Angular Velocity Of Galactic Rotation Research Articles

Kinematics of the Galaxy from Young Open Star Clusters with Data from the Gaia EDR3 Catalogue

We have analyzed the kinematics of open star clusters (OSCs) with the proper motions and distances calculated by Hao et al. based on Gaia EDR3 data. The mean line-of-sight velocities are known for a number of clusters from this list. We show that the Galactic rotation parameters determined from samples of OSCs with various ages are in good agreement between themselves. The most interesting results have been obtained from a sample of 967 youngest OSCs with a mean age of 18 Myr. In particular, we have found the following parameters of the angular velocity of Galactic rotation using only their proper motions and distances: $\Omega_0 =28.01\pm0.15$ km s$^{-1}$ kpc$^{-1},$ $\Omega^{'}_0=-3.674\pm0.040$ km s$^{-1}$ kpc$^{-2},$ and $\Omega^{''}_0=0.565\pm0.023$ km s$^{-1}$ kpc$^{-3}$. The circular rotation velocity of the solar neighborhood around the Galactic center here is $V_0=226.9\pm3.1$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.1\pm0.1$ kpc. The parameters of the spiral density wave have been determined from the space velocities of 233 young clusters. The amplitudes of the radial and tangential velocity perturbations produced by the spiral density wave are $f_R=9.1\pm0.8$ km s$^{-1}$ and $f_\theta=4.6\pm1.2$ km s$^{-1}$, respectively; the perturbation wavelengths are $\lambda_R=3.3\pm0.5$ kpc and $\lambda_\theta=2.6\pm0.6$ kpc for the the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave has been found to be $(\chi_\odot)_R\approx-180^\circ$.

Study of the Galactic Rotation Based on Masers and Radio Stars with VLBI Measurements of Their Parallaxes

Based on published data, we have produced a sample of 256 radio sources whose trigonometric parallaxes and proper motions were measured by VLBI. This sample contains Galactic masers associated with massive protostars and stars in active star-forming regions. It also includes young low-mass stars from the Gould Belt region whose radio observations were performed in continuum. Based on this, most complete sample of sources to date, we have estimated the velocities $(U,V,W)_\odot$ and the parameters of the angular velocity of Galactic rotation $\Omega_0, \Omega^{(1)}_0, ... , \Omega^{(4)}_0$ and obtained a new estimate of the distance fromthe Sun to the Galactic center, $R_0=8.15^{+0.04}_{-0.20}$ kpc. The parameters of the Galactic spiral density wave have been found from the series of radial, $V_R$, and residual tangential, $\Delta V_{circ}$, velocities of stars. The amplitudes of the radial and tangential velocity perturbations are $f_R=7.0\pm0.9$ km s$^{-1}$ and $f_\theta=3.8\pm1.1$ km s$^{-1}$, the perturbation wavelengths are $\lambda_R=2.3\pm0.2$ kpc and $\lambda_\theta=2.0\pm0.4$ kpc, and the Sun's phases in the spiral density wave are $(\chi_\odot)_R=-163^\circ\pm9^\circ$ and $(\chi_\odot)_\theta=-137^\circ\pm10^\circ$ for the adopted four-armed spiral pattern.

Galactic Rotation Parameters Based on Stars from Active Star-Forming Regions with Data from the Gaia DR2 Catalogue

We have studied a sample of more than 25 000 young stars with proper motions and trigonometric parallaxes from the Gaia DR2 catalogue. The relative errors of their parallaxes do not exceed 10\%. The selection of stars belonging to active star-forming regions was made by Marton et al. based on data from the Gaia DR2 catalogue by invoking infrared measurements from the WISE and Planck catalogues. Low-mass T Tauri stars constitute the majority of sample stars. The following parameters of the angular velocity of Galactic rotation have been found from them: $\Omega_0 =28.40\pm0.11$ km s$^{-1}$ kpc$^{-1}$, $\Omega^{'}_0=-3.933\pm0.033$ km s$^{-1}$ kpc$^{-2}$ and $\Omega^{''}_0=0.804\pm0.040$ km s$^{-1}$ kpc$^{-3}$. The Oort constants are $A=15.73\pm0.32$ km s$^{-1}$ kpc$^{-1}$ and $B=-12.67\pm0.34$ km s$^{-1}$ kpc$^{-1}$, while the circular rotation velocity of the solar neighborhood around the Galactic center is $V_0=227\pm4$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.0\pm0.15$ kpc.

