Distortion of the stellar velocity field parameters due to systematic variations of parallaxes over the celestial sphere

We study the effect of systematic variations in stellar parallaxes over the celestial sphere on the results of a kinematic analysis of stellar proper motions. Our approach is based on the representation of stellar parallaxes by scalar spherical harmonics and on the decomposition of stellar proper motions into a system of vector spherical harmonics. We derive theoretical relations that relate the coefficients of the decomposition of stellar proper motions into toroidal and spheroidal harmonics to the coefficients of the decomposition of stellar parallaxes into scalar spherical harmonics. We have established that the systematic variations of parallaxes over the celestial sphere distort all parameters of the linear Ogorodnikov-Milne model and can be responsible for the appearance of beyond-the-model harmonics. We have performed a kinematic analysis of the proper motions of blue-white and red giants based on Hipparcos data. The parallaxes of blue-white giants show a strong dependence on Galactic latitude (with predominant contraction along the Galactic equator). In contrast, the deviations of the parallaxes from the mean for red giants are localized only in two regions of the celestial sphere. For these samples, the effect of parallax variations over the celestial sphere on kinematic parameters has turned out to be comparable to their rms errors. The global solutions performed using both samples have revealed strong beyond-the-model kinematic effects described by second-order toroidal harmonics and third-order spheroidal harmonics. Using the solutions performed separately in the northern and southern Galactic hemispheres, we have established that not the systematic variations of parallaxes over the celestial sphere but the retardation of Galactic rotation with increasing distance of stars from the principal Galactic plane is mainly responsible for the appearance of these harmonics. Based on these samples of stars, we have estimated the magnitude of the vertical Galactic rotation velocity gradient to be 18.0±2.9 and 22.7±2.2 km s^?1 kpc^?1, respectively.     

Investigation of the kinematics and structure of the Galaxy in the vicinity of the North galactic pole

In the framework of the programme of studying the meridional section of the Galaxy (MEGA) the absolute proper motions of more than 11000 stars with respect to 3000 galaxies and their stellar magnitudes in the B, V Johnson system are determined in two sky regions near the North Galactic Pole (NGP) by means of Tautenburg Schmidt plates. The limiting and completing apparent stellar magnitudes are B = 20.4 and 18.3 mag, the overall and the investigated sky areas are 16.4 and 14.6 square degrees, respectively. Distances have been determined using the stellar magnitudes, colours, proper motions and reduced proper motions. Stellar kinematics, eccentricities of Galactic orbits, spatial distribution and changes of these characteristics with Z-distance from the Galactic plane are obtained up to 15 kpc. Four subsystems distinguished in the NGP direction, respectively with semithicknesses of 0.25, 0.38, 0.67, 1.48 kpc and density ellipsoid axial ratios of 0.09, 0.20, 0.28, 0.49 show mean velocities in the Galactic rotation direction relative to the LSR of 5.6 ± 0.6, − 11.0 ± 0.6, − 62.5 ± 1.2, − 181.6 ± 4.4 km/s, and ages of 0.1, 0.4, 0.9, 1 of the Galaxy age.     

Red giant clump in the Tycho-2 catalogue

The Tycho-2 proper motions and Tycho-2 and 2MASS photometry are used to select 97348 red giant clump (RGC) stars. The interstellar extinction and photometric distance are calculated for each of the stars. The selected stars are shown to form a selection-unbiased sample of RGC stars within about 350 pc of the Sun with the addition of more distant stars. The distribution of the selected stars in space and their motion are consistent with the assumption that the RGC contains Galactic disk stars with various ages and metallicities, including a significant fraction of stars younger than 1 Gyr with masses of more than 2M _⊙. These young stars show differences of their statistical characteristics from those of older RGC stars, including differences in the variations of their distribution density with distance from the Galactic plane and in the dispersion of their velocities found using radial velocities and proper motions. The Sun has been found to rise above the Galactic plane by 13 ± 1 pc. The distribution density of the stars under consideration in space is probably determined by the Local Spiral Arm and the distribution of absorbing matter in the plane of the Gould Belt.     

