Multicolour CCD Photometric Study of Galactic Star Clusters SAI 63 and SAI 75

We present U B V I CCD photometric observations obtained in the field of open clusters SAI 63 and SAI 75. CCD optical data obtained for the first time for these clusters are used to derive the fundamental parameters of the clusters. Stellar surface density profile indicates that radii of SAI 63 and SAI 75 are ～3^′.5 and 2^′.5 respectively. The reddenings E(B?V) are 0.44±0.05 and 0.34±0.05 mag for SAI 63 and SAI 75 respectively while the corresponding distances are 2.2 ± 0.2 and 3.5±0.3 kpc. An age of 450 ± 50 Myr for SAI 63 and 90 ± 10 Myr for SAI 75 is determined using the theoretical isochrones of Z=0.019. Our analysis shows that reddening law is normal towards SAI 75.     

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.     

Estimation of the solar galactocentric distance and galactic rotation velocity from near-solar-circle objects

We have tested the method of determining the solar Galactocentric distance R ₀ and Galactic rotation velocity V ₀ modified by Sofue et al. using near-solar-circle objects. The motion of objects relative to the local standard of rest has been properly taken into account. We show that when such young objects as star-forming regions or Cepheids are analyzed, allowance for the perturbations produced by the Galactic spiral density wave improves the statistical significance of the estimates. The estimate of R ₀ = 7.25 ± 0.32 kpc has been obtained from 19 star-forming regions. The following estimates have been obtained from a sample of 14 Cepheids (with pulsation periods P > 5 ^d ): R ₀ = 7.66 ± 0.36 kpc and V ₀ = 267 ± 17 km s^?1. We consider the influence of the adopted Oort constant A and the character of stellar proper motions (Hipparcos or UCAC4). The following estimates have been obtained from a sample of 18 Cepheids with stellar proper motions from the UCAC4 catalog: R ₀ = 7.64 ± 0.32 kpc and V ₀ = 217 ± 11 km s^?1.     

Evolutionary studies of the young star clusters: NGC 1960, NGC 2453 and NGC 2384

We report the analysis of the young star clusters NGC 1960, NGC 2453 and NGC 2384 observed in the J (1.12 μm), H (1.65 μm) and K′ (2.2 μm) bands. Estimates of reddening, distance and age as E(B?V)=0.25, d=1380 pc and t=31.6 to 125 Myr for NGC 1960, E(B?V)=0.47, d=3311 pc and t=40 to 200 Myr for NGC 2453 and E(B?V)=0.25, d=3162 pc and t=55 to 125 Myr for NGC 2384 have been obtained. Also, we have extended the color–magnitude diagrams of these clusters to the fainter end and thus extended the luminosity functions to fainter magnitudes. The evolution of the main sequence and luminosity functions of these clusters have been compared with themselves as well as Lyngå 2 and NGC 1582.     

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.     

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 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°.     

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.     

The young open cluster Trumpler 3

We present a photometric and spectroscopic study of the poorly investigated open cluster Trumpler 3. Basic parameters such as the age of 70 ± 10 Myr, the color excess E (B – V) = 0.30 ± 0.02 mag, the distance of 0.69 ± 0.03 kpc and the limiting radius of 12′ were redetermined and compared with previous preliminary studies. The distance of 0.65 ± 0.09 kpc was determined independently by spectral parallaxes. Simultaneously, our analysis allowed us to estimate a total number of members to be N_tot = 570 ± 90 and a total mass of the cluster to be M_tot = 270 ± 40 M_⊙. We also determined a state of cluster's dynamical evolution. We conclude that Trumpler 3 is a young low‐massive stellar ensemble with a typical mass function slope, located near to the outer edge of the Galaxy's Orion Spur. As a result of a wide‐field search for short period variable stars, 24 variables were discovered in the cluster's area. Only one of them – a variable of the γ ‐Dor type – was found to be a likely cluster member (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Galactic rotation curve and spiral density wave parameters from 73 masers

Based on kinematic data on masers with known trigonometric parallaxes and measurements of the velocities of HI clouds at tangential points in the inner Galaxy, we have refined the parameters of the Allen-Santillan model Galactic potential and constructed the Galactic rotation curve in a wide range of Galactocentric distances, from 0 to 20 kpc. The circular rotation velocity of the Sun for the adopted Galactocentric distance R ₀ = 8 kpc is V ₀ = 239 ± 16 km s^?1. We have obtained the series of residual tangential, ΔV _θ , and radial, V _R , velocities for 73 masers. Based on these series, we have determined the parameters of the Galactic spiral density wave satisfying the linear Lin-Shu model using the method of periodogram analysis that we proposed previously. The tangential and radial perturbation amplitudes are f _θ = 7.0±1.2 km s^?1 and f _R = 7.8±0.7 km s^?1, respectively, the perturbation wave length is λ = 2.3±0.4 kpc, and the pitch angle of the spiral pattern in a two-armed model is i = ?5.2° ±0.7°. The phase of the Sun ζ _⊙ in the spiral density wave is ?50° ± 15° and ?160° ± 15° from the residual tangential and radial velocities, respectively.     

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.     

