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1.
The aim of the present investigation will be to develop a theory of the light changes of the eclipsing systems in which one (or both) components oscillate(s) freely-radially or non-radially-in period(s) which may (though need not) be synchronized with that of their orbit. The light curves exhibited by systems with oscillating components will, in general, beasymmetric; and these oscillations may, in fact, be the cause of asymmetries observed in many eclipsing systems with evolved components (for which such oscillations-far from being anomalous-should be the rule rather than exception). The present paper will be concerned with an investigation of photometric phenomena arising from oscillations of theeclipsing components of close binary systems-cutting off (partly or wholly) the star (spherical or distorted) which undergoes eclipse.In Section 2, which follows a brief introductory survey aiming to place the entire subject in its historical perspective, a theory will be given of the light curves of close binary systems, in the frequency-domain, which are affected byradial oscillations of the eclipsed or eclipsing star; while Sections 3 and 4 will be devoted to a similar treatment ofnon-radial oscillation of the secondary (eclipsing) component distorted by equilibrium tides, or axial rotation with constant angular velocity. As will be shown, a frequency-domain approach will enable us to describe all these phenomena in algebraic terms; with auxiliary results required to this end relegated to three Appendices to the main text (in order not to render the latter too discursive and impede the main line of the argument).A similar treatment of photometric phenomena which may arise in such systems from oscillations of their components which undergo eclipse is being postponed for a subsequent communication.  相似文献   

2.
The aim of the present paper will be to generalize the methods for computation of the elements of eclipsing binary systems in the frequency-domain, summarized in our recent Paper I (Kopal, 1981), to the case ofclose systems, in which photometric proximity effects become conspicuous and must be taken into account before the methods previously outlined in Paper I become directly applicable.Following a brief introduction to the subject given in Section 1, Section 2 summarizes (and comments upon) the difficulties previously encountered in separation of the photometric proximity and eclipse effects. In Section 3 we develop an alternative new approach to the problem by modulation of the light curves throughout the entire orbital cycle, intended to filter out proximity effects from the observed light changes and isolate those due to eclipses; while in Section 4 we shall present a numerical application of the new method to an analysis of the observed light changes of the eclipsing system W Ursae Maioris.In Section 5 we shall present a quantitative investigation of the photometric effects of distortion on the light changes of close eclipsing systems within eclipses-the most complicated part of the whole problem-with numerical application to the system of U Sagittae carried out in the concluding Section 6.Appendices 1–3 contain numerical data which should facilitate application of the methods developed and illustrated in Sections 3–4; while Appendix 4 will be reserved for a mathematical proof of certain expansions used in Section 5, which would have been too discursive for the main text.  相似文献   

3.
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   

4.
The aim of the present paper has been to analyse the light changes of the close eclipsing system AK Herculis in the frequency domain. This analysis is based on Kopal's new theory recently developed for the study of light variations—between minima as well as within eclipses—of close eclipsing binaries whose components are distorted by axial rotation and mutual tidal action.A new method for the separation of the photometric proximity and eclipse effects directly from the observed data is also presented. In this method no rectification is needed. New elements taking into account the photometric perturbations are also given.  相似文献   

5.
The aim of the present paper will be to develop from the fundamental equations of hydrodynamics a theory of dynamical tides in close binary systems, the components of which are regarded to consist of heterogeneous viscous fluid, and to revolve around their common centre of gravity in eccentric orbits; moreover, the equatorial planes of their axial rotation and the orbital plane need not be co-planar, but all may be inclined to the invariable plane of the system of arbitrary amounts. The changes in the pressure or density invoked by time-dependent deformation will be regarded as adiabatic; but, in the equilibrium state, both the density and viscosity of the material of our components may be arbitrary functions of the radial distance.Following a brief exposition in Section 2 of the fundamental equations linearized to small oscillations — be these free or forced — in Section 3 we shall particularize them to describe spheroidal deformations; with due regard to all terms arising from viscosity. Section 4 will contain a specification of the boundary conditions to be imposed upon such oscillations; and in Section 5 we shall solve the problem of non-radial oscillations of self-gravitating inviscid configurations in terms of hypergeometric series. The remaining Sections 6–8 will be devoted to a discussion of the phenomena arising from viscosity: in particular, we shall solve in a closed form the problem of non-radial oscillations of incompressible viscous globes in the terms of Bessel functions. It will be shown that the effect of viscosity — like those of compressibility — tend to de-stabilize all non-radial oscillations of homogeneous configurations.At the other extreme, a similar treatment of a mass-point model — as well as of one exhibiting high but finite degree of central condensation — is being postponed for a subsequent communication.  相似文献   