The red giant branch in the Tycho-2 catalogue

Based on multicolor photometry from the 2MASS and Tycho-2 catalogues, we have produced a sample of 38 368 branch red giants that has less than 1% of admixtures and is complete within 500 pc of the Sun. The sample includes 30 671 K giants, 7544Mgiants, 49 C giants, and 104 suspected supergiants or S stars. The photometric distances have been calculated for K, M, and C stars with an accuracy of 40%. Tycho-2 proper motions and PCRV radial velocities are used to analyze the stellar kinematics. The decrease in the stellar distribution density with distance from the Galactic equator approximated by the barometric law, contrary to the Besanconmodel of the Galaxy, and the kinematic parameters calculated using the Ogorodnikov-Milne model characterize the overwhelming majority of the selected K and M giants as disk stars with ages of more than 3 Gyr. A small number of K and M giants are extremely young or, conversely, thick-disk ones. The latter show a nonuniform distribution in the phase space of coordinates and velocities, arguing against isothermality and full relaxation of the disk and for the theory of dynamical streams or superclusters. The spatial distribution and kinematics of the selected C stars force us to consider them as asymptotic branch giants with masses of more than 2M _⊙ and ages of less than 2 Gyr probably associated with the Gould Belt. The offset of the Sun above the Galactic equator has been found from the distribution of stars to be 13 ± 2 pc, which coincides with the previously obtained value for the clump red giants.     

Predicted star counts and mean parallaxes down to the 23rd magnitude

Star counts and mean parallaxes as a function of B, V, R magnitudes down to 23 are presented. The data were computed by the use of two fundamental equations of stellar statistics. The assumed model considers the Galaxy as a symmetrical system with respect to its rotation axis and to its equatorial plane and as composed of the thin disk (main sequence and red giants), the thick disk and spheroid populations. Numbers of stars and mean parallaxes were derived in bins of galactic longitude and latitude of 30° and 10°, respectively. For the computation of the mean parallaxes depending on Galactic coordinates and magnitudes, series of products of Hermite and Legendre polynomials and of Fourier terms were used. The results of this paper may help in the planning of future survey missions and in the design of new telescopes. In addition, mean parallaxes can be used to derive corrections to absolute parallaxes and proper motions for any position in the sky.     

Photometric detection of high proper motions in dense stellar fields using difference image analysis

The difference image analysis (DIA) of the images obtained by the Optical Gravitational Lensing Experiment (OGLE-II) revealed a peculiar artefact in the sample of stars proposed as variable by Woźniak in one of the Galactic bulge fields: the occurrence of pairs of candidate variables showing anti-correlated light curves monotonic over a period of 3 yr. This effect can be understood, quantified and related to the stellar proper motions. DIA photometry supplemented with a simple model offers an effective and easy way to detect high proper motion stars in very dense stellar fields, where conventional astrometric searches are extremely inefficient.     

Investigation of the motions of fast stars based on observations with the Pulkovo normal astrograph

Astrometric CCD observations of 1123 stars with large proper motions (μ > 300 mas yr⁻¹) from the LSPM (I/298) catalog in the declination zone +30°–+70° have been carried out with the Pulkovo normal astrograph since 2006. The observational program includes mostly stars that previously have not entered into high-accuracy projects to determine the proper motions. Our studies are aimed at determining new proper motions of fast stars in the HCRF/UCAC3 system and searching for stars with invisible companions in the immediate Galactic neighborhoods of the Sun. Having analyzed about 10 000 CCD frames, we have obtained the equatorial coordinates of 414 program stars in the HCRF/UCAC3 system at an accuracy level of 10–50 mas and determined their new proper motions. To derive the proper motions, we have used the data from several star catalogs and surveys (M2000, CMC14, 2MASS, SDSS) as early epochs. The epoch differences range from 5 to 13 years (on average, about 10 years); the mean accuracy of the derived proper motions is 4–5 mas yr⁻¹. For 70 stars, we have revealed significant differences between the derived proper motions and those from the LSPM and I/306A catalogs (these proper motions characterize the mean motion of the photocenter in 50 years or more). Apart from systematic errors, these differences can result from the existence of invisible components of the program stars.     

