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.     

Investigation of properties of galaxy clusters in the Hercules supercluster region

We investigated the properties of galaxy clusters in the region of the Hercules supercluster using observational data from the SDSS and 2MASS catalogs and the NED. We have selected 13 galaxy clusters with a total dynamical mass of 4.82 × 10¹⁵ M _⊙ in a 100 × 45 Mpc supercluster region in the plane of the sky (0.030 < z < 0.041). In addition, our sample includes eight clusters from the immediate neighborhoods of the superclusters and ten field clusters at the same z. The derived properties of the rich Hercules supercluster are shown in comparison with the data for the poor Leo supercluster. The main parameters of the virialized galaxy cluster regions in the near infrared (K _s ) for the Hercules supercluster differ from those for the Leo supercluster: the number of galaxies and the total luminosity (to a limiting magnitude of ?21 _· ^m 5) increase with cluster mass (L _K,200 ∝ M ₂₀₀ ^0.91±0.07 and N ₂₀₀ ∝ M ₂₀₀ ^0.94±0.07 ), but the dependences are steeper by 0.28 and 0.22. In the virialized cluster regions, the fraction of early-type galaxies selected by the bulge contribution, concentration index, and u t= r color is, on average, 66% (60% in Leo, 70% in the field) among the galaxies brighter than ?23 _· ^m 3 and 54% (51% in Leo, 61% in the field) among the galaxies brighter than ?22 _· ^m 3. The fraction of early-type galaxies in the superclusters does not change with galaxy cluster mass and luminosity. The composite luminosity function of the rich Hercules supercluster is described by a Schechter function and does not differ from the luminosity function of the poor Leo supercluster for the luminosity interval [?26 ^m , ?21 _· ^m 5] but differs from the field luminosity function at the same z determined from ten galaxy clusters.     

Analysis of historical meteor and meteor shower records: Korea, China, and Japan

We have compiled and analyzed historical Korean meteor and meteor shower records in three Korean official history books, Samguksagi which covers the three Kingdoms period (57 B.C.-A.D. 935), Goryeosa of Goryeo dynasty (A.D. 918-1392), and Joseonwangjosillok of Joseon dynasty (A.D. 1392-1910). We have found 3861 meteor and 31 meteor shower records. We have confirmed the peaks of Perseids and an excess due to the mixture of Orionids, north-Taurids, or Leonids through the Monte Carlo test. The peaks persist from the period of Goryeo dynasty to that of Joseon dynasty, for almost one thousand years. Korean records show a decrease of Perseids activity and an increase of Orionids/north-Taurids/Leonids activity. We have also analyzed seasonal variation of sporadic meteors from Korean records. We confirm the seasonal variation of sporadic meteors from the records of Joseon dynasty with the maximum number of events being roughly 1.7 times the minimum. The Korean records are compared with Chinese and Japanese records for the same periods. Major features in Chinese meteor shower records are quite consistent with those of Korean records, particularly for the last millennium. Japanese records also show Perseids feature and Orionids/north-Taurids/Leonids feature, although they are less prominent compared to those of Korean or Chinese records.     

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.     

VLF detection of fireballs

The results from 80 hours of simultaneous visual/video and VLF recordings made during the Lyrids, Perseids, Orionids, Leonids and Geminids are presented. All meteor magnitudes from –11 to +4 have been sampled at least once during these observations. The only positive VLF fireball detection was made at 19:57:32 UT on August 11, 1993 from the South of France. We present a Fourier transform analysis of this event and we also derive a lower limit to the electrical field strength produced by the fireball at the antenna. Our present observations suggest a lower limit of M_v –10 ± 1 for a fireball to produce a VLF signal.     

Volume Filling Factors of the DIG in M 31

The volume filling factor f _v of the diffuse ionized gas in the bright emission ring of M 31 is derived from radio continuumobservations. The dependence of f _v on the local mean electron density n _e is a power law, f _v(n _e) = a n _e ^-bwith a = 0.011± 0.003 and b = -1.2± 0.3, where n _e is in cm^-3. The same power law was recently found for the DIG in the solar neighbourhood from pulsar data.     

