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

Zdeněk Kopal 《Astrophysics and Space Science》1988,144(1-2):557-586

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.  相似文献   

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

Zdeněk Kopal 《Astrophysics and Space Science》1980,71(1):65-74

The aim of the present paper has been to investigate the effects, on radial velocities of the components of close binary systems, of atmospheric gas motions caused by mutual irradiation of the two stars. Such motions can produce systematic differences between the observed radial velocity and that of the centre of mass of the respective star, varying with the phase, and give rise to spurious, deformations of the star's radial-velocity curve which have nothing to do with its axial rotation or orbital motion.Quantitative determination of this effect will be given for the simplified case in which the symmetry of gas motion can be described in terms of zonal harmonics of arbitrary degree, and a brief comparison made with the observed radial velocities of the B9-component of the eclipsing system U Cephei, which is known to move in a circular orbit, but exhibits a radial-velocity curve of marked skew-symmetry.  相似文献   

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

W. D. Cochran  A. P. Hatzes 《Astrophysics and Space Science》1996,241(1):43-60

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.  相似文献   

The effects of viscous friction on axial rotation of celestial bodies     

Zdeněk Kopal 《Astrophysics and Space Science》1972,16(1):3-51

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Fourier analysis of the light curves of eclipsing variables,V     

Zdeněk Kopal 《Astrophysics and Space Science》1975,38(1):191-241

The methods of analysis of the light changes of eclipsing variables in the frequency-domain, developed in our previous papers (Kopal 1975a, b, c, d) for an interpretation of mutual eclipses in systems consisting of spherical stars, have now been extended to analyse the light variations — between minima as well as within eclipses — ofclose binaries whose components are distorted by axial rotation and mutual tidal action. Following a brief introduction (Section 1) in which the need of this new approach will be expounded, in Sections 2 and 3 we shall deduce the theoretical changes of close eclipsing systems between minima (Section 2) as well as within eclipses (Section 3), which in Sections 4 and 5 will be analysed in the frequency-domain; and explicit formulae obtained which should enable us to separate the photometric proximity and eclipse effects directly from the observed data as they stand-without the need of any preliminary ‘rectification’. Section 6 will contain the explicit forms of the expressions for photometric perturbations in the frequency-domain, due to rotational and tidal distortion of both stars; and the concluding Section 7 will then be concerned with practical aspects of the application of these new methods to an analysis of the observed light changes of close eclipsing systems — in which the proximity and eclipse effects cannot be distinguished from each other by mere inspection.  相似文献   

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

V. P. Grinin  A. S. Mitskevich  L. V. Tambovtseva 《Astronomy Letters》2006,32(2):110-119

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.  相似文献   

Fourier analysis of the light curves of eclipsing variables,I     

Zdeněk Kopal 《Astrophysics and Space Science》1975,34(2):431-457

The aim of the present paper will be to pioneer a new approach to the analysis of the light changes of eclipsing binary systems in the frequency domain, and to point out its merits in comparison with a conventional treatment of the same problem in the time-domain which has been developed so far. Following an introductory section in which the broad features of our problem will be set forth, Section 2 will contain an outline, and critique, of the time-domain approach. Section 3 will give an explicit treatment of the light changes arising from total and annular eclipses in the frequency domain — a problem which we succeeded in solving in close algebraic form. Section 4 will extend this treatment to the case of partial eclipses; and in the concluding Section 5 the relative merits of our new results will be discussed in broader perspective. Sections 3 and 4 contain explicit results pertaining to mutual eclipses of spherical stars exhibiting uniformly bright discs. An extension of these results to the case of arbitrary limb-darkening, and taking account of mutual distortion of both components, will be given in subsequent communications.  相似文献   

