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.     

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.     

Analysis of the three-dimensional stellar velocity field using vector spherical functions

We apply vector spherical functions to problems of stellar kinematics. Using these functions allows all of the systematic components in the stellar velocity field to be revealed without being attached to a specific physical model. Comparison of the theoretical decomposition coefficients of the equations for a particular kinematical model with observational data can provide precise information about whether the model is compatible with the observations and can reveal systematic components that are not described by this model. The formalism of vector spherical functions is particularly well suited for analyzing the present and future (e.g., GAIA) catalogs containing all three velocity vector components: the propermotions in both coordinates and the radial velocity. We show that there are systematic components in the proper motions of Hipparcos stars that cannot be interpreted in terms of the linear Ogorodnikov-Milne model. The same result is also confirmed by an analysis of the radial velocities for these stars.     

Application of vector spherical harmonics for kinematic analysis of stars from zonal catalogues

We solve the problem on a kinematic analysis of the three-dimensional velocity field of stars from zonal catalogues, i.e., catalogues in which the stars are presented at all right ascensions in some declination zones. We have constructed a system of vector spherical harmonics with the properties of completeness and orthogonality for a chosen declination zone. We suggest a method that allows the Ogorodnikov-Milne model parameters in the Galactic coordinate system to be estimated by analyzing the proper motions and radial velocities of stars in the equatorial coordinate system. The vector spherical harmonics are shown to have the following advantages over the standard approach based on a direct leastsquares estimation of the parameters for a specific model. First, in contrast to the standard approach, the new method can reveal all systematic components of the velocity field irrespective of a particular model. Second, it allows one to get rid of the correlation between the sought-for parameters, which presents a serious problem for the conventional method in the case of zonal catalogues. Third, the method of vector spherical harmonics allows the kinematic parameters to be estimated at least by two techniques. Comparison of these two solutions makes it possible to test the standard kinematic model for compatibility with the observational data. The developed method has been tested on the basis of numerical experiments and applied for a kinematic analysis of the proper motions of Tycho-2 stars in the southern hemisphere for which the parallaxes can be estimated using data from the Tycho-2 Spectral Type Catalogue.     

Information from the Kinematics of F and G Stars in the Solar Neighborhood

We have calculated the orbital parameters for 90 stars in Chen et al. and updated the kinematic data for stars in Edvardsson et al. by using the accurate Hipparcos parallaxes and proper motions, and recalculated the \\\\\\\\\\\\-element abundances in Edvardsson et al. in a way consistent with Chen et al. The two sets of data are combined in a study of stellar populations and characteristics of F & G stars in the solar neighborhood. We confirm the result of Chen et al. that a distinguishable group of stars may belong to the thick disk rather than the thin disk. The ages for the stars are determined using the theoretical isochrones of VandenBerg et al. The age-metallicity relation is investigated for different subgroups according to distance from the sun and galactic orbital parameters. It is found that a mixing of stars with different orbital parameters significantly affect the age-metallicity relation for the disk. Stars with orbits confined to the solar circle all have metallicities [Fe/H] > -0.3 irresp     

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.     

Investigation of the Galactic bar based on photometry and stellar proper motions

A new method for selecting stars in the Galactic bar based on 2MASS infrared photometry in combination with stellar proper motions from the Kharkiv XPM catalogue has been implemented. In accordance with this method, red clump and red giant branch stars are preselected on the color-magnitude diagram and their photometric distances are calculated. Since the stellar proper motions are indicators of a larger velocity dispersion toward the bar and the spiral arms compared to the stars with circular orbits, applying the constraints on the proper motions of the preselected stars that take into account the Galactic rotation has allowed the background stars to be eliminated. Based on a joint analysis of the velocities of the selected stars and their distribution on the Galactic plane, we have confidently identified the segment of the Galactic bar nearest to the Sun with an orientation of 20°–25° with respect to the Galactic center-Sun direction and a semimajor axis of no more than 3 kpc.     

Formation of stellar associations

The Rayleigh-Taylor instability forms massive complexes. When 10²¹ atoms cm^–2 are gathered, X-rays which heat the gas and UV-rays which ionize carbon are absorbed. A layer should appear with temperatures as low as 6 K and density to 4×10³ cm^–3. Finally the layer is fragmented into stars whose masses may even be less than one solar mass. The temperature of the layer should increase with time because part of free carbon is gradually absorbed by dust. Therefore more massive stars should appear after less massive stars. The stars which are formed kept near the layer by its gravitation. When their total mass becomes comparable with the mass of the layer, they should fall to the galactic plane in agreement with observed proper motions of several studied stellar systems.     

Gravitational loss-cone instability in stellar systems with retrograde orbit precession

We study spherical and disc clusters in a near-Keplerian potential of galactic centres or massive black holes. In such a potential orbit precession is commonly retrograde, that is, the direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly-radial orbits. We show that if there is a loss-cone at low angular momentum (e.g. due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics   l ≥ 3  . If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independent of azimuthal number m . The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum.
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems.     

Dynamical study of wide pairs of stars based on data from the WDS catalog

Using the method of apparent motion parameters, we have studied the relative motion of the components in 561 pairs of wide (ρ > 2″) and relatively nearby (Hipparcos parallaxes > 0.01″) visual double stars based on data from the WDS catalog. The minimum masses of the double stars have been calculated at given parallaxes. We have identified 358 optical pairs. For 11 stellar pairs, we have found the minimum mass to exceed the estimate corresponding to their spectral types and luminosities. This excess is 5–7 M _⊙ for two stars, ADS 7446 and 9701.     

