Testing the Distance Scale of the Gaia TGAS Catalogue by the Kinematic Method

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 Ω'₀ 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)_⊙ = (9.28, 20.35, 7.36) ± (0.05, 0.07, 0.05) km s^?1, the angular velocity of Galactic rotation Ω⁰ = 27.24 ± 0.30 km s?1 kpc?1, and its first derivative Ω'₀ = ?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 Ω'₀ = 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.     

Thick disk kinematics from data on red clump giants at the north galactic pole

The distribution of radial (U) and rotational (V) velocities of red clump giants was studied as a function of their heights above the galactic plane. The stars of this type were selected from the compiled catalogue of stellar proper motions and infrared photometry at the north galactic pole with the use of the diagram “color-reduced proper motion.” According to the data on 1800 red clump giants located at heights from 1 to 3 kpc (mostly thick disk stars), mean kinematic parameters of the thick disk were determined: U ₀ = −18 ± 2 km/s, V ₀ = −56 ± 1 km/s, σ _U = 72 ± 2 km/s, and σ _V = 58 ± 1 km/s. The velocity of asymmetric drift V ₀ and velocity variances σ _U , σ _V are shown to depend on heights above the galactic plane.     

The Velocity Field of Young Stars in the Solar Neighbourhood

A sample of O- and B-type stars with Hipparcos astrometric data, ages computed from Strömgren photometry and radial velocities, has been used to characterize the structure, age and kinematics of the Gould Belt system. The local spiral structure of our galaxy is determined from this sample, and also from a sample of Hipparcos Cepheid stars. The Gould Belt, with an orientation with respect to the galactic plane ofi _G = 16-22^° and Ω_G =275-295^°, extends up to a distance of 600 pc from the Sun. Roughly the 60-65% of the O and B stars younger than 60 Myr in the solar neighbourhood belong to this structure. Our results indicate that the kinematical behaviour of this system is complex, with an expansion motion in the solar neighbourhood (R<300 pc).In the frame of the Lin's theory, and analysing the O and B stars further than 600 pc and the Cepheids, we found a galactic spiral structure characterized by a 4-arm spiral pattern with the Sun located atψ_⊙ = 350-355 ± 30^° – near the Sagittarius-Carina arm– and outside the corotation circle. The angular rotation speed of the spiral pattern was found to be Ω_p = 31-32 ± 4 kms^-1 kpc^-1.     

Estimation of the galactic spiral pattern speed from Cepheids

To study the peculiarities of the Galactic spiral density wave, we have analyzed the space velocities of Galactic Cepheids with propermotions from the Hipparcos catalog and line-of-sight velocities from various sources. First, based on the entire sample of 185 stars and taking R ₀ = 8 kpc, we have found the components of the peculiar solar velocity (u _⊙, v _⊙) = (7.6, 11.6) ± (0.8, 1.1) km s^?1, the angular velocity of Galactic rotation Ω₀ = 27.5 ± 0.5 km s^?1 kpc^?1 and its derivatives Ω′₀ = ?4.12 ± 0.10 km s^?1 kpc^?2 and Ω″₀ = 0.85 ± 0.07 km s^?1 kpc^?3, the amplitudes of the velocity perturbations in the spiral density wave f _R = ?6.8 ± 0.7 and f _θ = 3.3 ± 0.5 km s^?1, the pitch angle of a two-armed spiral pattern (m = 2) i = ?4.6° ± 0.1° (which corresponds to a wavelength λ = 2.0 ± 0.1 kpc), and the phase of the Sun in the spiral density wave χ_⊙ = ?193° ± 5°. The phase χ_⊙ has been found to change noticeably with the mean age of the sample. Having analyzed these phase shifts, we have determined the mean value of the angular velocity difference Ω _p ? Ω, which depends significantly on the calibrations used to estimate the individual ages of Cepheids. When estimating the ages of Cepheids based on Efremov’s calibration, we have found |Ω _p ? Ω₀| = 10 ± 1_stat ± 3_syst km s^?1 kpc^?1. The ratio of the radial component of the gravitational force produced by the spiral arms to the total gravitational force of the Galaxy has been estimated to be f _r0 = 0.04 ± 0.01.     

