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.     

On the Rotational Temperature of AlH in Sunspots

A search has been carried out for the presence of rotational lines of two bands of the (0, 0) and (1, 1) A ¹Π?–?X ¹Σ⁺ system of the AlH molecule in the high resolution Fourier Transform Spectra of sunspots observed at the National Solar Observatory at Kitt Peak. Though the presence of the AlH molecule in sunspots was confirmed by Wallace, Hinkle, and Livingston (An Atlas of Sunspot Umbral Spectra in the Visible from 15?000 to 25?000 cm^?1 (3920 to 6664 Å), Tech. Rep. 00-001, National Solar Observatory, Tucson, AZ, 2000), there is no report on the rotational temperature in the literature by identifying AlH molecular lines. The results obtained in this new search using a suitable identification technique are compared with the results reported by Wallace, Hinkle, and Livingston (2000). In view of the fact that the rotational temperatures of the molecules could be used to test photospheric and sunspot models, the effective rotational temperature for the (0, 0) band of the A?–?X system of AlH molecule is estimated by measuring the equivalent widths of well resolved spectral lines and its value justifies the existence of the AlH molecule in sunspots.     

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.     

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.     

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.     

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.     

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.     

Comet C/2010X1 (Elenin). Unrealized expectations

We present the analysis of the photometric and spectroscopic data obtained for comet C/2010 X1 (Elenin) when it was at a distance of 2.92 AU from the Sun. The observations were made at the prime focus of the 6-m BTA telescope with the SCORPIO focal reducer. The magnitude of the comet, measured in the R _c -band with an 9?? aperture radius amounted to 16?8 ± 0?1. The computed dust production rate was estimated to be about 6 kg/s. The cometary coma manifested the emissions in the (0?C0) band of the CN molecule violet system, and a number of emission band heads of the C₃ molecule. The gas production rate of the molecules is determined using the Haser model and amounts to 1.41 × 10²⁴ and 4.20 × 10²³ molecules per second for CN and C₃, respectively. The ratio of gas production rates log[Q(C₃)/Q(CN)] is equal to ?0.85, which is close to the mean value, determined for a significant number of comets. A normalized gradient of the cometary dust reflectivity, calculated for the 4430?C6840 ? spectral range amounts to 14.3 ± 1.2%.     

Photoelectric lightcurves and rotation periods of the asteroids 46 Hestia and 115 Thyra

Results of photoelectric observations of the asteriods 46 Hestia and 115 Thyra, performed in a cooperative program between the Torino and Table Mountain Observatories, are presented. The rotation periods and the maximum amplitudes are: P_syn = 21^h.0.4 ± 0^h.01, Amplitude = 0.12 mag and P_syn = 7^h.241 ± 0.^h.001, Amplitude = 0.20 mag, for Hestia and Thyra, respectively. The multiple-scattering factors, Q, inferred from the phase relation data are 0.054 ± 0.003 and 0.058 ± 0.002 for Hestia and Thyra, respectively. The low value obtained for Thyra disagrees with the mean one given by Bowell and Lumme (1979, in Asteroids (T. Gehrels, Ed.), pp. 132–169. University of Arizona Press, Tucson) for S-type asteroids.     

Gravity field of Mars from Mariner 9 tracking data

Further reduction of Doppler tracking data from Mariner 9 confirms our earlier conclusion that the gravity field of Mars is considerably rougher than the fields of either the Earth or the Moon. The largest positive gravity anomaly uncovered is in the Tharsis region which is also topographically high and geologically unusual. The best determined coefficients of the harmonic expansion of the gravitational potential are: J₂ = (1.96 ± 10.01) × 10^?3 ; C₂₂ = ?(5.1 ± 0.2) × 10^?5; and S₂₂ = (3.4 ± 0.2) × 10^?5. The other coefficients have not been well determined on an individual basis, but the ensemble yields a useful model for the gravity field for all longitudes in the vicinity of 23° South latitude which corresponds to the periapse position for the orbiter.The value obtained for the inverse mass of Mars (3 098 720 ± 70 M⊙^?1) is in good agreement with prior determinations from Mariner flyby trajectories. The direction found for the rotational pole of Mars, referred to the mean equinox and equator of 1950.0, is characterized by α = 317°.3 ± 0°.2, δ = 52°.7 ± 0°.2. This result is in excellent agreement with Sinclair's recent value, determined from earth-based observations of Mars' satellites, but differs by about 0°.5 from the previously accepted value. Other important physical constants that have either been refined or confirmed by the Mariner 9 data include: (i) the dynamical flattening, f = (5.24 ± 0.02) × 10^?3; (ii) the maximum principal moment of inertia, C = (0.375 ± 0.006) MR²; and (iii) the period of precession of Mars' pole, P ? (1.73 ± 0.03) × 10⁵ yr, corresponding to a rate of 7.4 sec of arc per 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.     

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.     

Worldwide photometry and lightcurve observations of 16 Psyche during the 1975–1976 apparition

We present 26 lightcurves of 16 Psyche from 1975 and 1976. The synodic period during this apparition was 4^h.1958. Combining photometric data from this opposition with those from previous apparitions allowed us to derive a mean phase coefficient in V of 0.026 ± 0.002 mag/deg and to establish that Psyche's absolute V₀ magnitude and rotational amplitude vary with aspect; at 90° aspect, V₀(1, 0) = 6.27 ± 0.05 and the lightcurve amplitude is 0.30 mag, while at 0° or 180° aspect, V₀(1, 0) = 6.02 ± 0.02 and the amplitude is ?0.03 mag. This behavior is accounted for if, to first order, Psyche's shape is that of a triaxial ellipsoid with axial ratios near 5:4:3. Colors at zero phase are U-B = 0.26 ± 0.01 and B-V = 0.71 ± 0.01. Color phase coefficients are <0.001 mag/deg in U-B and 0.0010 ± 0.0004 mag/deg in B-V.     

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.     

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.     

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.