An analysis of the radial velocity curves of close binary systems,I

The aim of the present paper will be to develop a theory of the radial-velocity changes of the components of close binary systems, with special attention to phenomena arising from finite dimensions of such components and their mutual distortion as well as irradiation. It is particularly stressed that the deformability of fluid stars and gas motions in their atmospheres can give rise to systematic differences between the observed radial velocities of such stars and those of their mass centres.In Section 2 (which follows a brief statement of the problem outlined in Section 1) we shall introduce the coordinate systems subsequently employed to treat various aspects of our problem: Section 3 will be concerned with an extraction of information from the radial-velocity component of absolute motions of the mass-centres of such stars; and in Section 4 we shall generalize the classical work by an investigation of radial velocities at any point of the apparent disks of distorted components, and their relation to the motion of their centres of mass. Section 5 will contain an evaluation of the effects of distortion, on radial velocity, averaged over the entire visible disk of the respective star at different phases; and in Section 6 we shall extend the same treatment to stars undergoing eclipses.An investigation of the effects, on the observed radial velocities, of atmospheric streaming caused by mutual irradiation of the two stars is being postponed for a subsequent communication.     

The effects of mutual irradiation on the observed radial velocity of the components of close binary systems

The aim of the present paper will be to investigate the effects, on the observed radial velocities of the components of close binary systems, of atmospheric motions caused by mutual irradiation of the two stars. Such motions can (and, in general, will) produce systematic differences between the observed radial velocity and that of the centre of mass of the respective star — differences varying with with the phase and thus giving rise to spurious deformations of the star's radial-velocity curves due to orbital motion. A failure to separate the two could (and in general, will) vitiate the physical elements deduced from these curves —such as the masses or absolute dimensions of the components and of the shape of their orbit; but in order to do so, an investigation of atmospheric motions invoked by irradiation becomes a necessary prerequisite.In the Introduction following this abstract, the problem at issue will be described in general terms, and phenomena outlined which should arise in this connection (together with the observations indicating their presence). In Section 2, general expressions for the radial velocity at any point of stellar surface arising from atmospheric motions will be formulated while Section 3 will isolate such velocities for components of close binary systems as are produced by mutual irradiation of their mates, in terms of hydrodynamical equations of radiative transfer describing the problem. In Sections 4 and 5, the effects of non-rotational motions on the observed radial velocities will be specified, and hydrodynamical equations formulated which specify atmospheric convection caused by irradiation of each component of a close binary by its mate. Linearized versions of such equations will be constructed in Section 6; while Section 7 contains an evaluation of the effects which such gas streams exert on the observed radial velocity of the stars.In the concluding Section 8 applications to practical cases are carried out. It will be shown that no reliable spectroscopic elements of close binary systems (including the masses and absolute dimensions of their components) can be obtained until the effects of atmospheric convection caused by mutual irradiation have been accounted for to permit us to convert the observed radial velocities (influenced as they are by the motion of as in which they originate) to those of the centre of mass of the respective stars.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Light scattering by moving dust grains in the immediate vicinity of young stars

We consider the problem of the distortion of the photospheric spectrum for a young star as its light is scattered in the inner accretion disk in the dust grain evaporation region. In T Tauri stars, this region is at a distance of the order of several stellar radii and is involved in the large-scale motions of matter with velocities of ～100 km s^?1 or higher. The light scattering in such a medium causes the frequency of the scattered radiation to be shifted due to the Doppler effect. We analyze the influence of this effect on the absorption line profiles in the spectra of T Tauri stars using classical results of the theory of radiative transfer. We consider two models of a scattering medium: (i) a homogeneous cylindrical surface and (ii) a cylindrical surface with an azimuth-dependent height (such conditions take place during the accretion of matter onto a star with an oblique magnetic dipole). We show that in the first case, the scattering of the photospheric radiation causes the absorption lines to broaden. If the motion of the circumstellar matter in the dust evaporation region is characterized by two velocity components, then the line profile of the scattered radiation is asymmetric, with the pattern of the asymmetry depending on the direction of the radial velocity. In the second case, the scattered radiation can cause periodic shifts of the absorption line centroid, which can be perceived by an observer as periodic radial-velocity variations in the star. We suggest that precisely this effect is responsible for the low-amplitude radial-velocity variations with periods close to the stellar rotation periods that have recently been found in some of the T Tauri stars.     

Rotation curve of our Galaxy forR>Ro

It is shown that the rise of rotation velocities in the outer regions of our Galaxy may be illusive, and is caused by an excessive simplification of the methods of processing the observational data. Taking into consideration the possibility of the radial motions of the gas, we demonstrate that the existing observational data do not conflict with the hypothesis of the flat rotation curve of our Galaxy. The bending of the outer regions of the galactic disk has no significant effect on the observed radial velocities of the gaseous complexes. It is also shown that the wavy form of the rotation curve may be evoked by the spiral density waves in the Galaxy.     