Schmidt plate survey towards the Galactic centre. 2. Stellar statistics in the direction of the Sagittarius-Carina arm

A study of the structure and kinematics of the Galaxy from Tautenburg Schmidt plates taken towards the Galactic centre (l = 17.0°, b = +0.8°) is presented. Proper motions and B, V magnitudes were determined for about 36 500 stars up to the limiting magnitude V = 16^m.8 in a field of 8.95 square degrees. Proper motion accuracy of about 3 mas/year has been obtained for stars brighter than V = 15^m. The rms errors of stellar magnitudes and (B–V) colours is about 0.1 mag. The majority of field stars in the survey are main sequence stars and red giants of the disk. They belong to the Local or Sagittarius-Carina arms, or they are located between these spiral arms. Comparing the modelled and observed distributions of magnitudes and colours, we specified the interstellar extinction determined in the preceding study of open clusters in this field. The luminosity function towards the Galactic centre was determined for stars with absolute magnitudes from -4^m.35 to +9^m. Kinematical and spatial distribution parameters up to 4 kpc from the Sun were obtained as a function of galactocentric distance.     

Schmidt survey in the Galactic anticentre direction. 1. Investigation of open clusters

A study of four open clusters in the direction of the Galactic anticentre (l = 186°, b = +2°) is presented. In a field of 8.32 square degrees proper motions and B magnitudes for about 79 000 stars down to 19.5 were determined on Tautenburg Schmidt plates. For more than 15 500 of them U magnitudes down to 17.3 could be obtained. Additionally, OCA Schmidt plates were used to determine V, R magnitudes in a larger field of 24.45 square degrees for 271 000 stars down to V = 18.2. For stars brighter than V = 15.5 an accuracy of about 1.5 mas/yr has been estimated for proper motions. The rms errors of stellar magnitudes and colour indices are 0.09 – 0.12 mag. Several open clusters have been already known in this direction of the sky, e.g. NGC 2168 or M 35 (C 0605+243), NGC 2158 (C 0604+241) and IC 2157 (C 0601+240). Inspecting the plates and analysing the colour-magnitude diagrams and published data, we could identify an additional anonymous cluster C 0605+242 with a projection on the sky near the centre of M 35 but at a larger distance from the Sun. The cluster membership determination was carried out using information on spatial and proper motion distributions of stars in the field. The colour-magnitude diagrams were derived down to the limiting stellar magnitude. For each cluster the interstellar extinction A_v, the diameters of the core and corona, the ages and spatial velocity components (V,W) relative to the LSR in the Y,Z – Galactic directions were determined. The distances to the clusters of 960 pc, 2 600 pc, 2 520 pc and 3 700 pc were obtained for M 35, IC 2157, C 0605+242 and NGC 2158. They show the loci of the clusters in the Local and Perseus spiral arms and at external border of Perseus arm, respectively.     

Proper motions,absolute magnitudes and spatial distribution of Zirconium stars

The computational algorithm to determine the the proper motions of Zirconium stars on the basis of catalogues “Carte du Ciel” and on the recent photographic observations carried out with the 70cm Abastumani meniscus telescope is presented. It allowed to determine the proper motions of 288 stars in the region around α Per with a rms error of ± 0,004 arcsec/yr. Applying the method proper motions of 74 Zirconium stars and 146 control stars have been obtained. The error of proper motions obtained for the North Zone (δ > −2°) 109 AGK₃ control stars is ± 0.006 arcsec/yr. On the basis of proper motins absolute magnitudes were separately calculated for the MCLPZS and LASZS. For the MCLPZS the average absolute visual magnitude at maximum, corresponding to the mean period of P = 350 days, equals −3^ϕm.9. For the LASZS the mean absolute visual magnitude, corresponding to the apparent median ones equals −1^ϕm.9. Low luminosity (M_v = −1^ϕmϕ9) Zirconium stars escape rather far (at a distance of up to 2 kpc) to the South from the Galactic plane into the region l ∼ 240 – 260°, where its assumed to be a connection with the Large Magellanic Cloud (LMC) begins to appear. Low luminosity Zirconium stars are weakly correlated with position of the Galaxy spiral arms. The MCLPZS show a somewhat other distribution.     