Kinematics of the Galaxy from a Sample of Young Open Star Clusters with Data from the Gaia DR2 Catalogue

We have selected a sample of 326 young $(\log t<8)$ open star clusters with the proper motions and distances calculated by various authors from Gaia DR2 data. The mean values of their line-of-sight velocities have also been taken from various publications. As a result of our kinematic analysis, we have found the following parameters of the angular velocity of Galactic rotation: $\Omega_0=29.34\pm0.31$ km s$^{-1}$ kpc$^{-1}$, $\Omega'_0=-4.012\pm0.074$ km s$^{-1}$ kpc$^{-2}$, and $\Omega''_0=0.779\pm0.062$ km s$^{-1}$ kpc$^{-3}$. The circular rotation velocity of the solar neighborhood around the Galactic center is $V_0=235\pm5$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.0\pm0.15$ kpc. The amplitudes of the tangential and radial velocity perturbations produced by the spiral density wave are $f_\theta=3.8\pm1.2$ km s$^{-1}$ and $f_R=4.7\pm1.0$ km s$^{-1}$, respectively; the perturbation wavelengths are $\lambda_\theta=2.3\pm0.5$ kpc and $\lambda_R=2.2\pm0.5$ kpc for the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave is close to $-120\pm10^\circ.$

Properties of the Tycho-2 catalogue from Gaia data release

Based on the measurements performed in the first 14 months of Gaia operation, we have solved the problem of obtaining the systematic differences between the stellar positions and proper motions of the TGAS (Tycho–Gaia Astrometric Solution) and Tycho-2 catalogues. By dividing the common stars from the TGAS and Tycho-2 catalogues into three G-magnitude groups for mean values of $$10\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{m} 5,11\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{m} 5,and13\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{m} 0,$$ we have obtained the systematic differences between the stellar equatorial coordinates and proper motions of both catalogues in the form of a decomposition into vector spherical harmonics by taking into account the magnitude equation. The systematic components have been extracted from the individual differences with a probability of 0.977–0.999. The constructed model of systematic differences allows any position measurements performed using Tycho-2 as a reference catalogue to be transformed to the TGAS frame. An important fact is the existence of a magnitude equation in the systematic differences: when passing from bright (G = 10 m ) to faint (G = 13 m ) stars, the systematic position differences change within the range from approximately −40 to 15 mas, while the systematic proper motion differences change from −3 to 3 mas yr−1. The orientation and mutual rotation parameters of the Tycho-2 and TGAS frames have also been found to be different for stars of different magnitudes: when passing from bright to faint stars, the rotation angle of the Tycho-2 frame relative to TGAS changes from 3.51 to 5.63 mas, while the angular velocity of rotation changes from 0.35 to 1.22 mas yr−1. Based on the developed method that allows the extent to which the systematic errors in the equatorial propermotions of stars affect the results of a kinematic analysis of the Galactic proper motions to be estimated within the Ogorodnikov–Milne model, we have shown that the slope of the Galactic rotation curve and the Oort parameter C are most sensitive to the transition from the Tycho-2 frame to the TGAS one. Their relative changes after the transformation to the TGAS frame reach 56 and 100%, respectively. At the same time, the changes in the estimates of the Oort parameters A and B as well as the linear velocity of the Sun relative to the Galactic center, the Galactic rotation period, the ratio of the epicyclic frequency to the angular velocity of Galactic rotation, and the mass of the Galaxy within the Galactocentric distance of the Sun are not so large, being 2−10%.

TRIGONOMETRIC DISTANCE AND PROPER MOTION OF IRAS 20056+3350: A MASSIVE STAR FORMING REGION ON THE SOLAR CIRCLE

We report our measurement of the trigonometric distance and proper motion of IRAS 20056+3350, obtained from the annual parallax of H2O masers. Our distance of D = 4.69 +0.65 −0.51 kpc, which is 2.8 times larger than the near kinematic distance adopted in the literature, places IRAS 20056+3350 at the leading tip of the Local arm and proximal to the Solar circle. Using our distance we re-evaluate past observations to reveal IRAS 20056+3350 as a site of massive star formation at a young stage of evolution. This result is consistent with the spectral energy distribution of the source evaluated with published photometric data from UKIDSS, WISE, AKARI, IRAS and sub-millimetre continuum. Both analytical approaches reveal the luminosity of the region to be 2.4×10 4 L⊙, and suggest that IRAS 20056+3350 is forming an embedded star of ≥16M⊙. We estimated the proper motion of IRAS 20056+3350 to be (µ�cos�, µ�) = (−2.62±0.33, −5.65±0.52) mas yr −1 from the group motion of H2O masers, and use our results to estimate the angular velocity of Galactic rotation at the Galactocentric distance of the Sun, 0 = 29.75±2.29 km s −1 kpc −1 ,