The halo-to-disk mass ratio in late-type galaxies

Dynamical modeling of stellar disks without bulges is used to derive the dependence of the central stellar radial-velocity dispersion on the dark-halo mass. A sample of late-type galaxies with known central stellar velocity dispersions and maximum gas rotation velocities was drawn from the LEDA database. The sample-averaged ratio of the halo mass within four radial disk scale lengths to the disk mass is 80%. Objects whose halo mass can be a factor of 2 or more larger than the disk mass were identified.     

Radial velocity searches for other planetary systems:Current status and future prospects

Measurement of variations in the radial velocities of stars due to the reflex orbital motion of the star around the planetary-system barycenter constitutes a powerful method of searching for substellar or planetary mass companions. After several years of patient data acquisition, radial-velocity searches for planetary systems around other stars are now beginning to bear fruit. In late 1995 and early 1996, three candidate systems were announced with Jovian-mass planets around solar-type stars. The current paradigm for low-mass star formation suggests that planetary systems should be able to form in the circumstellar disks surrounding young stellar objects. These newly discovered systems, and other discoveries which will soon follow them, will test critically our understanding of the processes of star- and planet-formation. We review the techniques used in these radial-velocity searches and their results to date. We then discuss planned improvements in the surveys, and the prospects for the next 20 years.     

High precision radial velocities of southern solar-type stars by cross-correlation

A system for obtaining high-precision radial velocities of solar-type stars by spectral cross-correlation has been established at the Mt John University Observatory. The use of a fibre-feed between the telescope and échelle spectrograph has enabled a stability such that we can achieve a precision of better than 50 m s^–1.A programme of radial-velocity observations of 29 southern solar-type stars—of which two are IAU radial velocity standard stars—is under way with the prime objective being a search for low-mass companions to the stars. Ten further IAU radial-velocity standard stars are also being monitored.     

Rigorous computation of proper motions and their effects on star positions

New rigorous formulas are given for the computation of the effects of proper motions and radial velocities on star positions, and for the transformation of proper motion components and radial velocities from one epoch to another. These expressions depend explicitly only on the values of the star's coordinates and distance, proper motion components and radial velocity, at the initial epoch.     

Particles in the nebular midplane: Collective effects and relative velocities

Abstract– In the absence of global turbulence, solid particles in the solar nebula tend to settle toward the midplane, forming a layer with enhanced solids/gas ratio. Shear relative to the surrounding pressure‐supported gas generates turbulence within the layer, inhibiting further settling and preventing gravitational instability. Turbulence and size‐dependent drift velocities cause collisions between particles. Relative velocities between small grains and meter‐sized bodies are typically about 50 m s^?1 for isolated particles; however, in a dense particle layer, collective effects alter the motion of the gas near the midplane. Here, we develop a numerical model for the coupled motions of gas and particles of arbitrary size, based on the assumption that turbulent viscosity transfers momentum on the scale of the Ekman length. The vertical distribution of particles is determined by a balance between settling and turbulent diffusion. Self‐consistent distributions of density, turbulent velocities, and radial fluxes of gas and particles of different sizes are determined. Collective effects generate turbulence that increases relative velocities between small particles, but reduce velocities between small grains and bodies of decimeter size or larger by bringing the layer’s motion closer to Keplerian. This effect may alleviate the “meter‐size barrier” to collisional growth of planetesimals.     

Nonstationarity of the atmosphere of <Emphasis Type="Italic">α</Emphasis> Cyg: II. Variability of the ion and H<Emphasis Type="Italic">β</Emphasis> line profiles

We report an efficient method for analyzing the radial-velocity and line-profile variability. We show that a detailed analysis of the variations of line profiles and velocity field in the stellar atmosphere requires the radial velocities to be measured separately for the blue and red halves of the absorption lines at different levels of their residual intensity. We applied this method to 120 CCD spectra taken in 1998–99 with the coude echelle spectrograph attached to the 2-m telescope of Shemakha Astronomical Observatory of National Academy of Sciences of Azerbaijan and analyzed the variations of the radial velocities and profiles of ion and Hβ lines in the spectrum of α Cyg. In the case of ion lines both halves of the absorption profile exhibit synchronous radial-velocity variations at all levels of line intensity. In the case of the Hβ line, which forms in the layers where stellar wind originates, the pattern of radial-velocity variations differs for the blue and red halves of the absorption profile. The variability pattern is the same at all levels in the red half of the profile, the blue half of the profile exhibits different variability patterns at different levels of residual line intensity. Identification and analysis of such variations allows us to study the nature of stellar-wind variability in the region of wind formation.The spectrum of α Cyg showed no line-profile or radial-velocity variations for six days in both halves of the absorption contour at all levels of line intensity. The star was in the quiescent phase.     

