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1.
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.  相似文献   

2.
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.  相似文献   

3.
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, ΩP = 21.7 ± 2.8 km s?1 kpc?1, which are comparable to and ΩP = 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.  相似文献   

4.
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.  相似文献   

5.
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°.  相似文献   

6.
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.  相似文献   

7.
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 ± 1stat ± 3syst 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.  相似文献   

8.
The space velocities of 200 long-period (P>5 days) classical Cepheids with known proper motions and line-of-sight velocities whose distances were estimated from the period-luminosity relation have been analyzed. The linear Ogorodnikov-Milne model has been applied, with the Galactic rotation having been excluded from the observed velocities in advance. Two significant gradients have been found in the Cepheid velocities, ?W/?Y = ?2.1 ± 0.7 km s?1 kpc?1 and ?V/?Z = 27 ± 10 km s?1 kpc?1. In such a case, the angular velocity of solid-body rotation around the Galactic X axis directed to the Galactic center is ?15 ± 5 km s?1 kpc?1.  相似文献   

9.
We use vector spherical harmonics for a kinematic analysis of the proper motions of stars from the Hipparcos, Tycho-2, and UCAC3 catalogues in the northern and southern Galactic hemispheres. We have found that the statistically reliable values of the Ogorodnikov-Milne model parameters M 32 + and M 32 ? have different signs in different hemispheres. This is a consequence of the Galaxy??s rotational retardation with distance from the principal Galactic plane. Based on various samples of stars from the above catalogues, we have obtained the following estimate for the magnitude of the vertical gradient of Galactic rotation velocity in the solar neighborhoods: (20.1 ± 2.9) < |?V??/?z| < (49.2 ± 0.8) km s?1 kpc?1. Another result that is revealed by our analysis of the parameters M 13 ? and M 13 + in different Galactic hemispheres is that the vertical gradient of expansion velocity for the stellar system ?V R /? z is positive in the northern hemisphere and negative in the southern one. This suggests that the expansion velocity V R increases with distance fromthe Galactic plane. We show that both these gradients give rise to an apparent acceleration of the solar motion along the x and y axes of the rectangular Galactic coordinate system. Our analysis of the parameters M 21 ? and M 12 + shows no significant differences in both hemispheres and has allowed us to determine the Oort parameters, to estimate the Galactic rotation velocity and period in the solar neighborhood, and to calculate the ratio of the epicyclic frequency to the angular velocity of Galactic rotation in the solar neighborhood. The derived diagonal elements of the velocity field deformation tensor suggest that the orientation of the rectangular Galactic coordinate system in space must be determined by taking into account not only the geometrical factors but also the dynamical ones. All these results agree well with these quantities estimated over the entire sphere by various authors.  相似文献   

10.
We analyze the three-dimensional kinematics of about 82 000 Tycho-2 stars belonging to the red giant clump (RGC). First, based on all of the currently available data, we have determined new, most probable components of the residual rotation vector of the optical realization of the ICRS/HIPPARCOS system relative to an inertial frame of reference, (ω x , ω y , ω z ) = (−0.11, 0.24, −0.52) ± (0.14, 0.10, 0.16) mas yr−1. The stellar proper motions in the form μα cos δ have then be corrected by applying the correction ω z = −0.52 mas yr−1. We show that, apart from their involvement in the general Galactic rotation described by the Oort constants A = 15.82 ± 0.21 km s−1 kpc−1 and B = −10.87 ± 0.15 km s−1 kpc−1, the RGC stars have kinematic peculiarities in the Galactic yz plane related to the kinematics of the warped stellar-gaseous Galactic disk. We show that the parameters of the linear Ogorodnikov-Milne model that describe the kinematics of RGC stars in the zx plane do not differ significantly from zero. The situation in the yz plane is different. For example, the component of the solid-body rotation vector of the local solar neighborhood around the Galactic x axis is M 32 = −2.6 ± 0.2 km s−1 kpc−1. Two parameters of the deformation tensor in this plane, namely M 23+ = 1.0 ± 0.2 km s−1 kpc−1 and M 33M 22 = −1.3 ± 0.4 km s−1 kpc−1, also differ significantly from zero. On the whole, the kinematics of the warped stellar-gaseous Galactic disk in the local solar neighborhood can be described as a rotation around the Galactic x axis (close to the line of nodes of this structure) with an angular velocity −3.1 ± 0.5 km s−1 kpc−1 ≤ ΩW ≤ −4.4 ± 0.5 km s−1 kpc−1.  相似文献   

11.
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.  相似文献   

12.
13.
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.  相似文献   

14.
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.  相似文献   

15.
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, VR, residual tangential, ΔVcirc, and vertical, W, velocities of OB stars by applying a periodogram analysis. The amplitudes of the radial, tangential, and vertical velocity perturbations are fR = 7.1± 0.3 km s?1, fθ = 6.5 ± 0.4 km s?1, and fW = 4.8± 0.8 km s?1, respectively; the perturbation wavelengths are λR = 3.3 ± 0.1 kpc, λθ = 2.3 ± 0.2 kpc, and λW = 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.  相似文献   

16.
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, Ω0 = ?3.50 ± 0.08 km s?1 kpc?2, and Ω0 = 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.  相似文献   

17.
Bobylev  V. V.  Bajkova  A. T. 《Astronomy Letters》2019,45(9):580-592

We have studied the kinematic properties of the candidates for hot subdwarfs (HSDs) selected by Geier et al. from theGaiaDR2 catalogue. We have used a total of 12 515 stars with relative trigonometric parallax errors less than 30%. The HSDs are shown to have different kinematics, depending on their positions on the celestial sphere. For example, the sample of low-latitude (|b| < 20°) HSDs rotates around the Galactic center with a linear velocity V0 = 221 ± 5 km s?1. This suggests that they belong to the Galactic thin disk. At the same time, they lag behind the local standard of rest by ΔV ~ 16 km s?1 due to the asymmetric drift. The high-latitude (|b| ≥ 20°) HSDs rotate with a considerably lower velocity, V = 168 ± 6 km s?1. Their lagging behind the local standard of rest is already ΔV ~ 40 km s?1. Based on the entire sample of 12 515 HSDs, we have found a positive rotation around the x axis significantly differing from zero with an angular velocity ω1 = 1.36±0.24 km s?1 kpc?1. We have studied the samples of HSDs that are complete within r < 1.5 kpc. Based on them, we have traced the evolution of the parameters of the residual velocity ellipsoid as a function of both latitude |b| and coordinate |z|. The following vertical disk scale heights have been found: h = 180 ± 6 and 290 ± 10 pc from the low- and high-latitude HSDs, respectively. A new estimate of the local stellar density Σout = 53 ± 4 M☉ kpc?2 has been obtained for zout = 0.56 kpc from the high-latitude HSDs.

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18.
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, ω0 = 4.18 ± 0.17 km s?1 kpc?2, ω0 = ?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.  相似文献   

19.
Bobylev  V. V.  Bajkova  A. T. 《Astronomy Letters》2019,45(6):331-340

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

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20.
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