Oort Constants Research Articles

Kinematical and ellipsoidal properties of the inner-halo hot subdwarfs observed in Gaia DR3 and LAMOST DR7

Here, we report the kinematical parameters of inner-halo hot subdwarfs located within (d≤15kpc) at high Galactic latitudes (bo≥20). The study included three program stars for one of the extreme He-rich groups (eHe-1) with eccentricity (e= 0.65) and the z-component of the angular momentum (Jz = 4288.66 kpc km s−1), the inner halo program I with 121 points (Teff≥24,000) and their subsections, i.e. inner halo program II (sdB; 79 points) with (40,000≥Teff≥24,000) and inner halo program III (sdO; 42 points) with (80,000≥Teff≥40,000). First, we calculated the spatial velocities (U¯,V¯,W¯;kms−1) along the Galactic coordinates (i.e., 25.73 ± ± 5.07, 28.79 ± 5.37, −14.51 ± 3.81) and their dispersion velocities (σ1,σ2,σ3;kms−1) = (161.94 ± 12.73, 140.31 ± 11.85, 101.57 ± 10.08) and subsequently their subsections sdB and sdO. Second, we calculated the vertex longitudes (l2) and the Solar motion (S⊙=41.246.42kms−1) as well as their subsections. Finally, based on the kinematic relation of the ratio (σ2/σ1) and our previously computed numerical value of the angular rotation rate (|A−B|=26.07±5.10;kms−1kpc−1), we obtained the average Oort's constants as (A&B;kms−1kpc−1) = (9.38 ± 0.33, −16.69 ± 0.25).

Kinematical and ellipsoidal properties of K dwarfs in the solar neighborhood of the Gaia era

AbstractThe study reports velocity ellipsoid parameters including the kinematical properties of K dwarf stars. Herein, two samples of K dwarf stars are presented with the solar neighborhood ( pc) for high (; 106 points) and low galactic latitudes (; 199 points). We calculated spatial velocities (, , and ; km s) along the galactic coordinates and the velocity dispersion (, , ; km s), the vertex longitude (), which have often differed significantly from zero like many of our analyses, i.e., (; 106 points) and (; 199 points). Moreover, we computed the solar motion, i.e., km s, and other solar elements (e.g., , , , and ). Finally, we estimated Oort's constants, i.e., km s kpc and ‐ km s kpc, both indicating that the rotational velocity was km s.

Oort Constants and Local Stellar Kinematics from GCNS

Oort constants and local kinematics are vital parameters with which to study the structure and dynamics of the Milky Way. When GCNS was published, it provided a clean sample of stars in the solar vicinity, which gives us an ideal tool with which to determine these parameters. Our aim was to calculate the reliable Oort constants with GCNS. We determined the Oort constants using the GCNS from Gaia EDR3 with d<100pc. The proper motions and radial velocities were fitted with a maximum likelihood model. The uncertainties were obtained with an MCMC method. The sample was carefully selected to obtain a reliable result. The result yields the Oort constants A=15.6±1.6kms−1kpc−1, B=−15.8±1.7kms−1kpc−1, C=−3.5±1.6kms−1kpc−1, and K=2.7±1.5kms−1kpc−1. The non-zero C and K imply that the local disc is in a non-asymmetric potential. With the Oort constants, we derived the local angular velocity Ω0≈A−B=31.4±2.3kms−1kpc−1. The solar motion (U⊙, V⊙, W⊙) was calculated as (10.1±0.1, 22.8±0.1, 7.8±0.1) kms−1.

Cosmic-Ray Convection–Diffusion Anisotropy

Under nonuniform convection, the distribution of diffusive particles can exhibit dipole and quadrupole anisotropy induced by the fluid inertial and shear force, respectively. These convection-related anisotropies, unlike the Compton–Getting effect, typically increase with the cosmic-ray (CR) energy, and are thus candidate contributors for the CR anisotropy. In consideration of the inertial effect, CR observational data can be used to set an upper limit on the average acceleration of the local interstellar medium in the equatorial plane to be on the order of 100 μm s−2. Using Oort constants, the quadrupole anisotropy above 200 TeV may be modeled with the shear effect arising from the Galactic differential rotation.