Active star-forming region in Orion KL, epoch 2012

Polarization measurements of the H₂O maser emission from the active region in Orion KL were carried out at epoch 2011?C2012 on the Svetloe-Zelenchukskaya radio interferometer. The bipolar outflow structure and polarized emission parameters have been determined. The emission from the components at v = 7.6 and 7.0 km s^?1 dominates in the line profile; the relative contribution of the former component has increased. The velocity of the bipolar outflow ejector region is almost equal to that of the local standard of rest v _LSR = 7.65 km s^?1, while the velocity of the remote component is v = 7.0 km s^?1. The emission from the bipolar outflow is observed at a distance up to 11 mas from the ejector. Its diameter does not exceed 0.3 mas. The outflow orientation in the plane of the sky is ?37°. The outflow velocity components along the line of sight differ by ??v = 0.3 km s^?1. The polarization levels of the bipolar outflow and the remote component reach m = 62 and 39%, respectively.     

Infrared luminosities of local-volume galaxies

Based on data from the Two-Micrometer All-Sky Survey (2MASS), we analyzed the infrared properties of 451 Local-Volume galaxies at distances D ≤ 10 Mpc. We determined the K-band luminosity function of the galaxies in the range of absolute magnitudes from ?25^m to ?11^m. The local luminosity density within 8 Mpc is 6.8 × 10⁸L_⊙ Mpc^?3, a factor of 1.5 ± 0.1 higher than the global mean K-band luminosity density. We determined the ratios of the virial mass to the K-band luminosity for nearby groups and clusters of galaxies. In the luminosity range from 5 × 10¹⁰ to 2 × 10¹³L_⊙, the dependence log(M/L_K) ∝ (0.27 ± 0.03) log L_K with a dispersion of ～0.1 comparable to the measurement errors of the masses and luminosities of the systems of galaxies holds for the groups and clusters of galaxies. The ensemble-averaged ratio, 〈M/L_K〉 ? (20–25) M_⊙/L_⊙, was found to be much smaller than the expected global ratio, (80–90)M_⊙/L_⊙, in the standard model with Ω_m = 0.27. This discrepancy can be eliminated if the bulk of the dark matter in the Universe is not associated with galaxies and their systems.     

Kinematics of the Gould Belt based on open clusters

We have redetermined the kinematic parameters of the Gould Belt using currently available data on the motion of nearby young (log t < 7.91) open clusters, OB associations, and moving stellar groups. Our modeling shows that the residual velocities reach their maximum values of ?4 km s^?1 for rotation (in the direction of Galactic rotation) and +4 km s^?1 for expansion at a distance from the kinematic center of ≈300 pc. We have taken the following parameters of the Gould Belt center: R ₀ = 150 pc and l ₀ = 128°. The whole structure is shown to move relative to the local standard of rest at a velocity of 10.7 ± 0.7 km s^?1 in the direction l = 274° ± 4° and b = ?1° ± 3°. Using the derived rotation velocity, we have estimated the virial mass of the Gould Belt to be 1.5 × 10⁶ M _⊙.     

A rare reflection effect eclipsing sdB+dM binary: 2M 1533+3759

In this paper, we report a rare reflection effect eclipsing sdB+dM binary, 2M?1533+3759. It is the seventh eclipsing sdB+dM binary that has been discovered to date. This system has an orbital period of 0.16177042 day and a velocity semi-amplitude of 71.1 km?s^?1. Using a grid of zero-metallicity NLTE model atmospheres, we derived T _eff=29250 K, log?g=5.58 and [He/H]=?2.37 from spectra taken near the reflection effection minimum. Lightcurve modeling resulted in a system mass ratio of 0.301 and an orbital inclination angle of 86.6°. The derived primary mass for 2M?1533+3759, 0.376±0.055 M _⊙, is significantly lower than the canonical mass (0.48 M _⊙) found for most previously investigated sdB stars. This implies an initial progenitor mass >1.8 M _⊙, at least a main sequence A star and perhaps even one massive enough to undergo non-degenerate helium ignition.     

Residual mass from atmospheric ablation of small meteoroids

Numerical solutions of the equations of meteor ablation in the Earth's atmosphere have been obtained using a variable step size Runge-Kutta technique in order to determine the size of the residual mass resulting from atmospheric flight. The equations used include effects of meteoroid heat capacity and thermal radiation, and a realistic atmospheric density profile. Results were obtained for initial masses in the range 10^?7–10^?2 g, and for initial velocities less than 24 km s^?1 (results indicated no appreciable residual mass for meteors with velocities above 24 km s^?1 in this mass range). The following function has been obtained to provide the logarithm of the ratio of the residual mass following atmospheric ablation to the original preatmospheric mass