Kinematics of the galaxy from Cepheids with proper motions from the Gaia DR1 catalogue

A sample of classical Cepheids with known distances and line-of-sight velocities has been supplemented with proper motions from the Gaia DR1 catalogue. Based on the velocities of 260 stars, we have found the components of the peculiar solar velocity vector (U, V, W)_⊙ = (7.90, 11.73, 7.39) ± (0.65, 0.77, 0.62) km s^?1 and the following parameters of the Galactic rotation curve: Ω₀ = 28.84 ± 0.33 km s^?1 kpc^?1, Ω′₀ = ?4.05 ± 0.10 km s^?1 kpc^?2, and Ω″₀ = 0.805 ± 0.067 km s^?1 kpc^?3 for the adopted solar Galactocentric distance R ₀ = 8 kpc; the linear rotation velocity of the local standard of rest is V ₀ = 231 ± 6 km s^?1.     

Kinematics of the galaxy from OB stars with proper motions from the Gaia DR1 catalogue

We consider two samples of OB stars with different distance scales that we have studied previously. The first and second samples consist of massive spectroscopic binaries with photometric distances and distances determined from interstellar calcium lines, respectively. The OB stars are located at heliocentric distances up to 7 kpc. We have identified them with the Gaia DR1 catalogue. Using the proper motions taken from the Gaia DR1 catalogue is shown to reduce the random errors in the Galactic rotation parameters compared to the previously known results. By analyzing the proper motions and parallaxes of 208 OB stars from the Gaia DR1 catalogue with a relative parallax error of less than 200%, we have found the following kinematic parameters: (U, V)_⊙ = (8.67, 6.63)± (0.88, 0.98) km s^?1, Ω₀ = 27.35 ± 0.77 km s^?1 kpc^?1, Ω′₀ = ?4.13 ± 0.13 km s^?1 kpc^?2, and Ω″₀ = 0.672 ± 0.070 km s^?1 kpc^?3, the Oort constants are A = ?16.53 ± 0.52 km s^?1 kpc^?1 and B = 10.82 ± 0.93 km s^?1 kpc^?1, and the linear circular rotation velocity of the local standard of rest around the Galactic rotation axis is V ₀ = 219 ± 8 km s^?1 for the adopted R ₀ = 8.0 ± 0.2 kpc. Based on the same stars, we have derived the rotation parameters only from their line-of-sight velocities. By comparing the estimated values of Ω′₀, we have found the distance scale factor for the Gaia DR1 catalogue to be close to unity: 0.96. Based on 238 OB stars of the combined sample with photometric distances for the stars of the first sample and distances in the calcium distance scale for the stars of the second sample, line-of-sight velocities, and proper motions from the Gaia DR1 catalogue, we have found the following kinematic parameters: (U, V, W)_⊙ = (8.19, 9.28, 8.79)± (0.74, 0.92, 0.74) km s^?1, Ω₀ = 31.53 ± 0.54 km s^?1 kpc^?1, Ω′₀ = ?4.44 ± 0.12 km s^?1 kpc^?2, and Ω″₀ = 0.706 ± 0.100 km s^?1 kpc^?3; here, A = ?17.77 ± 0.46 km s^?1 kpc^?1, B = 13.76 ± 0.71 km s^?1 kpc^?1, and V ₀ = 252 ± 8 km s^?1.     

Trigonometric parallaxes and a kinematically adjusted distance sale for OB associations

By directly comparing the photometric distances of Blaha and Humphreys (1989) (BH) to OB associations and field stars with the corresponding Hipparcos trigonometric parallaxes, we show that the BH distance scale is overestimated, on average, by 10–20%. This result is independently corroborated by applying the rigorous statistical-parallax method and its simplified analog (finding a kinematically adjusted rotation-curve solution from radial velocities and proper motions) to a sample of OB associations. These two methods lead us to conclude that the BH distance scale for OB associations should be shrunk, on average, by 11±6 and 24±10%, respectively. Kinematical parameters have been determined for the system of OB associations: u ₀ = 8.2 ± 1.3 km s^?1, v ₀ = 11.9 ± 1.1 km s^?1, w ₀ = 9.5 ± 0.9 km s^?1, σ _u = 8.2 ± 1.1 km s^?1, σ _v = 5.8 ± 0.8 km s^?1, σ _w = 5.0 ± 0.8 km s^?1, Ω₀ = 29.1 ± 1.0 km s^?1 kpc^?1, Ω₀′ = ?4.57 ± 0.20 km s^?1 kpc^?2, and Ω₀″ = 1.32 ± 0.14 km s^?1 kpc^?3. The distance scale for OB associations reduced by 20% matches the short Cepheid distance scale (Berdnikov and Efremov 1985; Sitnik and Mel’nik 1996). Our results are a further argument for the short distance scale in the Universe.     