The roche coordinates and their use in hydrodynamics or celestial mechanics     

Zdeněk Kopal 《Astrophysics and Space Science》1969,5(3):360-384

The aim of the present paper will be to introduce a new system of curvilinear coordinateshereafter referred to as Roche coordinates-in which spheres of constant radius are replaced by equipotential surfaces of a rotating gravitational dipole (which consists of two discrete points of finite mass, revolving around their common center of gravity); while the remaining coordinates are orthogonal to the equipotentials. It will be shown that the use of such coordinates offers a new method of approach to the solution of certain problems of particle dynamics (such as, for instance, the construction of certain types of trajectories in the restricted problem of three bodies); as well as of the hydrodynamics of gas streams in close binary systems, in which the equipotential surfaces of their components distorted by axial rotation and mutual tidal interaction constitute essential boundary conditions.Following a general outline of the problem in Section 1, the Roche coordinates associated with the equipotentials of a rotating gravitational dipole will be constructed in the plane case (Section 2), and their geometrical properties discussed. In Section 3, we shall transform the fundamental equations of hydrodynamics to their forms appropriate in the curvilinear Roche coordinates. The metric coefficients of this transformation will be formulated in a closed form in Section 4 in terms of the respective partial derivatives of the potential; while in Section 5 analytic expressions for the Roche coordinates will be given in the orbital plane of the dipole, which are exact as far as the distortion of the equipotential curves from circular form can be described by the second, third and, fourth harmonics.The concluding Section 6 will be devoted to a formulation of the equations of a mass-point in the restricted problem of three bodies in the Roche coordinates. Three special cases will be considered: (a) motion in the neighborhood of the equipotential curves; (b) motion in the direction normal to such curves; and (c) motion in the neighbourhood of the Lagrangian points. It will be shown that motion in one coordinate is possible only in limiting cases which will be enumerated; but twodimensional motions in which one velocity component is very much smaller than the other invite further study.A generalization of the plane Roche coordinates to three dimensions, with application to additional classes of problems, is being postponed for a subsequent paper.  相似文献   

Effects of rotation on internal structure of the stars     

Zdeněk Kopal 《Astrophysics and Space Science》1983,93(1):149-175

The aim of the present paper will be to establish the explicit form of the equations which govern the internal structure of stars rotating with constant angular velocity formulated in terms of Clairaut coordinates (cf. Kopal, 1980) in which the radial coordinate is replaced by the total potential, which for equilibrium configurations remains constant over distorted level surfaces. The introductory Section 1 contains an account of previous work on rotating stars, commencing with Milne (1923), von Zeipel (1924) and Chandrasekhar (1933), who all employed orthogonal coordinates for their analysis. In Section 2 we shall apply to this end the curvilinear Clairaut coordinates introduced already in our previous work (cf. Kopal, 1980, 1981); and although these are not orthogonal, this disadvantage is more than offset by the fact that, in their terms, the fundamental equation of our problem will assume the form of ordinary differential equations, subject to very simple boundary conditions. The explicit form of these equations — exact to terms of fourth order in surficial distortion caused by centrifugal force—will be obtained in Section 3; while in the concluding Section 4 these will be particularized (for the sake of comparison with work of previous investigators) to stars of initially polytropic structure. These will prove to be much simpler in Clairaut coordinates than they were in any previously used frame of reference. Lastly, in Appendix A we shall present the explicit forms, in Clairaut coordinates, of the differential operators which were needed to establish the results given in Sections 3–4; while Appendix B will summarize other auxiliary algebraic relations of which use was made to formulate our fourth-order theory developed in Section 3.  相似文献   

Fourier analysis of the light curves of eclipsing variables,XIV     

Zdeněk Kopal  Osman Demircan 《Astrophysics and Space Science》1978,55(1):241-261

The aim of the present paper will be to utilize the results obtained in the preceding papers of this series for the development of practical procedures for obtaining the elements of any eclipsing system from the observed photometric data by their analysis in the frequency-domain, for any type of eclipses, any proximity of the two components, and any degree of the law of limbdarkening of the eclipsed star.In Section 2, which follows a brief introduction to the subject, procedures will be developed which should permit us to perform such an analysis — by hand or automatic machine computation — for the case of mutual eclipses in binary systems the components of which can be regarded as spheres; and whose apparent discs are characterized by an arbitrary radially symmetrical distribution of surface brightness. In Section 3 we shall generalize these procedures to systems consisting of arbitrarily distorted stars.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.  相似文献   

