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.     

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.     

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.     

Kinematics of Stars from the TGAS (Gaia DR1) Catalogue

Based on the stellar proper motions of the TGAS (Gaia DR1) catalogue, we have analyzed the velocity field of main-sequence stars and red giants from the TGAS catalogue with heliocentric distances up to 1.5 kpc. We have obtained four variants of kinematic parameters corresponding to different methods of calculating the distances from the parallaxes of stars measured with large relative errors. We have established that within the Ogorodnikov–Milne model changing the variant of distances affects significantly only the solar velocity components relative to the chosen centroid of stars, provided that the solution is obtained in narrow ranges of distances (0.1 kpc). The estimates of all the remaining kinematic parameters change little. This allows the Oort coefficients and related Galactic rotation parameters as well as all the remaining Ogorodnikov–Milne model parameters (except for the solar terms) to be reliably estimated irrespective of the parallax measurement accuracy. The main results obtained from main-sequence stars in the range of distances from 0.1 to 1.5 kpc are: A = 16.29 ± 0.06 km s^?1 kpc^?1, B = ?11.90 ± 0.05 km s^?1 kpc^?1, C = ?2.99 ± 0.06 km s^?1 kpc^?1, K = ?4.04 ± 0.16 km s^?1 kpc^?1, and the Galactic rotation period P = 217.41 ± 0.60 Myr. The analogous results obtained from red giants in the range from 0.2 to 1.6 kpc are: the Oort constants A = 13.32 ± 0.09 km s^?1 kpc^?1, B = ?12.71 ± 0.06 km s^?1 kpc^?1, C = ?2.04 ± 0.08 km s^?1 kpc^?1, K = ?2.72 ± 0.19 km s^?1 kpc^?1, and the Galactic rotation period P = 236.03 ± 0.98 Myr. The Galactic rotation velocity gradient along the radius vector (the slope of the Galactic rotation curve) is ?4.32 ± 0.08 km s^?1 kpc^?1 for main-sequence stars and ?0.61 ± 0.11 km s^?1 kpc^?1 for red giants. This suggests that the Galactic rotation velocity determined from main-sequence stars decreases with increasing distance from the Galactic center faster than it does for red giants.     

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.     

Galactic kinematics from data on open star clusters from the MWSC catalogue

Open star clusters from the MWSC (Milky Way Star Clusters) catalogue have been used to determine the Galactic rotation parameters. The circular rotation velocity of the solar neighborhood around the Galactic center has been found from data on more than 2000 clusters of various ages to be V ₀ = 236 ± 6 km s^?1 for the adopted Galactocentric distance of the Sun R ₀ = 8.3 ± 0.2 kpc. The derived angular velocity parameters are Ω ₀ = 28.48 ± 0.36 km s^?1 kpc^?1, Ω’₀ = ?3.50 ± 0.08 km s^?1 kpc_?2, and Ω″₀ = 0.331 ± 0.037 km s^?1 kpc^?3. The influence of the spiral density wave has been detected only in the sample of clusters younger than 50 Myr. For these clusters the amplitudes of the tangential and radial velocity perturbations are f ^θ = 5.6 ± 1.6 km s^?1 and f _R = 7.7 ± 1.4 km s^?1, respectively; the perturbation wavelengths are λ _θ = 2.6 ± 0.5 kpc (i _θ = ^?11? ± 2?) and λ _R = 2.1 ± 0.5 kpc (i _R = ?9? ± 2?) for the adopted four-armed model (m = 4). The Sun’s phase in the spiral density wave is (χ_⊙)_θ = ?62? ± 9? and (χ_⊙)_R = ?85? ± 10? from the residual tangential and radial velocities, respectively.     