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?10²²Mx) and smaller elements ranging down to flux fibres (? 10¹⁸Mx). Some implications of similar features in other stars are discussed.     

Determining the orientation parameters of the ICRS/UCAC2 system using the Kharkov catalog of absolute stellar proper motions

The absolute proper motions of about 275 million stars from the Kharkov XPM catalog have been obtained by comparing their positions in the 2MASS and USNO-A2.0 catalogs with an epoch difference of about 45 yr for northern-hemisphere stars and about 17 yr for southern-hemisphere stars. The zero point of the system of absolute proper motions has been determined using 1.45 million galaxies. The equatorial components of the residual rotation vector of the ICRS/UCAC2 coordinate system relative to the system of extragalactic sources have been determined by comparing the XPM and UCAC2 stellar proper motions: ω _x,y,z = (−0.06, 0.17, −0.84) ± (0.15, 0.14, 0.14) mas yr⁻¹. These parameters have been calculated using about 1 million faintest UCAC2 stars with magnitudes R _UCAC2 > 16 ^m and J > 14 ^m . 7, for which the color and magnitude equation effects are negligible.     

Kinematics of the young stellar objects associated with the cometary globules in the Gum Nebula

An analysis of the proper motion measurements of the young stellar objects (YSOs) associated with the cometary globules (CGs) in the Gum Nebula is presented. While earlier studies based on the radial-velocity measurements of the CGs suggested expansion of the system of the CGs, the observed proper motion of the YSOs shows no evidence for expansion. In particular, the kinematics of two YSOs embedded in CGs are inconsistent with the supernova explosion of the companion of ζ Pup, about 1.5 Myr ago being the cause of the expansion of the system of the CGs. YSOs associated with the CGs share the average proper motion of the member stars of the Vela OB2 association. A few YSOs that have relatively large proper motions are found to show relatively low infrared excesses.     

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.     

Kiev photographic catalogues of stellar proper motions: Compilation and application

The works of the Goloseevo Observatory (Kiev, U.S.S.R.) on the compilation of catalogues of absolute proper motions measured with respect to faint galaxies are discussed. Using these catalogues, some astrometric and stellar characteristics have been obtained. Particular attention is paid to the problem of improving the accuracy of stellar position and proper motion determinations. The optimum procedure for compiling the consolidated catalogue intended for the improvement of fundamental reference frame, kinematic characteristics of stars as well as for the solution of applied problems is developed.     

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)     

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.     

Astrophysical supplements to the ASCC‐2.5. II. Membership probabilities in 520 Galactic open cluster sky areas

We present a catalogue (CSOCA) of stars residing in 520 Galactic open cluster sky areas which is the result of the kinematic (proper motion) and photometric member selection of stars listed in the homogeneous All‐sky Compiled Catalogue of 2.5Million Stars (ASCC‐2.5).We describe the structure and contents of the catalogue, the selection procedure applied, and the proper motion and photometric membership constraints adopted. In every cluster area the CSOCA contains the complete list of the ASCC‐2.5 stars regardless of their membership probability. For every star the CSOCA includes accurate J2000 equatorial coordinates, proper motions in the Hipparcos system, BV photometric data in the Johnson system, proper motion and photometric membership probabilities, as well as angular distances from the cluster centers for about 166 000 ASCC‐2.5 stars. If available, trigonometric parallaxes, spectral types, multiplicity and variability flags from the ASCC‐2.5, and radial velocities with their errors from the Catalogue of Radial Velocities of Galactic Stars with high precision Astrometric Data (CRVAD) are also given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On one classical problem in the radial orbit instability theory

Antonov’s classical problem of stability of a collisionless sphere with a purely radial motion of stars is considered as a limit of the problem in which stars move in nearly radial orbits. We provide the proper limiting equations that take into account the singularity in the density distribution at the sphere center and give their solutions. We show that there is instability for even and odd spherical harmonics, with all unstable modes being not slow. The growth rates of aperiodic even modes increase indefinitely when approaching purely radial models. The physics of the radial orbit instability is discussed.     

Astrophysical supplements to the ASCC‐2.5: Ia. Radial velocities of ∼55000 stars and mean radial velocities of 516 Galactic open clusters and associations

We present the 2nd version of the Catalogue of Radial Velocities with Astrometric Data (CRVAD‐2). This is the result of the cross‐identification of stars from the All‐Sky Compiled Catalogue of 2.5 Million Stars (ASCC‐2.5) with the General Catalogue of Radial Velocities and with other recently published radial velocity lists and catalogues. The CRVAD‐2 includes accurate J2000 equatorial coordinates, proper motions and trigonometric parallaxes in the Hipparcos system, B, V photometry in the Johnson system, spectral types, radial velocities (RVs), multiplicity and variability flags for 54907 ASCC‐2.5 stars. We have used the CRVAD‐2 for a new determination of mean RVs of 363 open clusters and stellar associations considering their established members from proper motions and photometry in the ASCC‐2.5. For 330 clusters and associations we compiled previously published mean RVs from the literature, critically reviewed and partly revised them. The resulting Catalogue of Radial Velocities of Open Clusters and Associations (CRVOCA) contains about 460 open clusters and about 60 stellar associations in the Solar neighbourhood. These numbers still represent less than 30% of the total number of about 1820 objects currently known in the Galaxy. The mean RVs of young clusters are generally better known than those of older ones. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)