Kinematics of Tycho-2 red giant clump stars

Based on the Ogorodnikov-Milne model, we analyze the proper motions of 95 633 red giant clump (RGC) stars from the Tycho-2 Catalogue. The following Oort constants have been found: A = 15.9 ± 0.2 km s^?1 kpc^?1 and B = ?12.0±0.2 km s^?1 kpc^?1. Using 3632 RGC stars with known proper motions, radial velocities, and photometric distances, we show that, apart from the star centroid velocity components relative to the Sun, only the model parameters that describe the stellar motions in the XY plane differ significantly from zero. We have studied the contraction (a negative K effect) of the system of RGC stars as a function of their heliocentric distance and elevation above the Galactic plane. For a sample of distant (500–1000 pc) RGC stars located near the Galactic plane (|z| < 200 pc) with an average distance of d = 0.7 kpc, the contraction velocity is shown to be Kd = ?3.5 ±0.9 km s^?1; a noticeable vertex deviation, l _xy = 9 _· ^o 1 ± 0 _· ^o 5, is also observed for them. For stars located well above the Galactic plane (|z| ≥200 pc), these effects are less pronounced, Kd = ?1.7 ± 0.5 km s^?1 and l _xy = 4 _· ^o 9 ± 0 _· ^o 6. Using RGC stars, we have found a rotation around the Galactic X axis directed toward the Galactic center with an angular velocity of ?2.5 ± 0.3 km s^?1 kpc^?1, which we associate with the warp of the Galactic stellar-gaseous disk.     

Analysis of the Z distribution of young objects in the Galactic thin disk

We have obtained new estimates of the Sun’s distance from the symmetry plane Z _⊙ and the vertical disk scale height h using currently available data on stellar OB associations, Wolf–Rayet stars, HII regions, and Cepheids. Based on individual determinations, we have calculated the mean Z _⊙ = ?16 ± 2 pc. Based on the model of a self-gravitating isothermal disk for the density distribution, we have found the following vertical disk scale heights: h = 40.2 ± 2.1 pc from OB associations, h = 47.8 ± 3.9 pc from Wolf–Rayet stars, h = 48.4 ± 2.5 pc from HII regions, and h = 66.2 ± 1.6 pc from Cepheids. We have estimated the surface, Σ = 6 kpc^?2, and volume, D(Z _⊙) = 50.6 kpc^?3, densities from a sample of OB associations. We have found that there could be ～5000 OB associations in the Galaxy.     

Determination of galactic rotation parameters and the solar galactocentric distance R 0 from 73 masers

We have determined the Galactic rotation parameters and the solar Galactocentric distance R ₀ by simultaneously solving Bottlinger’s kinematic equations using data on masers with known line-of-sight velocities and highly accurate trigonometric parallaxes and proper motions measured by VLBI. Our sample includes 73 masers spanning the range of Galactocentric distances from 3 to 14 kpc. The solutions found are Ω₀ = 28.86 ± 0.45 km s^?1 kpc^?1, Ω′₀ = ?3.96 ± 0.09 km s^?1 kpc^?2, Ω″₀ = 0.790 ± 0.027 km s^?1 kpc^?3, and R ₀ = 8.3 ± 0.2 kpc. In this case, the linear rotation velocity at the solar distance R ₀ is V = 241 ± 7 km s^?1. Note that we have obtained the R ₀ estimate, which is of greatest interest, from masers for the first time; it is in good agreement with the most recent estimates and even surpasses them in accuracy.     