On secular stability of tidally distorted stars of arbitrary structure     

Zdeněk Kopal 《Astrophysics and Space Science》1974,27(2):389-418

The aim of the present paper will be to develop a theory which should make it possible to investigate secular stability of close binary systems, consisting of tidally-distorted components of arbitrary internal structure, by a minimization of the potential energy of the system as a whole. In the second section which follows brief introductory remarks, appropriate expressions for the total potential energy of a close binary will be formulated. Section 3 will be concerned mainly with the nature of the tide-generating potential, and its effects on the shape of each star. In Section 4, the amplitudes of partial tides raised by this potential will be specified, for stars of arbitrary structure, correctly to terms of second order in superficial distortion; and in Section 5 we shall investigate the effects of interaction between rotation and tides to the same degree of approximation. The concluding Section 6 will then contain an explicit formulation of different constituents adding up to the total potential energy of the system, which can be used as a basis for its secular stability by the methods outlined already in our previous investigation (Kopal, 1973).  相似文献   

Radiative energy transfer in extended photospheres of the components of close binary systems     

Zdeněk Kopal 《Astrophysics and Space Science》1991,186(2):253-276

The aim of the present paper will be to set up, and solve, the equations governing transfer of radiation in semi-transparent envelopes of the stars; and, in order to do so, to employ a system of curvilinear (non-orthogonal) three-dimensional coordinates in which the radial coordinate has been identified with equipotential surfaces. Such coordinates are particularly suitable to a treatment of the problems arising in close binary systems, which render the outcome more than any other amenable to observable tests, but which has so far received but very scant attention.The introductory section of this paper will contain a statement of the problem; and its mathematical formulation in terms of Clairaut coordinates (cf. Kopal, 1980, 1989, Chapter V) will be outlined in Section 2; their methods in Section 3. Section 4 will then contain an application to the problem of distribution of surface brightness (limb-darkening) over the apparent discs of distorted components of close binary systems; while in Section 5 we shall do the same for radiative flux of distorted stars as a function of the phase (gravity darkening).The concluding Section 6 will then contain an outline of additional problems arising in this connection, to which we shall turn in successive parts of this series.  相似文献   

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

Kaylene Murdoch  J. B. Hearnshaw 《Astrophysics and Space Science》1991,186(2):169-177

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.  相似文献   

The Roche Coordinates in three dimensions and their application to problems of double-star astronomy     

Zdeněk Kopal 《Astrophysics and Space Science》1970,8(2):149-171

In a preceding paper (Kopal, 1969; in what follows referred to as Paper I) we introduced a new system of curvilinear coordinates-hereafter referred to as Roche Coordinates — in which spheres of constant radius in spherical polars have been replaced by surfaces of constant potential of a rotating gravitational dipole; while the angular coordinates are orthogonal to the equipotentials. In Paper I we established an explicit form of such a transformation, and related the Roche coordinates with polar coordinates (with which they coalesce in the immediate neighbourhood of each one of the two finite mass-points) in the plane case. The aim of the present investigation will be to generalize the definition of the Roche coordinates to three dimensions.The opening Section 1 of this paper will contain a general outline of the proposed three-dimensional transformation; and in Section 2 details of this transformation will be explicitly worked out correctly to quantities of first order in superficial distortion — an approximation which should prove adequate in regions surrounding the two finite masses; while in Section 3 we shall evaluate (to this degree of accuracy) the metric coefficients of the respective transformation, and its direction cosines, in both polar and curvilinear coordinates. Section 4 will then contain a formulation of the fundamental equations of hydrodynamics in terms of the three-dimensional Roche coordinates; and their advantages for a treatment of certain classes of dynamical problems encountered in doublestar astronomy will be illustrated in the concluding Section 5 by an investigation of the vibrational stability of the Roche model. We shall show that this model is capable of performing free radial oscillations which remain barotropic only if its equilibrium form is spherical (i.e., in the absence of any external mass in the neighbourhood); but not if it is distorted to any extent by rotation or tides.  相似文献   

Distribution of brightness over apparent discs of distorted stars     

Zdeněk Kopal  Filareti Zafiropoulos 《Astrophysics and Space Science》1983,91(2):299-317