自行与银河系研究的前沿

简述了精确测定相对自行的方法,特别介绍了在用2～3个历元的底片和CCD观测结果推导恒星自行的过程中如何消除光学视场畸变、星等差和色差的具体办法;并介绍了用星系把相对自行推算绝对自行的方法。还介绍了用自行资料研究银河系结构和演化的一些前沿课题,其中包括星团研究、与银河系兼并的矮星系的发现、暗物质的检测、外星行星的探测和银河系中心黑洞的质量估算等。最后评价了自行在研究银河系中的重要性,论述了我国研制4m光学/近红外望远镜的重要意义。     

Kinematics of Tycho-2 red giant clump stars

Based on the Ogorodnikov-Milne model, we analyze the proper motions of 95 633 red giant clump (RGC) stars from the Tycho-2 Catalogue. The following Oort constants have been found: A = 15.9 ± 0.2 km s^?1 kpc^?1 and B = ?12.0±0.2 km s^?1 kpc^?1. Using 3632 RGC stars with known proper motions, radial velocities, and photometric distances, we show that, apart from the star centroid velocity components relative to the Sun, only the model parameters that describe the stellar motions in the XY plane differ significantly from zero. We have studied the contraction (a negative K effect) of the system of RGC stars as a function of their heliocentric distance and elevation above the Galactic plane. For a sample of distant (500–1000 pc) RGC stars located near the Galactic plane (|z| < 200 pc) with an average distance of d = 0.7 kpc, the contraction velocity is shown to be Kd = ?3.5 ±0.9 km s^?1; a noticeable vertex deviation, l _xy = 9 _· ^o 1 ± 0 _· ^o 5, is also observed for them. For stars located well above the Galactic plane (|z| ≥200 pc), these effects are less pronounced, Kd = ?1.7 ± 0.5 km s^?1 and l _xy = 4 _· ^o 9 ± 0 _· ^o 6. Using RGC stars, we have found a rotation around the Galactic X axis directed toward the Galactic center with an angular velocity of ?2.5 ± 0.3 km s^?1 kpc^?1, which we associate with the warp of the Galactic stellar-gaseous disk.     

Restriction of motions in wide pairs in the Galactic field

The motions of the components of wide binary stars in the solar neighborhood in the regular Galactic gravitational field on time scales ～10¹⁰ yr have been studied numerically. The regions of restricted motions of the components in wide pairs have been found depending on the initial conditions: the magnitude of the relative velocity of the components, their mutual distance, and the inclination of the relative velocity vector to the Galactic plane. The size of the main part of the region of restricted motions is approximately equal to the tidal radius. Profound changes in the eccentricity of the binary orbit occur at inclinations close to 90°, which can lead to close approaches of the stars with a pericenter distance less than 1 AU. In the case of retrograde motions (the binary rotates in a direction opposite to the Galactic rotation), there is a region of restricted motions extending at least to 10 pc. Examples of the trajectories of relative motion of the stars and the change in osculating orbital elements are given for systems with restricted motions.     