Gaussian process model for the local stellar velocity field from Gaia data release 2

ABSTRACT We model the local stellar velocity field using position and velocity measurements for 4M stars from the second data release of Gaia. We determine the components of the mean or bulk velocity in $\sim 27\, 000$ spatially defined bins. Our assumption is that these quantities constitute a Gaussian process where the correlation between the bulk velocity at different locations is described by a simple covariance function or kernel. We use a sparse Gaussian process algorithm based on inducing points to construct a non-parametric, smooth, and differentiable model for the underlying mean stellar velocity field. We estimate the Oort constants A, B, C, and K and find values in excellent agreement with previous results. Maps of the velocity field within $2\, {\rm kpc}$ of the Sun reveal complicated substructures, which provide clear evidence that the local disc is in a state of disequilibrium. We present the first three-dimensional map of the divergence of the stellar velocity field and identify regions of the disc that may be undergoing compression and rarefaction.

Kinematics and ellipsoidal motion of the mid to late M‐type stars

AbstractTruly, kinematics in the Solar neighborhood has provided important information both for the structure and for the evolution of the Galaxy since the early 20th century. The relationship between Oort constants and the ratio of the velocity dispersion are important quantities in stellar kinematics. In the present paper, we calculated the kinematical parameters and the Oort constants of various samples of late to intermediate M‐type stars. We calculated the velocity dispersion in units of km s−1 for the samples under study. The longitude of the vertex having negative values with our analysis; that is, the program I (538 stars), ; program II (100 stars), and program III (60 stars), . We calculate the Oort constants as km s−1 kpc−1 and km s−‐1 kpc−1, and the rotational velocity . A possible explanation for the overestimated values of the second Oort constants has been presented.

Local stellar kinematics and Oort constants from the LAMOST A-type stars

ABSTRACT We estimate the solar peculiar velocities and Oort constants using a sample of 5627 A-type stars with $d\lt 0.6\, \rm kpc$ and $|z|\lt 0.1\, \rm kpc$, selected from the LAMOST (Large Sky Area Multi-Object Fiber Spectroscopic Telescope) surveys. The radial and tangential velocities of these A-type stars are fitted by using a non-axisymmetric model. The best-fitting result yields the solar peculiar velocities $(U_\odot ,V_\odot ,W_\odot)=(11.69\pm 0.68, 10.16\pm 0.51, 7.67\pm 0.10)\, \rm km\, s^{-1}$ and Oort constants $A=16.31\pm 0.89\, \rm km\, s^{-1}\, kpc^{-1}$, $B=-11.99\pm 0.79\, \rm km\, s^{-1}\, kpc^{-1}$, $C=-3.10\pm 0.48\, \rm km\, s^{-1}\, kpc^{-1}$, and $K=-1.25\pm 1.04\, \rm km\, s^{-1}\, kpc^{-1}$. $|K+C|\gt 4\, \rm km\, s^{-1}\, kpc^{-1}$ means that there is a radial velocity gradient in the extended local disc, implying that the local disc is in a non-asymmetric potential. Using the derived Oort constants, we derive the local angular velocity $\Omega \, {\approx }\, A-B=28.30\pm 1.19\, \rm km\, s^{-1}\, kpc^{-1}$. By using A-type star sample of different volumes, we further try to evaluate the impacts of the ridge pattern in the R–Vϕ plane on constraining the solar motions and Oort constants. As the volume becomes larger towards the anticentre direction, the values of A and B become larger (implying a steeper slope of the local rotation curve) and the value of V⊙ becomes smaller probably caused by the ridge structure and its signal increasing with distance.

The Science of Fundamental Catalogs

This review paper discusses the science of astrometric catalogs, their current applications and future prospects for making progress in fundamental astronomy, astrophysics and gravitational physics. We discuss the concept of fundamental catalogs, their practical realizations, and future perspectives. Particular attention is paid to the astrophysical implementations of the catalogs such as the measurement of the Oort constants, the secular aberration and parallax, and asteroseismology. We also consider the use of the fundamental catalogs in gravitational physics for testing general theory of relativity and detection of ultra-long gravitational waves of cosmological origin. PACS numbers: 04.20.Cv, 04.30.−w, 95.10.−a, 95.10.Jk, 95.30.−k.