Determination of the galactic rotation curve from OB stars

We consider three samples of O- and B-type stars from the solar neighborhood 0.6--4 kpc for which we have taken the distances, line-of-sight velocities, and proper motions from published sources. The first sample contains 120 massive spectroscopic binaries. O stars with spectroscopic distances from Patriarchi et al. constitute the second sample. The third sample consists of 168 OB3 stars whose distances have been determined from interstellar calcium lines. The angular velocity of Galactic rotation at the solar distance $\Omega_0,$ its two derivatives $\Omega'_0$ and $\Omega"_0,$ and the peculiar velocity components of the Sun $(U,V,W)_\odot$ are shown to be well determined from all three samples of stars. They are determined with the smallest errors from the sample of spectroscopic binary stars and the sample of stars with the calcium distance scale. The fine structure of the velocity field associated with the influence of the Galactic spiral density wave clearly manifests itself in the radial velocities of spectroscopic binary stars and in the sample of stars with the calcium distance scale.

VLBI observations of H2O maser annual parallax and proper motion in IRAS 20143+3634: Reflection on the Galactic constants

Abstract We report the results of very long baseline interferometry (VLBI) observations of H2O masers in the IRAS 20143+3634 star-forming region (SFR) using VERA (VLBI Exploration of Radio Astrometry). By tracking masers for a period of over two years we measured a trigonometric parallax of π = 0.367 ± 0.037 mas, corresponding to a source distance of $D = 2.72 ^{+0.31}_{-0.25}$ kpc and placing it in the Local spiral arm. Our trigonometric distance is just 60% of the previous estimation based on radial velocity, significantly impacting the astrophysics of the source. We measured proper motions of −2.99 ± 0.16 mas yr−1 and −4.37 ± 0.43 mas yr−1 in RA and Dec, respectively, which were used to estimate the peculiar motion of the source as (Us, Vs, Ws) = (−0.9 ± 2.9, −8.5 ± 1.6, +8.0 ± 4.3) km s−1 for R0 = 8 kpc and Θ0 = 221 km s−1, and (Us, Vs, Ws) = (−1.0 ± 2.9, −9.3 ± 1.5, +8.0 ± 4.3) km s−1 for R0 = 8.5 kpc and Θ0 = 235 km s−1. IRAS 20143+3634 was found to be located near the tangent point in the Cygnus direction. Using our observations we derived the angular velocity of Galactic rotation of the local standard of rest (LSR), Ω0 = 27.3 ± 1.6 km s−1 kpc−1, which is consistent with previous values derived using VLBI astrometry of SFRs at the tangent points and Solar circle. It is higher than the value recommended by the International Astronomical Union of Ω0 = 25.9 km s−1 kpc−1 which was calculated using the Galactocentric distance of the Sun and circular velocity of the LSR.

Kinematics of stars in the northern and southern galactic hemispheres

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 M32+ and M32− 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 M13− and M13+ in different Galactic hemispheres is that the vertical gradient of expansion velocity for the stellar system ∂VR/∂z is positive in the northern hemisphere and negative in the southern one. This suggests that the expansion velocity VR 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 M21− and M12+ 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.

Searching for possible siblings of the sun from a common cluster based on stellar space velocities

Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative of the angular velocity of Galactic rotation {\Omega}'0 and the external reconciliation with Humphreys's distance scale for OB associations refined by Mel'nik and Dambis show that the initial distances should be reduced by \approx 20%. Given this correction, the heliocentric distances of these stars lie within the range 0.6-2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R0=8 kpc, has allowed the following parameters to be determined:(1) the solar peculiar velocity components (U_o,V_o,W_o)=(8.9,10.3,6.8)\pm(0.6,1.0,0.4) km/s;(2) the Galactic rotation parameters {\Omega}_o=-31.5\pm0.9 km/s/kpc, {\Omega}'_o=+4.49\pm0.12 km/s/kpc^2, {\Omega}"_o=-1.05\pm0.38 km/s/kpc^3, (the corresponding Oort constants are A=17.9\pm0.5 km/s/kpc, B=-13.6\pm1.0 km/s/kpc and the circular rotation velocity of the solar neighborhood is |V_o|=252\pm14 km/s); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, f_R = -12.5\pm1.1 km/s and f_{\theta}=2.0\pm1.6 km/s; the pitch angle for the two-armed spiral pattern i=-5.3\pm0.3 degrees, with the wavelength of the spiral density wave at the solar distance being {\lambda}=2.3\pm0.2 kpc; the Sun's phase in the spiral wave {\chi}_o=-91\pm4 degrees.