Astrophysical supplements to the ASCC‐2.5. I. Radial velocity data

We present a catalogue of radial velocities of Galactic stars with high precision astrometric data CRVAD which is the result of the cross‐identification of star lists from the General Catalog of Average Radial Velocities (GCRV) and from the homogeneous All‐sky Compiled Catalogue of 2.5Million Stars (ASCC‐2.5). The CRVAD includes accurate J2000 equatorial coordinates, proper motions and trigonometric parallaxes in the Hipparcos system, Johnson's BV photometric data, spectral types, multiplicity and variability flags from the ASCC‐2.5, and radial velocities, stellar magnitudes and spectral types from the GCRV for 34553 ASCC‐2.5 stars. The CRVAD was used for the construction of a sample of standard stars with accurate astrometric, photometric and radial velocity data for the RAVE project. A second application of the CRVAD , the radial velocity determination for 292 open clusters (including 97 with previously unknown radial velocities), using their newly defined members from proper motions and photometry in the ASCC‐2.5, is briefly described. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Globular Clusters: Absolute Proper Motions and Galactic Orbits

We cross-match objects from several different astronomical catalogs to determine the absolute proper motions of stars within the 30-arcmin radius fields of 115 Milky-Way globular clusters with the accuracy of 1–2 mas yr^?1. The proper motions are based on positional data recovered from the USNO-B1, 2MASS, URAT1, ALLWISE, UCAC5, and Gaia DR1 surveys with up to ten positions spanning an epoch difference of up to about 65 years, and reduced to Gaia DR1 TGAS frame using UCAC5 as the reference catalog. Cluster members are photometrically identified by selecting horizontal- and red-giant branch stars on color–magnitude diagrams, and the mean absolute proper motions of the clusters with a typical formal error of about 0.4 mas yr^?1 are computed by averaging the proper motions of selected members. The inferred absolute proper motions of clusters are combined with available radial-velocity data and heliocentric distance estimates to compute the cluster orbits in terms of the Galactic potential models based on Miyamoto and Nagai disk, Hernquist spheroid, and modified isothermal dark-matter halo (axisymmetric model without a bar) and the same model + rotating Ferre’s bar (non-axisymmetric). Five distant clusters have higher-than-escape velocities, most likely due to large errors of computed transversal velocities, whereas the computed orbits of all other clusters remain bound to the Galaxy. Unlike previously published results, we find the bar to affect substantially the orbits of most of the clusters, even those at large Galactocentric distances, bringing appreciable chaotization, especially in the portions of the orbits close to the Galactic center, and stretching out the orbits of some of the thick-disk clusters.     

Programme of the Galactic meridian: Star counts and Galactic models 2. Distribution of absolute proper motions

A comparison of the observed distribution of absolute proper motions with a kinematical model of the Galaxy is presented. Proper motions with respect to galaxies were obtained for about 40 000 stars along the main Galactic meridian and in two fields near the North Galactic pole (programme MEGA). The Galaxy is considered as composed of the disk (main sequence and disk red giants), the thick disk and spheroid populations. For each subsystem, spatial velocity components and their dispersions were computed. The distribution of kinematical parameters were modelled for stars located in different directions of the Galaxy.     

Kinematic control of the inertiality of the system of Tycho-2 and UCAC2 stellar proper motions

Based on the Ogorodnikov-Milne model, we analyze the proper motions of Tycho-2 and UCAC2 stars. We have established that the model component that describes the rotation of all stars under consideration around the Galactic y axis differs significantly from zero at various magnitudes. We interpret this rotation found using the most distant stars as a residual rotation of the ICRS/Tycho-2 system relative to the inertial reference frame. For the most distant (d≈900 pc) Tycho-2 and UCAC2 stars, the mean rotation around the Galactic y axis has been found to be M ₁₃ ^? =?0.37±0.04 mas yr^?1. The proper motions of UCAC2 stars with magnitudes in the range 12–15^m are shown to be distorted appreciably by the magnitude equation in μ_α cos δ, which has the strongest effect for northern-sky stars with a coefficient of ?0.60±0.05 mas yr^?1 mag^?1. We have detected no significant effect of the magnitude equation in the proper motions of UCAC2 stars brighter than ≈11^m.     