Kinematic modelling of clusters with Gaia: the death throes of the Hyades

ABSTRACT The precision of the Gaia data offers a unique opportunity to study the internal velocity field of star clusters. We develop and validate a forward-modelling method for the internal motions of stars in a cluster. The model allows an anisotropic velocity dispersion matrix and linear velocity gradient describing rotation and shear, combines radial velocities available for a subset of stars, and accounts for contamination from background sources via a mixture model. We apply the method to Gaia DR2 data of the Hyades cluster and its tidal tails, dividing and comparing the kinematics of stars within and beyond 10 pc, which is roughly the tidal radius of the cluster. While the velocity dispersion for the cluster is nearly isotropic, the velocity ellipsoid for the tails is clearly elongated with the major axis pointing towards the Galactic centre. We find positive and negative expansions at ≈2σ significance in Galactic azimuthal and vertical directions for the cluster but no rotation. The tidal tails are stretching in a direction tilted from the Galactic centre while equally contracting as the cluster in Galactic vertical direction. The tails have a shear (A) of 16.90 ± 0.92 $\mathrm{m}\, \mathrm{s}^{-1}\, \mathrm{pc}^{-1}$ and a vorticity (B) of −6.48 ± 1.15 $\mathrm{m}\, \mathrm{s}^{-1}\, \mathrm{pc}^{-1}$, values distinct from the local Oort constants. By solving the Jeans equations for flattened models of the Hyades, we show that the observed velocity dispersions are a factor of ≈2 greater than required for virial equilibrium due to tidal heating and disruption. From simple models of the mass loss, we estimate that the Hyades is close to final dissolution with only a further ≲30 Myr left.

Kinematics and Velocity Ellipsoid of Halo Red Giants

In the present paper, we aim to determine the kinematical properties, velocity ellipsoid, and Oort constants using a sample of halo red giants. The study is based mainly on the space and radial velocities of about 1583 red giant stars collected from the SEGUE-1 and SEGUE-2 surveys. We divided the sample into three subsamples, the inner halo, the outer halo and the stars near the galactic plane. The fitting of the radial velocity equation gives a the mean of Oort constants, A = 15.6 +- 1.6 km s-1 kpc-1 and B= -13.9 +- 1.8 km s-1 kpc-1, the angular velocity |A-B|= 29.5 +- 0.2 km s-1 kpc-1 implying a rotational velocity of 221.25 +- 26.66 km s-1 if we take the distance to the Galactic center as 7.5 kpc.

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.

Galactic Rotation and the Oort Constants in the Solar Vicinity

Abstract Gaia DR2 data are used to calculate the Oort constants and derive the Galactic rotational properties in this work. We choose the solar vicinity stars with a “clean” sample within 500 pc. The Oort constants are then fitted through the relation between the proper motions as a function of Galactic longitude l. A maximum likelihood method is adopted to obtain the Oort constants and the uncertainties are produced by a Markov Chain Monte Carlo technique with the sample. Our results for the Oort constants are A = 15.1 ± 0.1 km s−1 kpc−1, B = −13.4 ± 0.1 km s−1 kpc−1, C = −2.7 ± 0.1 km s−1 kpc−1, and K = −1.7 ± 0.2 km s−1 kpc−1 respectively. The nonzero values of C and K represent a nonaxisymmetric model for the Galaxy. According to our results, the angular velocity and the circular velocity decreases in solar vicinity. The local radial velocity also decreases along the radial direction due to C + K being negative.

The Lives of Stars: Insights from the TGAS–RAVE–LAMOST Data Set

Abstract In this paper, we investigate how the chemical and kinematic properties of stars vary as a function of age. Using data from a variety of photometric, astrometric, and spectroscopic surveys, we calculate the ages, phase space information, and orbits for ∼125,000 stars covering a wide range of stellar parameters. We find indications that the inner regions of the disk reached high levels of enrichment early, while the outer regions were more substantially enriched in intermediate and recent epochs. We consider these enrichment histories through comparison of the ages of stars, their metallicities, and kinematic properties, such as their angular momentum in the solar neighborhood (which is a proxy for orbital radius). We calculate rates at which the velocity dispersions evolve, investigate the Oort constants for populations of different ages (finding a slightly negative ∂V C/∂R and ∂V R /∂R for all ages, which is most negative for the oldest stars), as well as examine the behavior of the deviation angle of the velocity vertex as a function of age (which we find to fall from ∼15° for the 2 Gyr old population to ∼6° at around 6.5 Gyr of age, after which it remains unchanged). We find evidence for stellar churning, and find that the churned stars have a slightly younger age distribution than the rest of the data.

