Theory of the light curves of eclipsing systems with oscillating components,II

In continuation of our preceding investigation (Kopal, 1982c) of photometric consequences of free oscillations — radial or nonradial — of the eclipsing component on the light changes of close binary systems, the aim of the present paper will be to extend the scope of our inquiry to include the effects of similar oscillations of the component which undergoes eclipse, with arbitrary period and phase.In Sections 2 and 3 which follow a brief introduction to the particular aspect of the problem treated in this paper, a theory will be given of photometric effects caused by arbitrary harmonic oscillations of the components of eclipsing binary systems distorted by equilibrium tides, or by axial rotation with constant angular velocity. A translation of these effects into the frequency domain constitutes a problem which is solvable in a closed form only if the eclipse in question ends in totality. In any other case, the desired effects can be mathematically described only in terms of infinite series (of satisfactory asymptotic properties); and a construction of their explicit forms will be given in the Appendix.     

Fourier analysis of the light curves of eclipsing variables,V

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.     

Analysis of the light curves of PV Cassiopeiae by use of automatized fourier techniques

UBV Light Curves of the eclipsing binary system PV Cassiopeiae have been investigated using recently developed frequency-domain techniques. This analysis is based on Kopal's new theory for the study of the light variations, between minima as well as within eclipses, of eclipsing binaries whose components undistorted or distorted by axial rotation and mutual tidal action.A method for the distinguishing of the photometric proximity and eclipse effects directly from the observed data is also presented. In this method no rectification is needed. The automated method has been tested successfully on the light curves of PV Cassiopeiae. Finally, a comparative discussion is given of Kopal's and Kitamura's methods of the light curves analysis.     

Fourier analysis of the light curves of eclipsing variables,XIV

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.     

A photometric study of a new short period eclipsing sdB binary NSVS 07826147

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.     

On using the beaming effect to measure spin-orbit alignment in stellar binaries with Sun-like components

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.     

Computation of the elements of close eclipsing systems in the frequency-domain

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.     

Photometric elements of V364 cassiopeiae

TheUBV photometric observations of the eclipsing binary V364 Cas have been discussed. Two sets of photometric elements, one based on the Russell and Merrill methods and the other based on Kopal's new method of the analysis of the light curves of eclipsing binary stars in the frequency-domain, have been derived. Using the observed colour indicesU-B andB-V, the spectral types of the systemic components are estimated. An examination of all the available times of minimum light of V364 Cas does not reveal any change in its orbital period.     

Fourier techniques for an analysis of eclipsing binary light curves,VII

A Laplace and a Hankel transform of the light curves of eclipsing binary star systems have been expressed in terms of the eclipse elements (L ₁,r _1,2 andi) of the spherical basic model. These general expressions can be used for the solution of the eclipse elements of the systems in terms of the observed quantities.     

New classification and basic stellar parameters of SU Equulei

The variable star SU Equulei was classified as a close binary with an eclipse light curve previously categorized as WUMa type. The aim of this paper is a review of this old classification on the basis of new observations and a new determination of variable star ephemeris as well as the determination of SU Equ spectral type and distance. New photometric observations in different colours allow a precise determination of the period of variability and yield more accurate light curves allowing a re‐classification of the type of variability. We find the best period of variability to be half the old value. The shape of the light curve is inconsistent with an eclipse curve but consistent with an RR Lyrae type c classification. From the B, V, and R colours we deduce a new spectral classification. SU Equulei is an RRc Lyrae type variable of spectral class A8 at a distance of ≈12.4 kpc instead of a late‐type eclipsing binary (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fourier techniques for an analysis of eclipsing binary light curves: IV

The aim of the present paper is to establish two further series expansions (alternative to those given in Demircan, 1979a, b, c), for the observed light changes of eclipsing binary system. The coefficients of these expansions have also been expressed in the form of general series expansions in terms of the eclipse elementsr _1.2,i andL ₁ of the spherical model on which all other distorted models may be based (Kopal, 1975, 1976) in an analysis in the frequency-domain.     

A photometric study of the eclipsing binary 68 u Her

The aim of this paper is to present and study the light curves (B andV) of the eclipsing binary 68 u Her from the photometric observations made at Al-Battani Observatory.New photometric elements have been obtained by a Fourier analysis of the light changes in the frequency-domain.     

Photometric investigation of the short period eclipsing binary star V719 Her

The Behlen observatory 0.76 m telescope CCD photometer is used to obtain 347 observations of the short period (P0^d.4) eclipsing binary star V719 Her. The observations done withV andR bandpass filters were made on 6 nights in 1993. Previously published light elements and the present five timings of minimum provide a new epoch and a more accurate orbital period of 0.4009828 days. Our analyses show that the period of the system appears to decrease. We recommend future monitoring of the eclipse minima for this system. No published spectral classification for V719 Her exists. From the color,V-R=0.391, we estimate it to be about F5.The 1993 version of the Wilson Devinney model gave the photometric solutions. The adopted solution indicates that V719 Her is a W UMa type contact binary. The mass ratio,q=(m ₂/m ₁, where star 1 eclipse at the primary minimum)=0.296 suggests that V719 Her is a WUMa system with type-A (transit during primary eclipse) configuration. The secondary minimum shows a total eclipse. V719 Her with period less than 0.5 and spectral class F5, is probably a zero-age contact system. Since our photometric solution shows that the luminosity difference between the components is very large, we suspect that V719 Her is most likely a single line spectroscopic binary. We recommend spectroscopic study of this system.     