Galactic kinematics from a sample of young massive stars

Based on published sources, we have created a kinematic database on 220 massive (> 10 M _⊙) young Galactic star systems located within ≤3 kpc of the Sun. Out of them, ≈100 objects are spectroscopic binary and multiple star systems whose components are massive OB stars; the remaining objects are massive Hipparcos B stars with parallax errors of no more than 10%. Based on the entire sample, we have constructed the Galactic rotation curve, determined the circular rotation velocity of the solar neighborhood around the Galactic center at R ₀ = 8kpc, V ₀ = 259±16 km s^?1, and obtained the following spiral density wave parameters: the amplitudes of the radial and azimuthal velocity perturbations f _R = ?10.8 ± 1.2 km s^?1 and f _θ = 7.9 ± 1.3 km s^?1, respectively; the pitch angle for a two-armed spiral pattern i = ?6.0° ± 0.4°, with the wavelength of the spiral density wave near the Sun being λ = 2.6 ± 0.2 kpc; and the radial phase of the Sun in χ _⊙ = ?120° ± 4°. We show that such peculiarities of the Gould Belt as the local expansion of the system, the velocity ellipsoid vertex deviation, and the significant additional rotation can be explained in terms of the density wave theory. All these effects decrease noticeably once the influence of the spiral density wave on the velocities of nearby stars has been taken into account. The influence of Gould Belt stars on the Galactic parameter estimates has also been revealed. Eliminating them from the kinematic equations has led to the following new values of the spiral density wave parameters: f _θ = 2.9 ± 2.1 km s^?1 and χ _⊙ = ?104° ± 6°.     

Parameters of the local warp of the stellar-gaseous galactic disk from the kinematics of Tycho-2 nearby red giant clump stars

We analyze the three-dimensional kinematics of about 82 000 Tycho-2 stars belonging to the red giant clump (RGC). First, based on all of the currently available data, we have determined new, most probable components of the residual rotation vector of the optical realization of the ICRS/HIPPARCOS system relative to an inertial frame of reference, (ω _x , ω _y , ω _z ) = (−0.11, 0.24, −0.52) ± (0.14, 0.10, 0.16) mas yr⁻¹. The stellar proper motions in the form μ_α cos δ have then be corrected by applying the correction ω _z = −0.52 mas yr⁻¹. We show that, apart from their involvement in the general Galactic rotation described by the Oort constants A = 15.82 ± 0.21 km s⁻¹ kpc⁻¹ and B = −10.87 ± 0.15 km s⁻¹ kpc⁻¹, the RGC stars have kinematic peculiarities in the Galactic yz plane related to the kinematics of the warped stellar-gaseous Galactic disk. We show that the parameters of the linear Ogorodnikov-Milne model that describe the kinematics of RGC stars in the zx plane do not differ significantly from zero. The situation in the yz plane is different. For example, the component of the solid-body rotation vector of the local solar neighborhood around the Galactic x axis is M ₃₂⁻ = −2.6 ± 0.2 km s⁻¹ kpc⁻¹. Two parameters of the deformation tensor in this plane, namely M ₂₃⁺ = 1.0 ± 0.2 km s⁻¹ kpc⁻¹ and M ₃₃ − M ₂₂ = −1.3 ± 0.4 km s⁻¹ kpc⁻¹, also differ significantly from zero. On the whole, the kinematics of the warped stellar-gaseous Galactic disk in the local solar neighborhood can be described as a rotation around the Galactic x axis (close to the line of nodes of this structure) with an angular velocity −3.1 ± 0.5 km s⁻¹ kpc⁻¹ ≤ Ω_W ≤ −4.4 ± 0.5 km s⁻¹ kpc⁻¹.     

Kinematics of the Galaxy from OB Stars with Data from the Gaia DR2 Catalogue

We have selected and analyzed a sample of OB stars with known line-of-sight velocities determined through ground-based observations and with trigonometric parallaxes and propermotions from the Gaia DR2 catalogue. Some of the stars in our sample have distance estimates made from calcium lines. A direct comparison with the trigonometric distance scale has shown that the calcium distance scale should be reduced by 13%. The following parameters of the Galactic rotation curve have been determined from 495 OB stars with relative parallax errors less than 30%: (U, V,W)_⊙ = (8.16, 11.19, 8.55)± (0.48, 0.56, 0.48) km s^?1, Ω₀ = 28.92 ± 0.39 km s^?1 kpc^?1, Ω'₀ = ?4.087 ± 0.083 km s^?1 kpc^?2, and Ω″ ₀ = 0.703 ± 0.067 km s?1 kpc^?3, where the circular velocity of the local standard of rest is V0 = 231 ± 5 km s^?1 (for the adopted R₀ = 8.0 ± 0.15 kpc). The parameters of the Galactic spiral density wave have been found from the series of radial, V_R, residual tangential, ΔV_circ, and vertical, W, velocities of OB stars by applying a periodogram analysis. The amplitudes of the radial, tangential, and vertical velocity perturbations are f_R = 7.1± 0.3 km s^?1, f_θ = 6.5 ± 0.4 km s^?1, and f_W = 4.8± 0.8 km s^?1, respectively; the perturbation wavelengths are λ_R = 3.3 ± 0.1 kpc, λ_θ = 2.3 ± 0.2 kpc, and λ_W = 2.6 ± 0.5 kpc; and the Sun’s radial phase in the spiral density wave is (χ_⊙)_R = ?135? ± 5?, (χ_⊙)θ = ?123? ± 8?, and (χ_⊙)_W = ?132? ± 21? for the adopted four-armed spiral pattern.     

