We applied the currently most comprehensive version of the statistical-parallax technique to derive kinematical parameters of the maser sample with 136 sources. Our kinematic model comprises the overall rotation of the Galactic disk and the spiral density-wave effects. We take into account the variation of radial velocity dispersion with Galactocentric distance. The best description of the velocity field is provided by the model with constant radial and vertical velocity dispersions, (σU 0, σW 0) ≈ (9.4 ± 0.9 , 5.9 ± 0.8) km/s. We compute flat Galactic rotation curve over the Galactocentric distance interval from 3 to 15 kpc and find the local circular rotation velocity to be V 0 ≈ (235 − 238) km/s ±7 km/s. We also determine the parameters of the four-armed spiral pattern (pitch angle i ≈ (−10.4 ± 0.3) • and the phase of the Sun χ 0 ≈ (125 ± 10) • ). The radial and tangential spiral perturbations are about f R ≈ (−6.9 ± 1.4) km/s, f Θ ≈ (+2.8 ± 1.0) km/s. The kinematic data yield a solar Galactocentric distance of R 0 ≈ (8.24 ± 0.12) kpc. Based on rotation curve parameters and the asymmetric drift we Infer the exponential disk scale H D ≈ (2.7 ± 0.2) kpc under assumption of marginal stability of the intermediate-age disk, and finally we estimate the minimum local surface disk density, Σ(R 0 ) > (26 ± 3) M ⊙ pc −2 .

The spatial velocities of all 28 currently known masers having trigonometric parallaxes, proper motion and line-of-site velocities are reanalysed using the Bottlinger equations. These masers are associated with 25 active star-forming regions and are located in the range of galactocentric distances 3 < R < 14 kpc. To determine the Galactic rotation parameters, we have used the first three Taylor expansion terms of angular rotation velocity at the galactocentric distance of the Sun, R 0 = 8 kpc. We have obtained the following solutions: 0 = −31.0 ± 1.2 km s −1 kpc −1 , 0 = 4.46 ± 0.21 km s −1 kpc −2 , 0 = −0.876 ± 0.067 km s −1 kpc −3 ; Oort constants, A = 17.8 ± 0.8 km s −1 kpc −1 , B = −13.2 ± 1.5 km s −1 kpc −1 ; the circular velocity of the solar neighbourhood rotation V 0 = 248 ± 14 km s −1 . A Fourier analysis of the galactocentric radial velocities of masers V R has allowed us to estimate the wavelength λ = 2.0 ± 0.2 kpc and peak velocity f R = 6.5 ± 2 km s −1 of periodic perturbations from the density wave and velocity of the perturbations 4 ± 1 km s −1 near the location of the Sun. The phase of the Sun in the density wave is estimated as χ ≈ −130 • ± 10 • . Taking into account perturbations evoked by the spiral density wave, we have obtained the following non-perturbed components of the peculiar solar velocity with respect to the local standard of rest (LSR): (U , V , W ) LSR = (5.5, 11, 8.5) ± (2.2, 1.7, 1.2) km s −1 .