H2O maser flare in NGC 7538 S

We investigate the H₂O maser flare that occurred in the source NGC 7538 S during 1998–2005 in the radial-velocity range from ?57 to ?52 km s^?1. We have found a large number of emission features, suggesting that the medium where the flare occurred is highly fragmented. We have identified four spectral groups of emission features. All groups are most likely associated with the cluster of maser spots located in the center of an elongated structure and related to a massive rotating disk. The observed pattern of variations in the fluxes and radial velocities of the features can be explained by the presence of inhomogeneities in the medium, which can form elongated structures like filaments or chains. The mean extent of this structure is estimated to be 6–8 AU. Two cycles of maser activity have been observed, 1998–2002 and 2003–2005, which may be determined by the cyclic activity of the central object, a massive O-type protostar.     

银河系中球状星团的空间运动

球状星团是银河系中最古老的天体类型之一,其累积光度很大,是银晕中重要的示踪天体。已以发现的银河系球状星团有１４０多个,其中１２０个银心距Ｒ〈４０Ｋｐｃ的星团已被准确地测定了视向速度。根据结数据以及球状星团金属度的统计分析,可以把球状星团次系再进一步分成某些不同的族群。目前已经测定过绝对自行的球状星团只有３８个,尽管这些自行的精度比视向速度和距离的精度差很多,然而,由此可以得出三维的空间速度,在统计     

Kinematic parameters of young subsystems and the galactic rotation curve

We analyze the space velocities of blue supergiants, long-period Cepheids, and young open star clusters (OSCs), as well as the H I and H II radial-velocity fields by the maximum-likelihood method. The distance scales of the objects are matched both by comparing the first derivatives of the angular velocity Ω′ determined separately from radial velocities and proper motions and by the statistical-parallax method. The former method yields a short distance scale (for R₀=7.5 kpc, the assumed distances should be increased by 4%), whereas the latter method yields a long distance scale (for R₀=8.5 kpc, the assumed distances should be increased by 16%). We cannot choose between these two methods. Similarly, the distance scale of blue supergiants should be shortened by 9% and lengthened by 3%, respectively. The H II distance scale is matched with the distance scale of Cepheids and OSCs by comparing the derivatives Ω′ determined for H II from radial velocities and for Cepheids and OSCs from space velocities. As a result, the distances to H II regions should be increased by 5% in the short distance scale. We constructed the Galactic rotation curve in the Galactocentric distance range 2–14 kpc from the radial velocities of all objects with allowance for the difference between the residual-velocity distributions. The axial ratio of the Cepheid+OSC velocity ellipsoid is well described by the Lindblad relation, while σ_u≈σ_v for gas. The following rotation-curve parameters were obtained: Ω₀=(27.5±1.4) km s^?1 kpc^?1 and A=(17.1±0.5) km s^?1 kpc^?1 for the short distance scale (R₀=7.5 kpc); and Ω₀=(26.6±1.4) km s^?1 kpc^?1 and A=(15.4±0.5) km s^?1 kpc^?1 for the long distance scale (R₀=8.5 kpc). We propose a new method for determining the angular velocity Ω₀ from stellar radial velocities alone by using the Lindblad relation. Good agreement between the inferred Ω₀ and our calculations based on space velocities suggests that the Lindblad relation holds throughout the entire sample volume. Our analysis of the heliocentric velocities for samples of young objects reveals noticeable streaming motions (with a velocity lag of ～7 km s^?1 relative to the LSR), whereas a direct computation of the perturbation amplitudes in terms of the linear density-wave theory yields a small amplitude for the tangential perturbations.     

Proper motions in the field of the globular cluster NGC 6934

We measured relative proper motions with a typical accuracy of 1.0 milliarcsec/year (mas/a) for 2000 stars in a 1°4 × 1°4 field around the low-latitude globular cluster NGC 6934. Four plates taken with the Bonn double refractor, spanning an epoch difference of 62 years, were digitized completely. Within the tidal radius of the cluster, we find 106 stars with proper motion errors less than 5 mas/a. Membership probalilities are computed taking into account the individual proper motion errors and the radial distances to the cluster centre. We derive the mean relative proper motion of NGC 6934 using stars with high membership probabilities from radial velocities (Smith and Bell 1986) or from their location in the colour-magnitude diagram (Harris and Racine 1973). The relative proper motions of four Hipparcos stars in the field will be used to obtain the absolute proper motion of NGC 6934 once the extragalactically calibrated Hipparcos Output Catalogue is available.     