$\text{log r = 4.7 ?0.33v}{}_{\mathrm{\infty }}\text{?0.013v}{}_{\mathrm{\infty }}{}^2\text{+ 1.2 log m}{}_{\mathrm{\infty }}\text{+ 0.08 log}{}^2\text{m}{}_{\mathrm{\infty }}\text{?0.083v}{}_{\mathrm{\infty }}\text{log m}{}_{\mathrm{\infty }}\text{M}$

The pre-atmospheric mass and velocity are represented by m_∞ and v_∞.When the results are expressed in terms of the size of the residual mass following atmospheric ablation as a function of the initial mass and velocity, it is found that the final residual mass is almost independent of the original mass of the meteoroid, but very strongly dependent on the original velocity. For example, the residual mass is very nearly 10^?7 g for a meteoroid with velocity 18 kms^?1 for initial masses from 10^?7 to 10^?3 g. On the other hand, a slight change in the initial velocity to 20 km s^?1 will shift the residual mass to approx. 10^?8 g. This strong velocity dependence coupled with the weak dependence on the original mass has important consequences for the sampling of ablation product micrometeorites.     

Spectroscopic Orbit of the Eclipsing Binary AI Draconis

New radial velocity measurements of the Algol-type eclipsing binary AI Dra, based on Reticon observations, are presented. The velocity measures themselves are based on fitting theoretical profiles, generated by a physical model of the binary, to the observed cross-correlation function (ccf). Such profiles match this function very well, much better in fact that Gaussian profiles which are generally used. Measuring the ccf's with Gaussian profiles yields following results: m_p sin³ i=2.55± 0.05m_⊙, m_s sin³ i = 1.14 ± 0.03m_⊙, (a_p + a_s) sin i=7.34 ±0.05R_⊙, and m_p/m_s =2.23± 0.05. Where as measuring the ccf's with theoretical profiles yields a mass ratio of 2.33 and following results: m_p sin³ i=2.84± 0.05m_⊙, m_s sin³ i=1.22 ± 0.03m_⊙, (a_p +a_s) sin i=7.56± 0.05R_⊙. The system comprising a semi-detached configuration. From the solution of a previously published light curved and combining it's results with the spectroscopic orbit, one can lead to the following physical parameters: m_p =2.99m_⊙, m_s =1.28m_⊙, > T_p < =9600 K, > T_s < =5400 K, > R_p < =2.35R_⊙, > R_s < =2.12R_⊙. The system comprising an AO primary and a secondary of G2 spectral type. This revised version was published online in July 2006 with corrections to the Cover Date.     

Corrections for the Lutz-Kelker bias for Galactic masers

Based on published data, we have collected information about Galactic maser sources with measured distances. In particular, 44 Galactic maser sources located in star-forming regions have trigonometric parallaxes, proper motions, and radial velocities. In addition, ten more radio sources with incomplete information are known, but their parallaxes have been measured with a high accuracy. For all 54 sources, we have calculated the corrections for the well-known Lutz-Kelker bias. Based on a sample of 44 sources, we have refined the parameters of the Galactic rotation curve. Thus, at R ₀ = 8kpc, the peculiar velocity components for the Sun are (U _⊙, V _⊙, W _⊙) = (7.5, 17.6, 8.4) ± (1.2, 1.2, 1.2) km s^?1 and the angular velocity components are ω ₀ = ?28.7 ± 0.5 km s^?1 kpc^?1, ω ₀′ = +4.17 ± 0.10 km s^?1 kpc^?2, and ω₀″ = ?0.87 ± 0.06 km s^?1 kpc^?3. The corresponding Oort constants are A = 16.7 ± 0.6 km s^?1 kpc^?1 and B = ?12.0 ± 1.0 km s^?1 kpc^?1; the circular rotation velocity of the solar neighborhood around the Galactic center is V ₀ = 230 ± 16 km s^?1. We have found that the corrections for the Lutz-Kelker bias affect the determination of the angular velocity ω ₀ most strongly; their effect on the remaining parameters is statistically insignificant. Within themodel of a two-armed spiral pattern, we have determined the pattern pitch angle $i = - 6_.^ \circ 5$ and the phase of the Sun in the spiral wave χ ₀ = 150°.     

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.     

Do the fundamental constants vary in the course of cosmological evolution?