Three three-component (bulge, disk, halo) model Galactic gravitational potentials differing by the expression for the dark matter halo are considered. The central (bulge) and disk components are described by the Miyamoto-Nagai expressions. The Allen-Santillán (I), Wilkinson-Evans (II), and Navarro-Frenk-White (III) models are used to describe the halo. A set of present-day observational data in the range of Galactocentric distances R from 0 to 200 kpc is used to refine the parameters of these models. For the Allen-Santillán model, a dimensionless coefficient γ has been included as a sought-for parameter for the first time. In the traditional and modified versions, γ = 2.0 and 6.3, respectively. Both versions are considered in this paper. The model rotation curves have been fitted to the observed velocities by taking into account the constraints on the local matter density ρ ⊙ = 0.1M ⊙ pc −3 and the force K z=1.1 /2πG = 77M ⊙ pc −2 acting perpendicularly to the Galactic plane. The Galactic mass within a sphere of radius 50 kpc, M G (R ≤ 50 kpc) ≈ (0.41 ± 0.12) × 10 12 M ⊙ , is shown to satisfy all three models. The differences between the models become increasingly significant with increasing radius R. In model I, the Galactic mass within a sphere of radius 200 kpc at γ = 2.0 turns out to be greatest among the models considered, M G (R ≤ 200 kpc) = (1.45 ± 0.30) × 10 12 M ⊙ , M G (R ≤ 200 kpc) = (1.29 ± 0.14) × 10 12 M ⊙ at γ = 6.3, and the smallest value has been found in model II, M G (R ≤ 200 kpc) = (0.61 ± 0.12) × 10 12 M ⊙ . In our view, model III is the best one among those considered, because it ensures the smallest residual between the data and the constructed model rotation curve provided that the constraints on the local parameters hold with a high accuracy. Here, the Galactic mass is M G (R ≤ 200 kpc) = (0.75 ± 0.19) × 10 12 M ⊙ . A comparative analysis with the models by Irrgang et al. (2013), including those using the integration of orbits for the two globular clusters NGC 104 and NGC 1851 as an example, has been performed. The third model is shown to have subjected to a significant improvement.

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To estimate the parameters of the Galactic spiral structure -namely, the pitch angle i and the number of spiral arms, -data on Galactic masers with known trigonometric parallaxes were used. We applied the well-known method based on analysis of the "position angle -distance logarithm" diagram. Estimates of the pitch angle i obtained from four segments of different arms belonging to the global Galactic structure are self-consistent and close to i = −13 • ± 1 • . The segment which is most interesting is that of the Outer arm. It contains only three masers. Hence, in order to obtain correct estimates, we also used the data on 12 very young star clusters with distances determined by Camargo et al. from infrared photometry. The estimates obtained allow us to conclude in favor of the four-armed model of the Galactic spiral structure.

Abstract-We consider stars with radial velocities, proper motions, and distance estimates from the RAVE4 catalogue. Based on a sample of more than 145000 stars at distances r < 0.5 kpc, we have found the following kinematic parameters: (U, V, W ) ⊙ = (9.12, 20.80, 7.66) ± (0.10, 0.10, 0.08) km s kpc −1 and B = −11.60 ± 0.77 km s −1 kpc −1 . The 2D velocity distributions in the UV, UW, and V W planes have been constructed using a local sample, r < 0.25 kpc, consisting of ∼47000 stars. A difference of the UV velocity distribution from the previously known ones constructed from a smaller amount of data has been revealed. It lies in the fact that our distribution has an extremely enhanced branch near the Wolf 630 peak. A previously unknown peak at (U, V ) = (−96, −10) km s −1 and a separate new feature in the Wolf 630 stream, with the coordinates of its center being (U, V ) = (30, −40) km s −1 , have been detected.

Dynamical information along with survey data on metallicity and in some cases age have been used recently by some authors to search for candidates of stars that were born in the cluster where the Sun formed. We have acquired high resolution, high signal-to-noise ratio spectra for 30 of these objects to determine, using detailed elemental abundance analysis, if they could be true solar siblings. Only two of the candidates are found to have solar chemical composition. Updated modeling of the stars' past orbits in a realistic Galactic potential reveals that one of them, HD 162826, satisfies both chemical and dynamical conditions for being a sibling of the Sun. Measurements of rare-element abundances for this star further confirm its solar composition, with the only possible exception of Sm. Analysis of long-term high-precision radial velocity data rules out the presence of hot Jupiters and confirms that this star is not in a binary system. We find that chemical tagging does not necessarily benefit from studying as many elements as possible, but instead from identifying and carefully measuring the abundances of those elements which show large star-to-star scatter at a given metallicity. Future searches employing data products from ongoing massive astrometric and spectroscopic surveys can be optimized by acknowledging this fact.

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