6.
NSVS?07826147 and NSVS?04818255 were suspected as possible eclipsing sdB binary systems by Kelley and Shaw. In order to investigate the short period eclipsing sdB binaries, we have listed them as our observing targets and began to monitor it from March 2009. Till now, we have obtained four complete CCD light curves and 16 high precise times of light minimum of NSVS?07826147. All light curves show strong reflection and a very narrow eclipse, which implies that NSVS?07826147 should be a new short period eclipsing sdB binary. For the system NSVS?04818255, no eclipse character was found in the light curves according to our observations. However, we found that a star near NSVS?04818255 is a close binary system with a period of about 0.32498 days. Up to now, only seven short period eclipsing sdB binary systems have been found, including NSVS?07826147. With the new precise epochs obtained by us, the new period of this system is derived as 0.16177046(5) days, which can be used to predict the epochs of light minimum. Furthermore, the light curves of NSVS?07826147 are analyzed using the Wilson–Van Hamme code and the testing photometric solutions are presented and discussed.  相似文献   

7.
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   

8.
The aim of the present note is to point out that observations of eclipsing variables within minima do not, in general, allow a separation of the quadratic terms of limb-darkening from the first-order effects of the gravity-darkening of distorted components undergoing eclipse. Only a difference of the two can be deduced from the observations, but — especially in close binaries — the net effect will be dominated by gravity-darkening.  相似文献   

9.
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   

10.
Following a brief history of measurement of eclipsing binary mass ratios from light curves, we show that photometric mass ratios for overcontact and semi-detached binaries are reliable because the relative stellar radii, R/a, are accurately measured and not, as commonly claimed, because of information in the light variation outside eclipse. We explore the accuracy of photometric mass ratios by solving synthetic data of typical precisions for a semi-detached and an overcontact binary for orbital inclinations from 89∘ down into the partial eclipse range.  相似文献   

11.
The BVR photometric light curves of the eclipsing binary BD And were obtained in 2008 and 2009. We estimated the mass ratio of the system as 0.97 and the photometric solutions were derived. The results show that BD And is a detached binary system, whose components have a little temperature difference of about 40 K. By analyzing photometric available light minimum times, we also derived an update ephemeris and found for the first time a possible periodic oscillation with an amplitude of 0.011 days and a period of 9.6 years. The results indicate that the periodic oscillation could be caused by a third component physically attached to the eclipsing binary. After removing the light variations due to the eclipses and proximity effects, the light-curve distortions are further explained by the pulsation of the primary component with a dominant period of ∼1 day. In accordance with the position of the primary component on the Hertzsprung–Russell diagram and its pulsation period, the primary component of BD And could be an excellent γ Doradus candidate. It is rarely phenomenon that a component of the eclipsing binary system is a γ Doradus variable.  相似文献   

12.
The methods of analysis of the light changes of eclipsing variables in the frequency domain, developed in our previous papers (Kopal, 1975b, c) for total or annular eclipses of arbitrarily limbdarkened stars, have now been extended to the case of partial eclipses of occultation as well as transit type. In Section 2 which follows brief introductory remarks the even Fourier sine coefficients are formulated — in the guise of the momentsA 2m of the light curve — in terms of the elements of the eclipse; and their use for a solution for the elements is detailed in Section 3. A brief appendix containing certain auxiliary tables to facilitate this task concludes the paper. An extension of the same method to an analysis of the light changes exhibited by close eclipsing systems — in which the photometric proximity effects arising from mutual distortion can no longer be ignored — will be given in the subsequent paper of this series.  相似文献   

13.
The beaming effect (aka Doppler boosting) induces a variation in the observed flux of a luminous object, following its observed radial velocity variation. We describe a photometric signal induced by the beaming effect during eclipse of binary systems, where the stellar components are late type Sun-like stars. The shape of this signal is sensitive to the angle between the eclipsed star’s spin axis and the orbital angular momentum axis, thereby allowing its measurement. We show that during eclipse there are in fact two effects, superimposed on the known eclipse light curve. One effect is produced by the rotation of the eclipsed star, and is the photometric analog of the spectroscopic Rossiter-McLaughlin effect, thereby it contains information about the sky-projected spin-orbit angle. The other effect is produced by the varying weighted difference, during eclipse, between the beaming signals of the two stars. We give approximated analytic expressions for the amplitudes of the two effects, and present a numerical simulation where we show the light curves for the two effects for various orbital orientations, for a low mass ratio stellar eclipsing binary system. We show that although the overall signal is small, it can be detected in the primary eclipse when using Kepler Long Cadence data of bright systems accumulated over the mission lifetime.  相似文献   