Kinematics of Stars from the TGAS (Gaia DR1) Catalogue

Based on the stellar proper motions of the TGAS (Gaia DR1) catalogue, we have analyzed the velocity field of main-sequence stars and red giants from the TGAS catalogue with heliocentric distances up to 1.5 kpc. We have obtained four variants of kinematic parameters corresponding to different methods of calculating the distances from the parallaxes of stars measured with large relative errors. We have established that within the Ogorodnikov–Milne model changing the variant of distances affects significantly only the solar velocity components relative to the chosen centroid of stars, provided that the solution is obtained in narrow ranges of distances (0.1 kpc). The estimates of all the remaining kinematic parameters change little. This allows the Oort coefficients and related Galactic rotation parameters as well as all the remaining Ogorodnikov–Milne model parameters (except for the solar terms) to be reliably estimated irrespective of the parallax measurement accuracy. The main results obtained from main-sequence stars in the range of distances from 0.1 to 1.5 kpc are: A = 16.29 ± 0.06 km s−1 kpc−1, B = −11.90 ± 0.05 km s−1 kpc−1, C = −2.99 ± 0.06 km s−1 kpc−1, K = −4.04 ± 0.16 km s−1 kpc−1, and the Galactic rotation period P = 217.41 ± 0.60 Myr. The analogous results obtained from red giants in the range from 0.2 to 1.6 kpc are: the Oort constants A = 13.32 ± 0.09 km s−1 kpc−1, B = −12.71 ± 0.06 km s−1 kpc−1, C = −2.04 ± 0.08 km s−1 kpc−1, K = −2.72 ± 0.19 km s−1 kpc−1, and the Galactic rotation period P = 236.03 ± 0.98 Myr. The Galactic rotation velocity gradient along the radius vector (the slope of the Galactic rotation curve) is −4.32 ± 0.08 km s−1 kpc−1 for main-sequence stars and −0.61 ± 0.11 km s−1 kpc−1 for red giants. This suggests that the Galactic rotation velocity determined from main-sequence stars decreases with increasing distance from the Galactic center faster than it does for red giants.

Galactic Kinematics Derived From Data in the RAVE5, UCAC4, PPMXL, and Gaia TGAS Catalogs

The spatial velocities of the stars with high-precision positions, proper motions and parallaxes from the Gaia TGAS catalog and line-of-sight velocities from the RAVE5 catalog are considered. From the sample of 92395 stars with the age estimates we have obtained the following kinematic parameters: (U,V,W)=(9.42,20.34,7.21)+/-0.12,0.10,0.09) km/s, \Omega=26.29+/-0.39 km/s/kpc and \Omega'=-3.89+/-0.08 km/s/kpc^2, where V0=210+/-6 km/s (for adopted R0=8.0+/-0.2 kpc), and the Oort constants A=15.57+/-0.31 km/s/kpc and B=-10.72+/-0.50 km/s/kpc. It is shown that the parameters \Omega and \Omega' are stable to the star age. A comparative analysis of the Bottlinger model parameters obtained separately from the RAVE5 catalog line-of-sight velocities and the Gaia TGAS, UCAC4 and PPMXL catalogs proper motion has been made. It is shown that these parameters are in good agreement with each other when derived from the proper motions of both the terrestrial catalogs and catalog Gaia TGAS. At the same time, it was established that the values of the Bottlinger model parameters obtained from the line-of-sight velocities can differ from the corresponding parameters obtained from the proper motions. The reduction of the line-of-sight velocities from the RAVE5 catalog is proposed for eliminating these differences.

Kinematics of our Galaxy from the PMA and TGAS catalogues

AbstractWe derive and compare kinematic parameters of the Galaxy using the PMA andGaiaTGAS data. Two methods are used in calculations: evaluation of the Ogorodnikov-Milne model (OMM) parameters by the least square method (LSM) and a decomposition on a set of vector spherical harmonics (VSH). We trace dependencies on the distance of the derived parameters including the Oort constants A and B and the rotational velocity of the GalaxyVrotat the Solar distance for the common sample of stars of mixed spectral composition of the PMA and TGAS catalogues. The distances were obtained from the TGAS parallaxes or from reduced proper motions for fainter stars.The A, B andVrotparameters derived from proper motions of both catalogues used show identical behaviour but the values are systematically shifted by about 0.5 mas/yr.The Oort B parameter derived from the PMA sample of red giants shows gradual decrease with increasing the distance while the Oort A has a minimum at about 2 kpc and then gradually increases.As for models chosen for calculations, first, we confirm conclusions of other authors about the existence of extra-model harmonics in the stellar velocity field. Secondly, not all parameters of the OMM are statistically significant, and the set of parameters depends on the stellar sample used.