Kinematic parameters of young subsystems and the galactic rotation curve

We analyze the space velocities of blue supergiants, long-period Cepheids, and young open star clusters (OSCs), as well as the H I and H II radial-velocity fields by the maximum-likelihood method. The distance scales of the objects are matched both by comparing the first derivatives of the angular velocity Ω′ determined separately from radial velocities and proper motions and by the statistical-parallax method. The former method yields a short distance scale (for R₀=7.5 kpc, the assumed distances should be increased by 4%), whereas the latter method yields a long distance scale (for R₀=8.5 kpc, the assumed distances should be increased by 16%). We cannot choose between these two methods. Similarly, the distance scale of blue supergiants should be shortened by 9% and lengthened by 3%, respectively. The H II distance scale is matched with the distance scale of Cepheids and OSCs by comparing the derivatives Ω′ determined for H II from radial velocities and for Cepheids and OSCs from space velocities. As a result, the distances to H II regions should be increased by 5% in the short distance scale. We constructed the Galactic rotation curve in the Galactocentric distance range 2–14 kpc from the radial velocities of all objects with allowance for the difference between the residual-velocity distributions. The axial ratio of the Cepheid+OSC velocity ellipsoid is well described by the Lindblad relation, while σ_u≈σ_v for gas. The following rotation-curve parameters were obtained: Ω₀=(27.5±1.4) km s^?1 kpc^?1 and A=(17.1±0.5) km s^?1 kpc^?1 for the short distance scale (R₀=7.5 kpc); and Ω₀=(26.6±1.4) km s^?1 kpc^?1 and A=(15.4±0.5) km s^?1 kpc^?1 for the long distance scale (R₀=8.5 kpc). We propose a new method for determining the angular velocity Ω₀ from stellar radial velocities alone by using the Lindblad relation. Good agreement between the inferred Ω₀ and our calculations based on space velocities suggests that the Lindblad relation holds throughout the entire sample volume. Our analysis of the heliocentric velocities for samples of young objects reveals noticeable streaming motions (with a velocity lag of ～7 km s^?1 relative to the LSR), whereas a direct computation of the perturbation amplitudes in terms of the linear density-wave theory yields a small amplitude for the tangential perturbations.     

A preliminary radial-velocity curve for the star <Emphasis Type="Italic">θ</Emphasis><Superscript>1</Superscript> Ori D

We measured the radial velocity of the star θ¹ Ori D from IUE spectra and used published observations. Based on these data, we determined the period of its radial-velocity variations, P=20.2675±0.0010 days, constructed the phase radial-velocity curve, and solved it by least squares. The spectroscopic orbital elements were found to be the following: the epoch of periastron passage E_p=JD 2430826.6±0.1, the system's center-of-mass velocity /Gg=32.4±1.0 km s^?1, K=14.3±1.5 km s^?1, Ω=3.3±0.1 rad, e=0.68±0.09, a₁ sin i = 3 × 10¹⁰ km, and f₁ = 0.0025M_⊙. Twice the period, P=40.528±0.002 days, is also consistent with the observations.     

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.     

Parameters of the spiral structure of the galaxy from data on δ Cephei stars

We determined the locations of Galactic spiral arm segments for various age groups from the available data on the positions, ages, radial velocities, and proper motions of 440 δ Cephei variables using a previously developed technique. We obtained such parameters of the Galactic spiral structure as the arm pitch angle, , and the pattern speed, Ω_P = 21.7 ± 2.8 km s^?1 kpc^?1, which are comparable to and Ω_P = 20.4 ± 2.5 km s^?1 kpc^?1, respectively, determined previously from open star clusters. Based on the radial velocities and proper motions of the sample stars, we derived the rotation curve of the Galaxy for the range of Galactocentric distances approximately from 6 to 15 kpc. Using the pattern speed, we determined the positions of the corotation region and the inner and outer Lindblad resonances. We estimated the perturbation amplitudes of the Galactic velocity field, f _R = ?1.8 ± 2.5 km s^?1 and f _? = +4.0 ± 3.4 km s^?1.     