Late-type members of young stellar kinematic groups – I. Single stars

This is the first paper of a series aimed at studying the properties of late-type members of young stellar kinematic groups. We concentrate our study on classical young moving groups such as the Local Association (Pleiades moving group,     , IC 2391 supercluster (35 Myr), Ursa Major group (Sirius supercluster, 300 Myr), and Hyades supercluster (600 Myr), as well as on recently identified groups such as the Castor moving group (200 Myr). In this paper we compile a preliminary list of single late-type possible members of some of these young stellar kinematic groups. Stars are selected from previously established members of stellar kinematic groups based on photometric and kinematic properties as well as from candidates based on other criteria such as their level of chromospheric activity, rotation rate and lithium abundance. Precise measurements of proper motions and parallaxes taken from the Hipparcos Catalogue, as well as from the Tycho-2 Catalogue, and published radial velocity measurements are used to calculate the Galactic space motions ( U , V , W ) and to apply Eggen's kinematic criteria in order to determine the membership of the selected stars to the different groups. Additional criteria using age-dating methods for late-type stars will be applied in forthcoming papers of this series. A further study of the list of stars compiled here could lead to a better understanding of the chromospheric activity and their age evolution, as well as of the star formation history in the solar neighbourhood. In addition, these stars are also potential search targets for direct imaging detection of substellar companions.     

Schmidt plate survey in the galactic centre direction. 1. Investigation of open clusters in the Sagittarius-Carina spiral arm

A study of four open clusters on Tautenburg Schmidt plates in the direction to the Galactic Centre (l = 17.0°, b = +0.8°) is presented. In a field of 8.95 square degrees proper motions and B, V magnitudes were determined for about 36 500 stars up to the limiting magnitudes B = 17^m.9, V = 16^m.8. For stars brighter than B = 16^m an accuracy of about 3 mas/year has been estimated for proper motions. The rms errors of stellar magnitudes and (B—V) colours is about 0.1 mag. There are two open clusters already known in this sky area: Trumpler 32 (C 1814-133) and NGC 6611 (C 1816-138). By the inspection of the plates two additional anonymous clusters were identified near the double star ADS 11285 or BD −14°5014 (C 1819-146) and near the star BD −14°5016 (C 1820-146). The cluster membership determination was carried out using information on spatial and proper motion distributions of stars in the field. The colour-magnitude diagrams up to the limiting stellar magnitude were constructed. For each cluster interstellar extinction A_V, diameters of the core and corona, ages and spatial velocity components (V, W) relative to the LSR in the Y, Z-galactic directions were derived. The distances to the clusters were obtained to 1720 pc, 2260 pc, 2130 pc and 2130 pc for Trumpler 32, NGC 6611, C 1819-146 and C 1820-146, respectively. All clusters are situated in the Sagittarius-Carina spiral arm. Their spatial location confirms the assumption that galactic spiral arms are close to logarithmic spirals with a characteristic angle of about 20 degrees.     

Kinematic analysis of stellar radial velocities by the spherical harmonics

A method for a kinematic analysis of stellar radial velocities using spherical harmonics is proposed. This approach does not depend on the specific kinematic model and allows both low-frequency and high-frequency kinematic radial velocity components to be analyzed. The possible systematic variations of distances with coordinates on the celestial sphere that, in turn, are modeled by a linear combination of spherical harmonics are taken into account. Theoretical relations showing how the coefficients of the decomposition of distances affect the coefficients of the decomposition of the radial velocities themselves have been derived. It is shown that the larger the mean distance to the sample of stars being analyzed, the greater the shift in the solar apex coordinates, while the shifts in the Oort parameter A are determined mainly by the ratio of the second zonal harmonic coefficient to the mean distance to the stars, i.e., by the degree of flattening of the spatial distribution of stars toward the Galactic plane. The distances to the stars for which radial velocity estimates are available in the CRVAD-2 catalog have been decomposed into spherical harmonics, and the existing variations of distances with coordinates are shown to exert no noticeable influence on both the solar motion components and the estimates of the Oort parameter A, because the stars from this catalog are comparatively close to the Sun (no farther than 500 pc). In addition, a kinematic component that has no explanation in terms of the three-dimensional Ogorodnikov-Milne model is shown to be detected in the stellar radial velocities, as in the case of stellar proper motions.