Galactic rotation in Gaia DR1

Abstract The spatial variations of the velocity field of local stars provide direct evidence of Galactic differential rotation. The local divergence, shear and vorticity of the velocity field – the traditional Oort constants – can be measured based purely on astrometric measurements and in particular depend linearly on proper motion and parallax. I use data for 304 267 main-sequence stars from the Gaia DR1 Tycho-Gaia Astrometric Solution to perform a local, precise measurement of the Oort constants at a typical heliocentric distance of 230 pc. The pattern of proper motions for these stars clearly displays the expected effects from differential rotation. I measure the Oort constants to be: A = 15.3 ± 0.4 km s−1 kpc−1, B = −11.9 ± 0.4 km s−1 kpc−1, C = −3.2 ± 0.4 km s−1 kpc−1 and K = −3.3 ± 0.6 km s−1 kpc−1, with no colour trend over a wide range of stellar populations. These first confident measurements of C and K clearly demonstrate the importance of non-axisymmetry for the velocity field of local stars and they provide strong constraints on non-axisymmetric models of the Milky Way.

Kinematic analysis of solar-neighborhood stars based on RAVE4 data

We consider stars with radial velocities, proper motions, and distance estimates from the RAVE4 catalogue. Based on a sample of more than 145000 stars at distances $r<0.5$~kpc, we have found the following kinematic parameters: (U,V,W)_\odot=(9.12, 20.80, 7.66)\pm(0.10, 0.10, 0.08) km s^{-1}, \Omega_0=28.71\pm0.63 km s^{-1} kpc^{-1}, and \Omega'_0=-4.28\pm0.11 km s^{-1} kpc^{-2}. This gives the linear rotation velocity V_0=230\pm12 km s^{-1} (for the adopted R_0= 8.0\pm0.4 kpc) and the Oort constants A=17.12\pm0.45 km s^{-1} kpc^{-1} and B=-11.60\pm0.77 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 \sim 47000 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.

Kinematics of solar neighborhood stars and its dependence on age and metallicity**Supported by the National Natural Science Foundation of China.

We have constructed a catalog containing the best available astrometric, photometric, radial velocity and astrophysical data for mainly F-type and G-type stars (called the Astrometric Catalog associated with Astrophysical Data, ACAD). This contains 27 553 records and is used for the purpose of analyzing stellar kinematics in the solar neighborhood. Using the Lindblad-Oort model and compiled ACAD, we calculated the solar motion and Oort constants in different age-metallicity bins. The evolution of kinematical parameters with stellar age and metallicity was investigated directly. The results show that the component of the solar motion in the direction of Galactic rotation (denoted S2) linearly increases with age, which may be a consequence of the scattering processes, and its value for a dynamical cold disk was found to be 8.0 ± 1.2 km s−1. S2 also linearly increases with metallicity, which indicates that radial migration is correlated to the metallicity gradient. On the other hand, the rotational velocity of the Sun around the Galactic center has no clear correlation with ages or metallicities of stars used in the estimation.

Intercomparison of kinematics derived from catalogues UCAC4, PPMXL and XPM with vector spherical harmonics

We present the first application of the vector spherical harmonics technique to the proper motions of the catalogues UCAC4, XPM and PPMXL for stars in the 11 to 17 mag range. The results obtained from the all-sky and from the Northern and Southern Galactic hemispheres solutions are discussed. The all-sky solution gave the parameters of the standard Ogorodnikov–Milne model (coordinates of the solar motion apex, the Oort constants, the angular speed of the local Galactic rotation, the slope of the local rotational velocity curve) which practically coincide with the traditional least-squares estimates. Essentially new is the fact that the all-sky vector spherical harmonics analysis detected the same strong and reliable extra-model harmonics in all the catalogues under consideration. In addition, the Northern and Southern hemisphere solutions (again in all the catalogues) gave the sign changes of the same Ogorodnikov–Milne parameters. It was shown that both effects are generated by the retardation of the Galaxy rotation with the increase of the distance from the principal Galactic plane. Each catalogue shows small decrease of the gradient estimates towards the faint stars, but the mean values of the gradient derived from the catalogues are in good agreement, namely – UCAC4: 40.1 ± 0.2; PPMXL: 36.2 ± 0.4 and XPM: 37.7 ± 0.1 km s−1 kpc−1.