The possible cosmological variation of the proton-to-electron mass ratio μ = m _p/m _e was estimated by measuring the H₂ wavelengths in the spectra of distant quasars. We analyze high-resolution (FWHM≈7 km s^?1) spectra of the two damped Lyman-α systems at redshifts z _abs=2.3377 and 3.0249 observed in the spectra of the quasars Q 1232+082 and Q 0347?382, respectively. Our analysis yielded the most conservative estimate for the possible variation of μ in the past ～ 10 Gyr, Δμ/μ = (5.7 ± 3.8) × 10^?5. Since the significance of this result does not exceed 1.5σ, further observations are needed to increase the statistical significance. This is the most stringent limit on the possible cosmological variation of μ to date.     

Particle size distributions in Saturn's rings from voyager 1 radio occultation

Observations of microwave opacity τ[λ] and near forward scatter from Saturn's rings at wavelengths λ of 3.6 and 13 cm from the Voyager 1 ring occultation experiment contain information regarding ring particle sizes in the range of about a = 0.01 to 15 m radius. The opacity measurements τ[3.6] and τ[13] are sufficient to constrain the scale factor n(a₀) and index q of a power law incremental size distribution n(a) = n(a₀)[a₀/a]^q, assuming known minimum and maximum sizes and a many-particle-thick model. The families of such distributions are highly convergent in the centimeter-size range. Forward scatter at 3.6 cm can be used to solve for a general distribution over the radius range $\text{1 ? a ? 15}\text{m}$ by integral inversion and inverse scattering methods, again assuming a many-particle-thick slab-type radiative transfer model. Distributions n(a) valid over $\text{0.01 ? a ? 15}\text{m}$ are obtained by combining the results from the two types of measurements above. Mass distributions may be computed directly from n(a). Such distributions, partly measured and partly synthesized, have been obtained for four features in the ring system centered at 1.35, 1.51, 2.01, and 2.12 Saturn radii (R_s). The size and mass distributions both cut off sharply at a ? 4–5 m; the mass distribution peaks over the narrow size range $\text{3 ? a ? 4}\text{m}$ for all four locations. No single power law distribution is consistent with the data over the entire interval $\text{0.01 ? a ? 5}\text{m}$, although a power law-type model is consistent with the data over a limited size range of $\text{0.01 ? a ? 1}\text{m}$, where the indices q = 3.4 and 3.3 are obtained from the slab model for the features located at 1.51 and 2.01 R_s. The fractional contribution of the suprameter particles to the microwave opacity in each feature appears to be about $\text{1}\text{3}\text{,}\text{1}\text{3}\text{,}\text{2}\text{3}\text{,}\text{and}\text{1}$, respectively, with the fraction at 2.12 R_s being the least certain. The cumulative surface mass per unit area obtained for the classical slab model is approximately 11, 16, 41, and 132 g/cm² for the four features, respectively, if the particles are solid H₂O ice. Both the fractional opacity and the mass density estimates represent upper bounds implied by the assumption of a uniformly mixed set of particles in a many-particle-thick vertical profile; lower estimates would result if the rings were assumed to be nearly a monolayer or if the vertical distribution of particles were size dependent.     

HD 1: The number‐one star in the sky

We present the first ever study of the bright star HD 1. The star was chosen arbitrarily just because of its outstanding Henry Draper number. Surprisingly, almost nothing is known about this bright 7.^m4 star. Our observations were performed as part of the commissioning of the robotic telescope facility STELLA and its fiber‐fed high‐resolution optical echelle spectrograph SES in the years 2007–2010. We found long‐term radial velocity variations with a full amplitude of 9 km s^–1 with an average velocity of –29.8 km s^–1 and suggest the star to be a hitherto unknown single‐lined spectroscopic binary. A preliminary orbit with a period of 6.2 years (2279±69 days) and an eccentricity of 0.50±0.01 is given. Its rms uncertainty is just 73 m s^–1. HD 1 appears to be a G9‐K0 giant of luminosity class IIIa with T_eff = 4850±100 K, logg = 2.0±0.2, L ≈ 155 L_⊙, a mass of 3.0±0.3 M_⊙, a radius of 17.7 R_⊙, and an age of ≈350 Myr. A relative abundance analysis led to a metallicity of [Fe/H] = –0.12 ± 0.09. The α ‐element silicon may indicate an overabundance of +0.13 though. The low strengths of some s‐process lines and a lower limit for the ¹²C/¹³C isotope ratio of ≥16 indicate that HD 1 is on the first ascend of the RGB. The absorption spectral lines appear rotationally broadened with a v sin i of 5.5±1.2 km s^–1 but no chromospheric activity is evident. We also present photometric monitoring BV (RI)_C data taken in parallel with STELLA. The star is likely a small‐amplitude (<10 mmag) photometric variable although no periodicity was found (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.