Galactic Rotation Based on OB Stars from the Gaia DR2 Catalogue

We have studied a sample containing ~6000 OB stars with proper motions and trigonometric parallaxes from the Gaia DR2 catalogue. The following parameters of the angular velocity of Galactic rotation have been found: Ω₀ = 29.70 ± 0.11 km s^-1 kpc^-1, Ω'₀ = -4.035 ± 0.031 km s^-1 kpc^-2, and Ω ₀ = 0.620 ± 0.014 km s^-1 kpc^-3. The circular rotation velocity of the solar neighborhood around the Galactic center is V₀ = 238 ± 5 km s^-1 for the adopted Galactocentric distance of the Sun R₀ = 8.0 ± 0.15 kpc. The amplitudes of the tangential and radial velocity perturbations produced by the spiral density wave are f_θ = 4.4 ± 1.4 kms^-1 and f_R = 5.1 ± 1.2 kms^-1, respectively; the perturbation wavelengths are λ_θ = 1.9 ± 0.5 kpc and λ_R = 2.1 ± 0.5 kpc for the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave is χ_⊙ = -178° ± 12°.

     

Photometric observations and modelling of the asteroid 85 Io in conjunction with data from an occultation event during the 1995–96 apparition

The asteroid 85 Io has been observed using CCD and photoelectric photometry on 18 nights during its 1995–96 and 1997 apparitions. We present the observed lightcurves, determined colour indices and modelling of the asteroid spin vector and shape. The colour indices (U-B = 0.35±0.02, B-V = 0.66±0.02, V-R = 0.34±0.02, R-I = 0.36±0.02) are as expected for a C-type asteroid. The allowed spin vector solutions have the pole co-ordinates λ₀ = 285±4°, β₀ = −52±9° or λ₀ = 108±10°, β₀ = −46±10° and λ₀ = 290±10°, β₀ = −16±10° with a retrograde sense of rotation and a sidereal period P_sid = 0^d.286463±0^d.000001. During the 1995–96 apparition the International Occultation Time Association (IOTA) observed an occultation event by 85 Io. The observations and modelling presented here were analysed together with the occultation data to develop improved constraints on the size of the asteroid. The derived value of 164 km is about 5% larger than the IRAS diameter. © 1999 Elsevier Science Ltd. All rights reserved.     

Galactic rotation parameters from data on open star clusters

Currently available data on the field of velocities V _r , V _l , V _b for open star clusters are used to perform a kinematic analysis of various samples that differ by heliocentric distance, age, and membership in individual structures (the Orion, Carina-Sagittarius, and Perseus arms). Based on 375 clusters located within 5 kpc of the Sun with ages up to 1 Gyr, we have determined the Galactic rotation parameters ω ₀ = ?26.0 ± 0.3 km s^?1 kpc^?1, ω′₀ = 4.18 ± 0.17 km s^?1 kpc^?2, ω″₀ = ?0.45 ± 0.06 km s^?1 kpc^?3, the system contraction parameter K = ?2.4 ± 0.1 km s^?1 kpc^?1, and the parameters of the kinematic center R ₀ = 7.4 ± 0.3 kpc and l ₀ = 0° ± 1°. The Galactocentric distance R ₀ in the model used has been found to depend significantly on the sample age. Thus, for example, it is 9.5 ± 0.7 and 5.6 ± 0.3 kpc for the samples of young (≤50 Myr) and old (>50 Myr) clusters, respectively. Our study of the kinematics of young open star clusters in various spiral arms has shown that the kinematic parameters are similar to the parameters obtained from the entire sample for the Carina-Sagittarius and Perseus arms and differ significantly from them for the Orion arm. The contraction effect is shown to be typical of star clusters with various ages. It is most pronounced for clusters with a mean age of ≈100 Myr, with the contraction velocity being Kr = ?4.3 ± 1.0 km s^?1.     