Galactic kinematics from OB3 stars with distances determined from interstellar Ca II lines

Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative of the angular velocity of Galactic rotation Ω′0 and the external reconciliation with Humphreys’s distance scale for OB associations refined by Mel’nik and Dambis show that the initial distances should be reduced by ≈20%. Given this correction, the heliocentric distances of these stars lie within the range 0.6–2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R 0 = 8 kpc, has allowed the following parameters to be determined: (1) the solar peculiar velocity components (u ⊙, v ⊙, ω ⊙) = (8.9, 10.3, 6.8) ± (0.6, 1.0, 0.4) km s−1; (2) the Galactic rotation parameters Ω0 = −31.5 ± 0.9 km s−1 kpc−1, Ω′0 = +4.49 ± 0.12 km s−1 kpc−2, Ω″0 = −1.05 ± 0.38 km s−1 kpc−3 (the corresponding Oort constants are A = 17.9 ± 0.5 km s−1 kpc−1, B = −13.6 ± 1.0 km s−1 kpc−1 and the circular rotation velocity of the solar neighborhood is |V 0| = 252 ± 14 km s−1); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, f R = −12.5±1.1 km s−1 and f ϑ = 2.0 ± 1.6 km s−1; the pitch angle for the two-armed spiral pattern i = −5.3° ± 0.3°, with the wavelength of the spiral density wave at the solar distance being λ = 2.3 ± 0.2 kpc; the Sun’s phase in the spiral wave x ⊙ = −91° ± 4°.

Galactic rotation curve from the space velocities of selected masers

Based on currently available observations of 28 maser sources in 25 star-forming regions with measured trigonometric parallaxes, proper motions, and radial velocities, we have constructed the rotation curve of the Galaxy. Taking different distances to the Galactic center R0, we have estimated the peculiar velocity of the Sun, the angular velocity of Galactic rotation, and its three derivatives. For R0 = 8 kpc, we have found the circular velocity of the Sun to be V0 = 243 ± 16 km s−1, which corresponds to a revolution period of 202 ± 10 Myr. We have obtained the Oort constants A = 16.9 ± 1.2 km s−1 kpc−1 and B = −13.5 ± 1.4 km s−1 kpc−1. Our simulation of the influence of a spiral density wave has shown that the peculiar velocity of the Sun with respect to the local standard of rest and the component (V⊙)LSR depend significantly on the Sun’s phase in the spiral wave.

Astrometry of Galactic Star-Forming Region Onsala 1 with VERA: Estimation of Angular Velocity of Galactic Rotation at the Sun

Abstract We conducted the astrometry of H$_2$O masers in the Galactic star-forming region Onsala 1 (ON 1) with the VLBI Exploration of Radio Astrometry (VERA). We measured a trigonometric parallax of 0.404$\ \pm\ $0.017 mas, corresponding to a distance of 2.47$\ \pm\ $0.11 kpc. ON 1 appears to be located near the tangent point at a Galactic longitude of 69$^\circ\!\!\!.$54. We estimated the angular velocity of the Galactic rotation at the Sun (the ratio of the Galactic rotation velocity at the Sun to the distance from the Sun to the Galactic center) to be $\Omega_0$$=$$\Theta_0 / R_0$$=$ 28.7$\ \pm\ $1.3 km s$^{-1}\ $kpc$^{-1}\ $ using the measured distance and proper motion of ON 1. This value is larger than the IAU recommended value of (220 km s$^{-1}/$8.5 kpc) $=$ 25.9 km s$^{-1}\ $ kpc$^{-1}\ $, but consistent with other results recently obtained with the VLBI technique.

Galactic rotation curve and the effect of density waves from data on young objects

Based on currently available data on the three-dimensional field of space velocities of young (<50 Myr) open star clusters and the radial velocities of HI clouds and star-forming (HII) regions, we have found the Galactic rotation curve in the range of Galactocentric distances 3 kpc <R<12 kpc using the first six terms of the Taylor expansion of the angular velocity of Galactic rotation in Bottlinger's equations. The Oort constants found are A= 15.5+-0.3 km/s/kpc and B=-12.2+-0.7 km/s/kpc. We have established that the centroid of the sample moves relative to the local standard of rest along the Galactic Y axis with a velocity of -6.2+-0.8 km/s. A Fourier spectral analysis of the velocity residuals from the derived rotation curve attributable to density waves reveals three dominant peaks with wavelengths of 2.5, 1.4, and 0.9 kpc and amplitudes of 4.7, 2.6, and 3.6 km/s, respectively. These have allowed us to estimate the distances between the density wave peaks, 1.9, 2.4, and 3.2 kpc as R increases, in agreement with the description of the density weave as a logarithmic spiral. The amplitude of the density wave perturbations is largest in the inner part of the Galaxy, about 9 km/s, and decreases to approximately 1 km/s in its outer part. A spectral analysis of the radial velocities of young open star clusters has confirmed the presence of periodic perturbations with an amplitude of 5.9+-1.1 km/s and a wavelength 1.7+-0.5 kpc. It shows that the phase of the Sun in the density wave is close to -90 degrees and the Sun is located in the interarm space near the outer edge of the Carina-Sagittarius arm.