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.     

Kinematic control of the inertiality of ICRS catalogs

We perform a kinematic analysis of the Hipparcos and TRC proper motions of stars by using a linear Ogorodnikov-Milne model. All of the distant (r>0.2 kpc) stars of the Hipparcos catalog have been found to rotate around the Galactic y axis with an angular velocity of M ₁₃ ^? =?0.36±0.09 mas yr^?1. One of the causes of this rotation may be an uncertainty in the lunisolar precession constant adopted when constructing the ICRS. In this case, the correction to the IAU (1976) lunisolar precession constant in longitude is shown to be Δp₁=?3.26±0.10 mas yr^?1. Based on the TRC catalog, we have determined the mean Oort constants: A=14.9±1.0 and B=?10.8±0.3 km s^?1 kpc^?1. The component of the model that describes the rotation of all TRC stars around the Galactic y axis is nonzero for all magnitudes, M ₁₃ ^? =?0.86±0.11 mas yr^?1.     

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.     

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.     

Rotation curve of the Galactic outer disk derived from radial velocities and UCAC3 proper motions of carbon stars

The availability of astrometric data and radial velocities of carbon stars near the Galactic plane enables us to investigate the kinematics of the Milky Way,especially the rotation curve.The recently published Third U.S.Naval Observatory CCD Astrograph Catalog (UCAC3) provides the opportunity to test this problem using three-dimensional velocity in order to obtain more reliable rotation curves.We intend to study the Galactic rotation curve up to 15 kpc using the radial velocities and proper motions of carbon stars.The motivation for using UCAC3 is to provide high precision proper motions which have hardly been used in determining the rotation velocity of tracers.Seventy-four carbon stars and carbon-rich Mira variables toward the anti-center direction (90°＜(e)＜ 270°,|b| ＜ 6°) are picked up from the literature then matched with UCAC3 carbon star candidates to obtain their proper motions.A rigorous geometrical method is employed to compute the rotation velocity of each object.Taking carbon stars as tracers,we find a fiat rotation curve of 210 ± 12kms-1assuming/to = 8.0 kpc for the gaiactocentric distance and V0 = 220 km s-1 for the rotation velocity of the Sun.Due to the uncertainties of distances,the rotation velocities are more dispersed if tangential velocities enter the calculation,compared to those derived from radial velocities only.However,the whole rotation curve shows coherence with previous results.Increasing observation and study of carbon stars would be desirable in order to provide more homogeneous data for the kinematical study of the Galactic disk.     

The distribution of microlensed light-curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light-curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.     

Method of ignoring the systematic variations of stellar parallaxes over the celestial sphere in a kinematic analysis of stellar proper motions

A method for determining the velocity field parameters free from the distortions due to the systematic variations of stellar parallaxes over the celestial sphere is proposed. The method is based on the approximation of parallaxes as a function of coordinates on the sphere using spherical harmonics and can be applied in those cases where the solar motion cannot be eliminated from the stellar proper motions. Numerical experiments have shown that our method is able to obtain accurate coordinates of the solar apex and to calculate the kinematic parameters of the Ogorodnikov-Milne model to within three coefficients of the decomposition of parallaxes into first-order spherical harmonics. Examples of applying the method to the stellar proper motions of the Hipparcos catalogue, which admits checking the results using trigonometric parallaxes, are provided. Such a check has been found to yield a positive result only for nearby stars at heliocentric distances that do not exceed 400 pc and for which the parallaxes were determined with a relative error of at least 30%. An interesting feature of this method is the possibility to construct the shape of the figure which is formed by the deviations of the parallaxes from the sphere corresponding to the average parallaxes of the stars under consideration. It should be specially emphasized that all of this is done in the complete absence of information about the stellar parallaxes. The “solar terms” of the stellar proper motions that are formed by the products of the parallaxes by the solar motion components relative to the centroid of stars are the main source of information about the parallaxes here.     

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.     

The Kharkiv XC1 catalog of stellar positions and proper motions as compared to modern catalogs

The positions and proper motions of the stars from the XC1 catalog are compared with the data of other modern catalogs of stars and extragalactic objects. We demonstrate that the XC1 system is free from significant systematic errors. The external error in the proper motions of the stars fainter than 15 ^m is estimated at 3–5 mas/yr, depending on magnitude.     

Astrometric control of the inertiality of the Hipparcos catalog

Based on the most complete list of the results of an individual comparison of the proper motions for stars of various programs common to the Hipparcos catalog, each of which is an independent realization of the inertial reference frame with regard to stellar proper motions, we redetermined the vector ω of residual rotation of the ICRS system relative to the extragalactic reference frame. The equatorial components of this vector were found to be the following: ω_x=+0.04±0.15 mas yr^?1, ω_y=+0.18±0.12 mas yr^?1, and ω_z=?0.35±0.09 mas yr^?1.     

Kinematic characteristics of the stellar complex loop III

Rostov State Pedagogical Institute. Translated from Astrofizika, Vol. 33, No. 2, pp. 281–290, September–October, 1990.     

Improved proper motion determinations for 15 open clusters based on the UCAC4 catalog

The proper motions of 15 nearby(d 1 kpc) open clusters(OCs) were recalculated using data from the UCAC4 catalog. Only evolved or main sequence stars inside a certain radius from the center of the cluster were used. The results significantly differ from the ones presented by Dias et al.(2014). This could be explained by a different approach in which we take the field star contamination into account. The present work aims to emphasize the importance of applying photometric criteria for the calculation of OC proper motions.     