The distance to the Galactic center determined by OB stars

The OB stars are concentrated near the Galactic plane and should permit a determination of the distance to the Galactic center. van Leeuwen’s new reduction of the Hipparcos catalog provides, after 824 Gould belt stars have been excluded, 6288 OB stars out to 1 kpc and Westin’s compilation an additional 112 stars between 1 kpc and 3 kpc. The reduction model involves 14 unknowns: the Oort A and B constants, the distance to the Galactic center R ₀, 2 second-order partial derivatives, the 3 components of solar motion, a K term, a first order partial derivative for motion perpendicular to the Galactic plane, a second-order partial for acceleration perpendicular to the plane, two terms for a possible expansion of the OB stars, and a C constant. The model is nonlinear, and the unknowns are calculated by use the simplex algorithm for nonlinear adjustment applied to 14313 equations of condition, 12694 in proper motion and 1619 in radial velocity. Various solutions were tried: an L₁ solution, a least squares solution with modest (2.7 %) trim of the data, and two robust least squares solutions (biweight and Welsch weighting) with more extreme trimming. The Welsch solution seems to give the best results and calculates a distance to the Galactic center 6.72±0.39 kpc. Statistical tests show that the data are homogeneous, that the reduction model seems adequate and conforms with the assumptions used in its derivation, and that the post-fit residuals are random. Inclusion of more terms, such as streaming motion induced by Galactic density waves, degrades the solution.     

Galactic kinematics from OB3 stars with distances determined from interstellar Ca II lines

Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative of the angular velocity of Galactic rotation Ω′₀ and the external reconciliation with Humphreys’s distance scale for OB associations refined by Mel’nik and Dambis show that the initial distances should be reduced by ≈20%. Given this correction, the heliocentric distances of these stars lie within the range 0.6–2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R ₀ = 8 kpc, has allowed the following parameters to be determined: (1) the solar peculiar velocity components (u _⊙, v _⊙, ω _⊙) = (8.9, 10.3, 6.8) ± (0.6, 1.0, 0.4) km s⁻¹; (2) the Galactic rotation parameters Ω₀ = −31.5 ± 0.9 km s⁻¹ kpc⁻¹, Ω′₀ = +4.49 ± 0.12 km s⁻¹ kpc⁻², Ω″₀ = −1.05 ± 0.38 km s⁻¹ kpc⁻³ (the corresponding Oort constants are A = 17.9 ± 0.5 km s⁻¹ kpc⁻¹, B = −13.6 ± 1.0 km s⁻¹ kpc⁻¹ and the circular rotation velocity of the solar neighborhood is |V ₀| = 252 ± 14 km s⁻¹); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, f _R = −12.5±1.1 km s⁻¹ and f _ϑ = 2.0 ± 1.6 km s⁻¹; the pitch angle for the two-armed spiral pattern i = −5.3° ± 0.3°, with the wavelength of the spiral density wave at the solar distance being λ = 2.3 ± 0.2 kpc; the Sun’s phase in the spiral wave x _⊙ = −91° ± 4°.     

Kinematic analysis of solar-neighborhood stars based on RAVE4 data

We consider stars with radial velocities, proper motions, and distance estimates from the RAVE4 catalogue. Based on a sample of more than 145 000 stars at distances r < 0.5 kpc, we have found the following kinematic parameters: \({\left( {U,{\kern 1pt} V,{\kern 1pt} W} \right)_ \odot }\) = (9.12, 20.80, 7.66) ± (0.10, 0.10, 0.08) km s^?1, Ω₀ = 28.71 ± 0.63 km s^?1 kpc^?1, and Ω₀ ^’ = ?4.28 ± 0.11 km s^?1 kpc^?2. This gives the linear rotation velocity V ₀ = 230 ± 12 km s^?1 (for the adopted R ₀ = 8.0 ± 0.4 kpc) and the Oort constants A = 17.12 ± 0.45 km s^?1 kpc^?1 and B = ?11.60 ± 0.77 km s^?1 kpc^?1. The 2D velocity distributions in the UV, UW, and VW planes have been constructed using a local sample, r < 0.25 kpc, consisting of ~47 000 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.