Kinematic control of the inertiality of ICRS catalogs

We perform a kinematic analysis of the Hipparcos and TRC proper motions of stars by using a linear Ogorodnikov-Milne model. All of the distant (r>0.2 kpc) stars of the Hipparcos catalog have been found to rotate around the Galactic y axis with an angular velocity of M ₁₃ ^? =?0.36±0.09 mas yr^?1. One of the causes of this rotation may be an uncertainty in the lunisolar precession constant adopted when constructing the ICRS. In this case, the correction to the IAU (1976) lunisolar precession constant in longitude is shown to be Δp₁=?3.26±0.10 mas yr^?1. Based on the TRC catalog, we have determined the mean Oort constants: A=14.9±1.0 and B=?10.8±0.3 km s^?1 kpc^?1. The component of the model that describes the rotation of all TRC stars around the Galactic y axis is nonzero for all magnitudes, M ₁₃ ^? =?0.86±0.11 mas yr^?1.     

Parameters of the spiral structure of the galaxy from data on open star clusters

We use data on open star clusters (OSCs) from the Homogeneous Catalog of OSC Parameters to determine some of the parameters of the spiral structure of our Galaxy: the pitch angle of the spiral arms \(i = 21\mathop .\limits^ \circ 5\), the pattern speed Ω_p = 20.4 ± 2.5 km s^?1 kpc^?1, and the initial phase of the spiral θ₀ = 206°. The spiral pattern of the Galaxy proves to have been virtually unchanged over the last billion years, and signatures of the concentration of objects toward the spiral arms can be traced back to this age. However, the number of spiral arms in the structure cannot be determined from OSCs.     

Results of a long-term monitoring of the multiple system SZ Cam

We present the results of the reduction of our photometric and spectroscopic observations for the eclipsing binary SZ Cam performed with the telescopes at the Astronomical Observatory of the Ural Federal University and the Special Astrophysical Observatory of the Russian Academy of Sciences in 1996–2014. Based on an 11-year-long photometric monitoring of SZ Cam, we have obtained new elements of its photometric orbit and parameters of its components. We have detected low-amplitude periodic light variations in SZ Cam that are possibly related to the ellipsoidal shape of the components of the spectroscopic binary third body. Based on published data and our new spectroscopy, we have found new values for the mass ratio, q = 0.72 ± 0.01, and parameters of the radial velocity curves of the components, V ₀ = ?3.6 ± 1.7 km s^?1, K ₁ = 190.2 ± 1.9 km s^?1, and K ₂ = 263.0 ± 2.4 km s^?1. The component masses have been estimated to be M ₁ = 16.1 M _⊙ and M ₂ = 11.6 M _⊙. We have obtained new light elements and parameters of the radial velocity curves for the third body, V ₀ ^3b = 4.2 ± 0.6 km s^?1 and K ₁ ^3b = 26.6 ± 0.8 km s^?1. We have improved the period of the relative orbit of SZ Cam and the third body, P _orb = 55.6 ± 1.5 yr.     

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 B-F Stars as a Function of Their Dereddened Color from Gaia and PCRV Data

Parallaxes with an accuracy better than 10% and proper motions from the Gaia DR1 TGAS catalogue, radial velocities from the Pulkovo Compilation of Radial Velocities (PCRV), accurate Tycho-2 photometry, theoretical PARSEC, MIST, YaPSI, BaSTI isochrones, and the most accurate reddening and interstellar extinction estimates have been used to analyze the kinematics of 9543 thin-disk B-F stars as a function of their dereddened color. The stars under consideration are located on the Hertzsprung–Russell diagram relative to the isochrones with an accuracy of a few hundredths of a magnitude, i.e., at the level of uncertainty in the parallax, photometry, reddening, extinction, and the isochrones themselves. This has allowed us to choose the most plausible reddening and extinction estimates and to conclude that the reddening and extinction were significantly underestimated in some kinematic studies of other authors. Owing to the higher accuracy of TGAS parallaxes than that of Hipparcos ones, the median accuracy of the velocity components U, V, W in this study has improved to 1.7 km s^?1, although outside the range ?0.1 ^m < (B _T ? V _T )₀ < 0.5 ^m the kinematic characteristics are noticeably biased due to the incompleteness of the sample. We have confirmed the variations in the mean velocity of stars relative to the Sun and the stellar velocity dispersion as a function of their dereddened color known from the Hipparcos data. Given the age estimates for the stars under consideration from the TRILEGAL model and the Geneva–Copenhagen survey, these variations may be considered as variations as a function of the stellar age. A comparison of our results with the results of other studies of the stellar kinematics near the Sun has shown that selection and reddening underestimation explain almost completely the discrepancies between the results. The dispersions and mean velocities from the results of reliable studies fit into a ±2 km s^?1 corridor, while the ratios σ _V /σ _U and σ _W /σ _U fit into ±0.05. Based on all reliable studies in the range ?0.1 ^m < (B _T ? V _T )₀ < 0.5^m, i.e., for an age from 0.23 to 2.4 Gyr, we have found: W_⊙ = 7.15 km s^?1, \({\sigma _U} = 16.0{e^{1.29({B_T} - {V_T})o}}\), \({\sigma _V} = 10.9{e^{1.11({B_T} - {V_T})o}}\), \({\sigma _W} = 6.8{e^{1.46({B_T} - {V_T})o}}\), the stellar velocity dispersions in km s^?1 are proportional to the age in Gyr raised to the power β _U = 0.33, β _V = 0.285, and β _W = 0.37.     