Absolute magnitudes and kinematic parameters of the subsystem of RR Lyrae variables

The statistical parallax technique is applied to a sample of 262 RRab Lyrae variables with published photoelectric photometry, metallicities, and radial velocities and with measured absolute proper motions. Hipparcos, PPM, NPM, and the Four-Million Star Catalog (Volchkov et al. 1992) were used as the sources of proper motions; the proper motions from the last three catalogs were reduced to the Hipparcos system. We determine parameters of the velocity distribution for halo [(U ₀, V ₀, W ₀) = (?9±12, ?214 ±10, ? 10, ?16±7) km s ^?1 and (σ _U , σ _V , σ _W ) = (164±11, 105±7, 95±7) km s ^?1] and thick-disk [(U ₀, V ₀, W ₀) = (?16±8, ?41±7, ?18±5) km s ^?1], and [(σ _U , σ _V , σ _W ) = (53±9, 42±8, 26±5) km s ^?1] RR Lyrae, as well as the intensity-averaged absolute magnitude for RR Lyrae of these populations: 〈M _V 〉 = 0.77 ± 0.10 and 〈M _V 〉 = +1.11 ± 0.25 for the halo and thickdisk objects, respectively. The metallicity dependence of the absolute magnitude of RR Lyrae is analyzed (〈M _V 〉 = (0.76 ± 0.12) + (0.26 ± 0.26) · ([Fe/H]+1.6)=1.17+0.26 · [Fe/H]). Our results are in satisfactory agreement with the ?M _V ?(RR)?[Fe/H]relation from Carney et al. (1992) (〈M _V 〉(RR)=1.01+0.15·[Fe/H]) obtained by Baade-Wesselink's method. They provide evidence for a short distance scale: the LMC distance modulus and the distance to the Galactic center are 18.22±0.11 and 7.4±0.5 kpc, respectively. The zero point of the distance scale and the kinematic parameters of the RR Lyrae populations are shown to be virtually independent of the source of absolute proper motions used and of whether they are reduced to the Hipparcos system or not.     

The structure and dynamics of young star clusters: King 16, NGC 1931, NGC 637 and NGC 189

In this paper, using 2MASS photometry, we study the structural and dynamical properties of four young star clusters viz. King 16, NGC 1931, NGC 637 and NGC 189. For the clusters King 16, NGC 1931, NGC 637 and NGC 189, we obtain the limiting radii of 7′, 12′, 6′ and 5′ which correspond to linear radii of 3.6 pc, 8.85 pc, 3.96 pc and 2.8 pc respectively. The reddening values E(B?V) obtained for the clusters are 0.85, 0.65–0.85, 0.6 and 0.53 and their true distances are 1786 pc, 3062 pc, 2270 pc and 912 pc respectively. Ages of the clusters are 6 Myr, 4 Myr, 4 Myr and 10 Myr respectively. We compare their structures, luminosity functions and mass functions (φ(M)=dN/dM ∝ M ^?(1+χ)) to the parameter τ=t _age /t _relax to study the star formation process and the dynamical evolution of these clusters. We find that, for our sample, mass seggregation is observed in clusters or their cores only when the ages of the clusters are comparable to their relaxation times (τ≥1). These results suggest mass seggregation due to dynamical effects. The values of χ, which characterize the overall mass functions for the clusters are 0.96±0.11, 1.16±0.18, 0.55±0.14 and 0.66±0.31 respectively. The change in χ as a function of radius is a good indicator of the dynamical state of clusters.     

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.     

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.     

Some properties of dust outside the galactic disk

The joint use of accurate near- and mid-infrared photometry from the 2MASS and WISE catalogues has allowed the variations of the extinction law and the dust grain size distribution in high Galactic latitudes (|b| > 50°) at distances up to 3 kpc from the Galactic midplane to be analyzed. The modified method of extrapolation of the extinction law applied to clump giants has turned out to be efficient for separating the spatial variations of the sample composition, metallicity, reddening, and properties of the medium. The detected spatial variations of the coefficientsE(H ? W1)/E(H ? Ks), E(H ? W2)/E(H ? Ks), and E(H ? W3)/E(H ? Ks) are similar for all high latitudes and depend only on the distance from the Galactic midplane. The ratio of short-wavelength extinction to long-wavelength one everywhere outside the Galactic disk has been found to be smaller than that in the disk and, accordingly, the mean dust grain size is larger, while the grain size distribution in the range 0.5–11 µm is shifted toward coarse dust. Specifically, the mean grain size initially increases sharply with distance from the Galactic midplane, then decreases gradually, approaching a value typical of the disk at |Z| ≈ 2.4 kpc, and, further out, stabilizes or may increase again. The coefficients under consideration change with coordinate Z with a period of about 1312 ± 40 pc, coinciding every 656 ± 20 pc to the south and the north and showing a significant anticorrelation between their values in the southern and northern hemispheres at intermediate Z. Thus, there exists a unified large-scale periodic structure of the interstellar medium at high latitudes within at least 5 kpc. The same periodic variations have also been found for the extinction coefficient R _V within 600 pc of the Galactic midplane through the reduction of different photometric data for stars of different classes.     

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 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.