5 mas, and calculated the orbits by the apparent motion parameter (AMP) method. The new orbit of ADS 9346 is: a = 5″.2, P = 2035 yr, and e = 0.46 at the system’s mass M = 2.5 M⊙. The new orbits of ADS 9701 are: ( a = 2″.9, P = 829 yr, e = 0.54, M = 4.3 M⊙) and ( a = 3″.8, P = 1157 yr, e = 0.53, M = 5.0 M⊙). [ABSTRACT FROM AUTHOR]