The aim of the present paper will be to establish the explicit form of the equations of radiative transfer, in plane-parallel atmospheres surrounding the stars which are distorted by axial rotation or tides, in curvilinear coordinates which parallel the distorted surface; with particular attention to the circumstances under which the effects arising from limb- and gravity-darkening are multiplicative and admit of algebraic separation. In Section 2 (which follows a general outline of our problem) the fundamental equations of the radiativetransfer problem will be formulated for the ‘grey’ case; and rewritten in Section 3 in terms of non-orthogonal coordinates in which the potential over a level surface in hydrostatic equilibrium replaces the radial coordinate of spherical polars. In Section 4 we shall proceed to construct an explicit solution of the corresponding transfer problem in a plane-parallel approximation; and to prove that the effects of limb- and gravity-darkening remain factorizable only to terms which are linear in the cosines μ of the angle of foreshortening. Lastly, in Section 5 we shall list additional problems, arising in this connection, which still await appropriate treatment.  相似文献   

Fourier analysis of the light curves of eclipsing variables,XI     

Zdeněk Kopal 《Astrophysics and Space Science》1977,50(1):225-246

The aim of the present paper will be to introduce a new definition of the loss of light suffered by mutual eclipses of the components of close binary systems: namely, as across-correlation of two apertures representing the eclipsing and eclipsed discs.The advantages of such a strategy over the more conventional (geometrical) approach are (a) greater symmetry of the respective expressions; (b) greater affinity of expressions arising from distortion with those expressing the light changes due to eclipses of spherical stars; and (c) greater freedom in dealing with the effects of particular distribution of brightness over the disc of the star undergoing eclipse (generalized limb-darkening), as well as of possible semi-transparency of the eclipsing component (Wolf-Rayet stars!). In point of fact, none of these tasks could be handled with equal ease by any other technique; nor could the corresponding loss of light be so automated by any other approach.In Section 2 which follows brief introductory remarks we shall evaluate the loss of light arising from distribution of brightness within the aperture undergoing eclipse, and appropriate opacity of the occulting disc. In Section 3 we shall take advantage of these new forms of our results to deduce a number of new properties of the eclipse functions — both algebraic and differential — which have so far escaped attention and which are of considerable practical interest. Lastly, in Section 4 we shall generalize the same concepts to the modification of the light changes caused by the departures of the respective apertures from circular forms.It will be shown that all these phenomena can be most naturally described in terms of Hankel transforms of the products of two Bessel functions with orders depending on the physical characteristics (distribution of brightness; opacity) of the two components; while the geometry of the system (i.e., the fractional radiir _1,2 of the two stars; or the inclinationi of their orbit) enter only through their arguments. Such formulation of our problem should bring a theory of the light changes of eclipsing variables in much closer contact with the adjacent parts of physical optics.  相似文献   

Intermediate-mass black holes in globular clusters     

A. A. Kiselev  Yu. N. Gnedin  N. A. Shakht  E. A. Grosheva 《Astrophysical Bulletin》2011,66(4):436-441

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.  相似文献   

Photoelectric radial velocities, Paper XVI 625 ninth-magnitude K0 stars in the six southern Clube Selected Areas     

R. F. Griffin  A. P. Cornell 《Monthly notices of the Royal Astronomical Society》2006,371(3):1140-1158

Paper XIII of this series presented radial velocities for 406 stars in certain of the Clube Selected Areas, a set of areas systematically arranged in Galactic coordinates. We now complete the survey by providing the radial velocities, mostly obtained at the European Southern Observatory (ESO), of 625 stars in the six southernmost Areas. Each star has been measured at least twice; the mean velocities have standard errors typically of 0.2–0.3 km s⁻¹. Additional observations made from Haute-Provence of many of the stars that are observable from there have helped to identify, and in some instances to characterize, the ∼70 spectroscopic binaries discovered in this programme. The final results of the programme, complementing those given in table 3 of Paper XIII, are summarized in Table 12 , which presents the mean velocities and velocity dispersions in the six southern Areas. It is noted that the difference between Paper XIII and this one as regards the provenance of the radial velocities has led to a small difference in zero-points, which is discussed in Section 3 and needs to be taken into account in any analysis of the combined data.