Photometric perturbations of distorted eclipsing systems within minima

The aim of the first part (Sections 1 and 2) of this paper will be to extend an analysis of the light curves of totally-eclipsing binary systems to the case in which the distortion of the shadow-cone of the eclipsing component must be taken account of in an analysis of the system's light changes within minima. Like in the case of total eclipses of spherical stars, an extension of the analysis of their light changes in the frequency-domain can likewise be carried out in a closed form, without a need to resort to automatic computers which may not be at the disposal of every investigator. In the second part (Sections 3 and 4) of this paper, the same procedure will be extended (albeit to a lesser degree of precision) toany type of eclipses—be these total, annular or partial; while a proof of the underlying formulae the reader will find collected in the Appendix. Again, in this more general case, while an access to automatic computers may be of advantage to incorporate the photometric perturbation arising from the distortion of the components mutually eclipsing each other, their use represents a convenience rather than necessity for our work.     

Analysis of the light curves of SX Aurigae,by automated fourier techniques

The aim of the present paper has beento analyse the light changes of the close eclipsing system SX Aurigae 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 method for the separation of the photometric proximityand eclipse effects directly from the observed data is also presented. In this method no rectification is needed. The automated method has been tested on the light curves of SX Aurigae. Finally, a comparative discussion is given of Kopal and Kitamura methods of thelight curves analysis.     

Photometric Mass Ratios of Eclipsing Binary Stars

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.     

Photometric investigation of the evolved contact binary system DN Aur

We present here the photometric light curve analyses of the eclipsing binary star DN Aur. The CCD photometry, performed at the Behlen observatory using the 0.76 m automated telescope gave 646 individual data points inV andR bandpass filters. From this data we have determined a new epoch and an orbital period of 0.6168891 days. The published spectral classification is F3.The Wilson-Devinney model was used to derive the photometric solutions. DN Aur is a W UMa type contact binary system. The mass ratio, (q=m ₂/m ₁0.210, where star 2 is eclipsed at the primary minimum) suggests that the system has A-type configuration. The computed light curve has a third light of about 22 percent and a total eclipse in the secondary minimum. A solution with a cool spot on the secondary component is also found. We recommend spectroscopic study of DN Aur even though the light curve analysis show it to be a single line spectroscopic system. Generally contact systems of spectral type F3 have periods ranging from 0.25 to 0.5 days. The longer period of DN Aur suggests that it is an evolved contact system with case A mass transfer.     

Fourier analysis of the light curves of eclipsing variables,XI

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.     

Photometric Investigation of the Eclipsing Binary Star KN Per

We used the Behlen observatory 0.76 m telescope and the CCD photometer to secure 689 observation of the eclipsing binary star KN Per. The observations were made on 8 nights during 1993 and 1994 with V and R bandpass filters. From 7 determinations of eclipse timings of minimum (V&R together), we have determined a new epoch and an orbital period of 0.8664604 days. The published spectral classification is A9. The 1993 version of the Wilson-Devinney model gave the photometric solutions. The adopted solution indicates that KN Per is a W UMa type contact binary. The mass ratio, q = (m₂/m₁, where star 1 eclipses at the primary minimum) = 0.23 suggests that KN Per is a W UMa system with A-type configuration. The secondary minimum shows a total eclipse. The asymmetry in the light curve is fitted with a cold spot on the secondary component of the system. The luminosity difference between the components is very large KN Per therefore, is most likely a single line spectroscopic binary. We recommend spectroscopic study of this system. Generally contact systems of spectral type A9 have periods ranging from 0.4 to 0.6 days. KN Per has considerably longer period and thus appears to be an evolved contact system with case B mass transfer. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fourier techniques for an analysis of eclipsing binary light curves: II

Some properties of the quantitiesB _2m (Smith, 1977) inherent in the frequency-domain approach have been deduced, and a general expression for them in terms of the eclipse elementsr _1,2,i andL ₁ of the basic model has been presented (Section 2).An expansion for the loss of light (1–l) into a Fourier sine series alone have been introduced, and its coefficientsb _m presented (Section 3) in terms of the same eclipse elements. A method of increasing the rate of convergence of this series has been given in Section 4. The methods for obtaining the elements of eclipsing binaries by making use of all these quantities in the frequency-domain can likewise be generalized to cover the photometric effects of gravitational and radiative interaction between the components.