Intermediate-mass black holes in globular clusters

The mass of central bodies in a number of Milky-Way globular clusters is estimated based on the stellar radial-velocity dispersion data. It is assumed that stars located close to the center of the cluster (i.e., to the black hole) rotate about it, have masses on the order of the solar mass, and that the mass of the gravitating center is greater by a factor of 1000. The radial velocities of stars in the vicinity of cluster centers are analyzed for two hypothetical extreme cases: (1) ordered orbital motion of stars about the gravitating center and (2) chaotic orbital motions. The masses inferred for most of the clusters (10²–10⁴ M _⊙) correspond to intermediate-mass black holes. Another important result of this study consists in the determination of the quantity l, the characteristic scale length of the additional spatial dimension. Given the age and mass of the globular cluster NGC 6397 we estimate l to be between 0.02 and 0.14 mm.     

Radial velocities of the photospheric matter in a solar flare with matter ejection

We present results of a study of photospheric horizontal motions at the initial and main phases of the solar flare which happened on September 4, 1990, near the solar limb. The flare was accompanied by matter ejection. Spectra of the flare were obtained using the AZU-26 horizontal solar telescope at the MAO NAS (Terskol observatory). We found variations of the matter motion velocity’s value and direction at different stages of the photosphere during the flare development. The velocity changed in a range from −4 to 2 km/s. Comparisons of the obtained data with variations of the chromospheric radial velocities showed that the horizontal matter motions in the photosphere and chromosphere are mostly directed toward the observer but at particular time moments their direction changed. At two different knots, the time shift of the photospheric velocities is different. The highest velocities were observed at the main phase of the flare. At the initial phase of the flare, in the matter ejection region, we note a velocity increase compared with its preflare value and at the flare knots.     

The mass of the Andromeda galaxy

This paper argues that the Milky Way galaxy is probably the largest member of the Local Group. The evidence comes from estimates of the total mass of the Andromeda galaxy (M31) derived from the three-dimensional positions and radial velocities of its satellite galaxies, as well as the projected positions and radial velocities of its distant globular clusters and planetary nebulae. The available data set comprises 10 satellite galaxies, 17 distant globular clusters and nine halo planetary nebulae with radial velocities. We find that the halo of Andromeda has a mass of together with a scalelength of 90 kpc and a predominantly isotropic velocity distribution. For comparison, our earlier estimate for the Milky Way halo is Although the error bars are admittedly large, this suggests that the total mass of M31 is probably less than that of the Milky Way . We verify the robustness of our results to changes in the modelling assumptions and to errors caused by the small size and incompleteness of the data set.
Our surprising claim can be checked in several ways in the near future. The numbers of satellite galaxies, planetary nebulae and globular clusters with radial velocities can be increased by ground-based spectroscopy, while the proper motions of the companion galaxies and the unresolved cores of the globular clusters can be measured using the astrometric satellites Space Interferometry Mission ( SIM ) and Global Astrometric Interferometer for Astrophysics ( GAIA ). Using 100 globular clusters at projected radii 20 R 50 kpc with both radial velocities and proper motions, it will be possible to estimate the mass within 50 kpc to an accuracy of 20 per cent. Measuring the proper motions of the companion galaxies with SIM and GAIA will reduce the uncertainty in the total mass caused by the small size of the data set to 22 per cent.     

The search for wide pairs among nearby stars

Summary The detectability and confirmation of wide pairs among nearby stars is difficult due to uncertainties in their motions arising from errors in the observational data. Statistical tests for wide pairs reveal the increasing unevenness in space motions with decreasing age. They cannot so easily distinguish between the supposed finer structure of wide pairs and triples, and larger clumps commonly associated with small moving groups and star streams. Improved radial velocities and parallaxes which are now possible, will decrease the error in space motion to well under one km s⁻¹, and this will permit such distinction to be made.     

Spectroscopic binaries near the north Galactic pole paper 24: HD 106104, 109281, 109463 and 110743

The four stars treated in this paper have been under observation with photoelectric radial-velocity spectrometers for many years. They have proved to be binaries with periods of 30, 1828, 1514 and 822 days respectively; the orbits are of modest eccentricity apart from that of HD 110743 which is indistinguishable from a circle. The mass functions are small, and no companion has been observed for any of the stars. HD 110743, a K dwarf, is much the nearest of the four, and its orbit is of short enough period for the photocentric motion to have been recognized byHipparcos. An eleventh-magnitude star rather more than 1≈ away from HD 106104 is shown to be a genuine physical companion, with practically identical radial velocity, proper motion and distance modulus, although the projected separation is about 13,000 AU.     

Spectroscopic binaries near the North Galactic pole

Photoelectric radial-velocity measurements show that 6 Boötis undergoes small periodic variations of velocity. An orbit with a 2.6-year period and a semi-amplitude of little more than 1 km s^-1 is derived. The amplitude is smaller by a factor of two than that of any plausible orbit previously derived from radial velocities.