A numerical study of local stellar motions

The orbits of over 10000 stars are integrated in a steady-state model of the Galaxy for a time 6.0×10⁸ yr. Initially, the stars are placed randomly inside spheres of 500 pc and 50 pc radius and are given random velocities, such that the sample has a Maxwellian or a spheroidal velocity distribution. The spheres are placed at the Sun's distance from the galactic centre (10 kpc) and are given a circular velocity of 250 km s^?1. The mean velocities and dispersions of stars within 1 kpc of an ‘observer’ moving at the circular velocity are calculated as functions of time. The quantities show a strong time-dependence with oscillations of period 10⁸ yr. The oscillations are independent of the mass model and occur also in an inverse square force field. A vertex deviation of the velocity ellipsoid, an asymmetric drift and aK-effect occur as natural consequences of the oscillations. Attempts to apply the Oort method for density determinations in the galactic plane are also influenced by the oscillations. Spiral density waves appear to have a small effect on the motions of the test stars.     

Using the reduced proper motions of Tycho-2 stars with <Emphasis Type="Italic">B-V</Emphasis> from 0.75 to 1.25: Monte Carlo simulations

The stellar composition of the Tycho-2 Catalogue in the range B-V = 0_· ^m 75–1_· ^m 25 has been reproduced through Monte Carlo simulations. For young and old stars of the red giant clump (RGC), the red giant branch, subgiants, red dwarfs, and thick-disk giants, we have specified the distributions in coordinates, velocities, B-V, and M _V as a function of B-V and calculated their reduced proper motions, photometric distances from the (B-V)-M _V calibration, and photoastrometric distances from the reduced proper motion-M _V calibration. Our simulations have shown the following: (1) a sample of thin-disk giants within 500 pc with an admixture of less than 10% of other stars can be produced; (2) a sample of dwarfs within 100 pc almost without any admixture of other stars can be produced; (3) the Local Spiral Arm affects the RGC composition of any magnitude-limited catalog in favor of giants younger than 2 Gyr; (4) the samples produced using reduced proper motions can be used for kinematic studies, provided that the biases of the quantities being determined are simulated and taken into account; (5) the photometric distances correlate with the photoastrometric ones because of the correlation between the proper motion and magnitude; (6) the photometric distances are closer to the true ones for the red giant branch and red dwarfs as the categories of stars with a clear (B-V)-M _V relation, while the photoastrometric distances are closer to the true ones for the RGC, subgiants, and thick-disk giants; (7) the calculated distances differ systematically from the true ones, but they can be used to analyze the three-dimensional distribution of stars. Our simulations confirm the validity of our previous selection of RGC stars from Tycho-2.     

OB stars in the Tycho-2 and 2MASS catalogues

The Tycho-2 proper motions and five-band Tycho-2 and 2MASS photometry for approximately 2.5 million common stars have been used to select OB stars and to determine the extinction and photometric distance for each of them. We have selected 37 485 stars and calculated their reddenings based on their positions in the two-color V _T -H, J-Ks diagrams relative to the zero-age main sequence and the theoretical reddening line for B5 stars. Tests confirm that the selected stars belong to the spectral types O-B with a small admixture of later types. We calculate the extinction coefficient R and its variations with Galactic longitude based on the positions of the selected stars in the two-color B _T -V _T , V _T -Ks diagram. The interstellar extinction for each star is calculated as the product of the reddening found and the coefficient R. The extinction and its variations with Galactic longitude agree well with the extinction based on the model by Arenou et al. (1992). Calibration of the relation between the absolute magnitude and reduced proper motion V _T − + 5 + 5 log μ for Hipparcos stars has allowed us to calculate the absolute magnitudes and photometric distances for the selected stars. The distances found agree with those derived from the Hipparcos parallaxes within 500 pc. The distribution of the stars and the extinction variations with distance found show that the selected stars form an almost complete sample of stars with spectral types earlier than B5 within about 750 pc of the Sun. The sample includes many noticeably reddened stars in the first and second Galactic quadrants that are absent from the Hipparcos and Tycho Spectral Types Catalogues. This slightly changes the pattern of the distribution of OB stars compared to the classical pattern based on Hipparcos. Original Russian Text ? G.A. Goncharov, 2008, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2008, Vol. 34, No. 1, pp. 10–20.     

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.     

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.     

Observing gravitational radiation with QSO proper motions and the SKA

We discuss the ability of the SKA to observe QSO proper motions induced by long-wavelength gravitational radiation. We find that the SKA, configured for VLBI with multiple beams at high frequency (8 GHz), is sensitive to a dimensionless characteristic strain of roughly 10⁻¹³, comparable to (and with very different errors than) other methods in the 1/yr frequency band such as pulsar timing.     

Discussions of the internal motions and mass segregation of M67 on the basis of accurate proper motions

The radius and virial mass of the old open cluster M67 are presented. The internal motion and mass segregation of the cluster are also discussed on the basis of accurate stellar proper motions obtained combining three independent proper motion catalogues of the cluster. Increases of the mean proper motion and the intrinsic dispersion of member stars with radial distance from the cluster center might suggest that the stars are escaping from the cluster. The stars in both inner and outer regions appear to be in isotropic orbits. At last, it is found that both space and velocity mass segregations exist for the old open cluster due to the dynamical evolution.