14.
It is shown that the erratic changes of the orbital period, which are observed in some detached eclipsing binary systems, cannot be interpreted as real if their light curves show changing anomalies with asymmetric minimum profiles. In this case the photometrically determined times of the minima do not coincide with the ideal geometric ones, which are unobservable. This fact and the applied reduction methods for deriving the photometric times of minima cause systematic period errors of cumulative character. The discussion of six photoelectrically-determined minima obtained within the last 20 yr, and earlier photographic ones of the 0d.479 period eclipsing binary XY UMa yields a constant period. The long cyclic light curve variations due to starspot activity of the larger and hotter component of this system are reflected in corresponding period oscillations. Dedicated to Dr. Ida Noddack on the occasion of her eightieth birthday.  相似文献   

15.
We present and discuss JHKLM photometry for five long-period binaries (VV Cep, ZZ CMi, WY Gem, ε Aur, and ζ Aur). The IR radiation from WY Gem may contain a component with a period of ～430 days, attributable to temperature pulsations of an M supergiant. The 3.5-and 5-μm radiation from the eclipsing binary ε Aur outside the eclipse exhibits excess (relative to the light from an F supergiant) fluxes which correspond to the emission from a cool source with a temperature of ～1000 K. For the eclipsing binary Aur, we present the hitherto unpublished results of our optical and IR photometry during 1982–1985, when a primary eclipse was observed in the system.  相似文献   

16.
The aim of the present paper will be to extend the Fourier methods of analysis of the light curves of eclipsing binaries, outlined in our previous communication (Kopal, 1975) in connection with systems whose components would appear as uniformly bright discs, to systems whose components exhibit discs characterized by an arbitrary radially-symmetrical distribution of brightness —i.e., an arbitrary law of darkening towards the limb — be it linear or nonlinear.In Section 2 which follows a few brief introductory remarks, fundamental equations will be set up which govern the light changes arising from the mutual eclipses of limb-darkened stars — be such eclipses total, partial or annular; and Section 3 will contain a closed algebraic solution for the elements of the occulation eclipses terminating in total phase. Such a solution proves to be no more complicated than it turned out to be for uniformly bright discs in our previous paper; and calls for no special functions for the purpose — as will be put in proper perspective in the concluding Section 4.The cases of transit eclipses terminating in an annular phase, of partial eclipses of occulation or transit type, will be similarly dealt with by Fourier methods in the next paper of the present series.  相似文献   

17.
The aim of the present paper will be to detail the procedure outlined in our previous investigations (Kopal, 1975; Kopalet al., 1976) for a solution of the elements of distorted eclipsing systems by a Fourier analysis of their light changes. This procedure—which constitutes an equivalent, in the frequency-domain, of rectification hitherto practised in the time-domain — should enable us to free the observed momentsA 2m of the light curves from all photometric effects of distortion (between minima as well as within eclipses) — a feat impossible in the time-domain except under very restricted conditions — and thus to make it possible to obtain the geometrical elements of the eclipses which should be free from any obvious source of systematic errors.  相似文献   

18.
The main aim of this paper will be to develop explicit form of the moments of the light curvesA 2m(r 1,r 2,i) required for the solution for the geometrical elementsr 1,2 andi of eclipsing systems exhibiting annular eclipses (Sections 2 and 3), as well as partial eclipses (Section 4).In the concluding Section 5 we shall demonstrate that — regardless of the type of eclipse and distribution of brightness on the apparent disc of the eclipsed star, or indeed of the shape of the eclipsing as well as eclipsed components — the momentsA 2m satisfy certain simple functional equations — a fact which relates them to other classes of functions previously studied in applied mathematics.  相似文献   

19.
We report multicolour photometric observations of the 2003 eclipse of the long-period (5.6 yr) eclipsing binary EE Cep. Measurements were obtained with ten telescopes at eight observatories in four countries. In most cases, UBV(RI)C broad band filters have been used. The light curve shape shows that the obscuring body is an almost dark disk around a low-luminosity central object. However, variations of the colour indices during the eclipse indicate that the obscuring body emits a considerable amount of radiation in the near infrared.  相似文献   

20.
The interest in the study of the Algol binary system Y Leonis is justified not only by its light curve having a very deep primary minimum, and pulsating character of its primary component, but also by the complex behavior of its O–C curve which is featured by the presence of long and short time scale modulations. Taking into account the previously inferred K spectral type of the secondary component, one may expect that one of the involved periodicities could be related to magnetic cycles of this star. We gave the Wilson-Devinney solution of the eclipse light curve using our observational data obtained during 2009. The long- and short-term photometric variability of Y Leo is approached both through literature data and new CCD data. Even though these data are scarce, they revealed significant variability in the maximum and minimum brightness of this binary system at long time-scale. The nature of the rapid photometric variations during the deepest phase of primary minima can hardly be explained only by weak δ Scuti pulsations of the primary component which is still visible in partial eclipses.  相似文献   

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