Systematic error of the Gaia DR1 TGAS parallaxes from data for the red giant clump

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: 0.18R ² 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 _H ) = ?1.49 ^m ± 0.04 ^m , mode(M _Ks ) = ?1.63 ^m ± 0.03 ^m , mode(M _W1) = ?1.67 ^m ± 0.05 ^m mode(M _W2) = ?1.67 ^m ± 0.05 ^m , mode(M _W3) = ?1.66 ^m ± 0.02 ^m , mode(M _W4) = ?1.73 ^m ± 0.03 ^m , as well as the corresponding estimates of their de-reddened colors.     

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.     

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.     

High Resolution Optical Spectroscopy of Hot Post-AGB Star Candidates LS IV-04 1 and LB3116

We present LTE analysis of high resolution optical spectra for B-type hot PAGB stars LS IV-04 1 and LB3116 (LSE 237). The spectra of these high Galactic latitude stars were obtained with the 3.9-m Anglo-Australian Telescope (AAT) and the UCLES spectrograph. The standard 1D LTE analysis with line-blanketed LTE model atmospheres and spectral synthesis provided fundamental atmospheric parameters of T_eff= 15 000±1000 K, log g= 2.5±0.2, ξ = 5.0±1.0 km s^?1, [M/H] = ?1.81 dex, and v sin i= 5 km s^?1 for LSIV-04 1 and T_eff= 16 000±1000 K, log g= 2.5±0.1, v sin i= 25 km s^?1, and [Fe/H] = ?0.93 dex for LB 3116. Chemical abundances of ten different elements were obtained. For LS IV-04 1, its derived model temperature contradicts with previous analysis results. The upper limits for its nitrogen and oxygen abundances were reported for the first time. The magnesium, silicon and calcium were overabundant (i.e. [Mg/Fe] = 0.8 dex, [Si/Fe] = 0.5 dex, [Ca/Fe] = 0.9 dex). With its metal-poor photosphere and V_LSR ≈ 96 km s^?1, LSIV-04 1 is likely a population II star and most probably a PAGB star. LTE abundances of LB 3116 were reported for the first time. The spectrum of this helium rich star shows 0.9 dex enhancement in the nitrogen. The photosphere of the star is slightly deficient in Mg, Si, and S. (i.e. [Mg/Fe] = ?0.2 dex, [Si/Fe] = ?0.4 dex, [S/Fe] = ?0.2 dex). The Al is slightly enhanced. The phosphorus is overabundant, i.e. [P/Fe] ≈ 1.7 ± 0.47 dex, hence LB3116 may be the first example of a PAGB star which is rich in phosphorus. With its high radial velocity (i.e.V_LSR = 73 km s^?1), and the deficiencies observed in C, Mg, Si, and S indicate that LB 3116 is likely a hot PAGB star at high galactic latitude.