The eclipsing binary AB Andromedae

In this paper the two newB- andV-light curves of the eclipsing variable star AB Andromedae, obtained during 1979 with the 48 in reflector of the National Observatory of Athens, are represented and discussed. General information of the system is given in the Introduction, while in Section 2 some observational and reductional details are given and the new light curves are represented. Section 3 deals with the period of the system and, finally, in Section 4 a general discussion is given.     

Fourier analysis of the light curves of eclipsing binaries in the case of transit eclipses,with application to the eclipsing system YZ Cassiopeiae

The aim of this paper is to extend the Fourier approach to the transit eclipses, terminating in annular phase, with an application to YZ Cassiopeiae. The results turn out to be more complicated than those obtained by Kopal for total eclipses. However, the solution can still be obtained by successive approximations without resorting to any tables of special functions.Section 1 contains an outline of the problem. In Section 2, the evaluation of the theoretical momentsA _2m for transit eclipses is given. An application of the Fourier method to the light curves of YZ Cas is presented in Section 3. Finally, in Section 4, a general discussion of the results is given.     

Determination of the elements of eclipsing variables,RW Gem and AY Cam,by Fourier analysis of their light changes

The aim of the present paper has been to present an analysis of the light curve of two eclipsing systems RW Gem and AY Cam by Fourier analysis of the light changes in the frequency domain which was developed by Kopal (1975a, b, c, d, e; 1976).In Section 1, the subject is introduced in a general way, with the intention of laying the foundation of the light curve analysis. Section 2 contains the evaluation of the empirical values of the theoretical momentA _2m is demonstrated, with the equation of the condition given. Then the equations forA _2m in terms of the elements of the total and the annular eclipses, including partial and annular phase of transit eclipse, follow.The analysis of the light curves of the two eclipsing binaries (RW Gem and AY Cam), the results and the discussion of our solution, are outlined in Section 3.     

Two new light curves of the eclipsing variableu Herculis

This paper presents two new light curves (inB andV) of the eclipsing variable staru Her which have been derived from photoelectric observations made at the National Observatory of Athens. General information of the system is given in the introduction, while Section 2 deals with some observational and reductional details. Section 3 gives the residuals O-C and Section 4 the normal points.     

Determination of the elements of eclipsing variables RW tauri and U sagittae by an analysis of the light changes in the frequency domain

The aim of the present paper has been to present an analysis of the light changes of two eclipsing systems RW Tau and U Sge in the frequency domain, which was developed by Kopal (1975a, b, c, d, e, 1976).Following a brief introduction, Section 2 contains the evaluation of the theoretical momentsA _2m. The determination of the preliminary elements and their improvement, taking into account the photometric perturbations, are given in Sections 3 and 4. A general discussion devoted to the whole analysis of the system is presented in Section 5.     

Fourier analysis of the light curves of eclipsing variables,X

The aim of the present paper will be to develop methods for computation of the Fourier transforms of the light curves of eclipsing variables — due to any type of eclipses — as a function of a continuous frequency variablev. For light curves which are symmetrical with respect to the conjunctions (but only then) these transforms prove to be real functions ofv, and expressible as rapidly convergent expansions in terms of the momentsA _2m+1 of the light curves of odd orders. The transforms are found to be strongly peaked in the low-frequency domain (attaining a maximum forv=0), and become numerically insignificant forv>3. This is even more true of their power spectra.The odd momentsA _2m+1 — not encountered so far in our previous papers — are shown in Section 3 of the present communication to be expressible as infinite series in terms of the even momentsA _2m well known to us from Papers I–IV; and polynomial expressions are developed for approximating them to any desired degree of accuracy. The numerical efficiency of such expressions will be tested in Section 4, by application to a practical case, with satisfactory results.Lastly, in Section 5, an appeal to the Wiener-Khinchin theorem (relating the power spectra with autocorrelation function of the light curves) and Parseval's theorem on Fourier series will enable us to extend our previous methods for a specification of quadratic moments of the light curves in terms of the linear ones.     

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

The aim of the present paper will be to translate the essential parts of the theory of Fourier analysis of the light changes of eclipsing variables into more practical terms; and describe procedures (illustrated by numerical examples) which should enable their users to obtain the desired results with maximum accuracy and minimum loss of information by processes which can be fully automated.In order to unfold in steps how this can be done, the scope of the present paper-the first of two-will be restricted to an exposition of the analysis of light changes caused by eclipses of spherical stars; while between minima due to this cause the light of the system should remain sensibly constant. An extension of our analysis to incorporate photometric effects arising from mutual distortion of the components of close eclipsing systems between minima as well as within eclipses is being postponed for the second communication.In developing this subject we shall single out for the user's attention only those parts of the whole theory which are of direct relevance to practical work. Their justification can be largely found in sources already published; and new developments essential for our work, not yet made public, will be relegated to several Appendices at the end of the text, in order not to render its text too discursive and deflect the reader's attention from the main theme of its narrative.After a brief outline of the subject given in Section 1, Section 2 will introduce the reader to practical aspects of the Fourier analysis of the light curves; and Section 3 will be devoted to its use to determine the numerical values of the momentsA _2m of the light curves which constitute the cornerstones for all subsequent work. Section 4 will describe an algebraization of the process of determination of the elements for the case of total (annular) eclipses; while Section 5 will do the same for partial eclipses. The concluding Section 6 will be devoted to an error analysis of our problem, and to an outline of the way by which the errors of the individual observations will compound to the uncertainty of the final results. Lastly, Appendices 1–5 concluding the paper will contain additional details of some aspects of our work, or proofs of new processes made use of to obtain our results, whose earlier inclusion would have made the main text too discursive.     

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.     

Fourier analysis of the light curves of eclipsing variables,XV

A new general expression for the theoretical momentsA _2m of the light curves of eclipsing systems has been presented in the form of infinite series expansion. In this expansion, the terms have been given as the product of two different polynomials which satisfy certain three-term recursion formulae, and the coefficients diminish rapidly with increasing number of terms. Thus, the numerical values of the theoretical momentsA _2m can be generated recursively up to four significant figures for any given set of eclipse elements. This can be utilized to solve the eclipse elements in two ways: (i) with an indirect method (for the procedures see Paper XIV, Kopal and Demircan, 1978), (ii) with a direct method as minimization to the observational momentsA _2m (area fitting). The procedures given in Paper XIV for obtaining the elements of any eclipsing system consisting of spherical stars have been automated by making use of the new expression for the momentsA _2m of the light curves. The theoretical functionsf ₀,f ₂,f ₄,f ₆,g ₂ andg ₄ which are the functions ofa andc ₀, have been used to solve the eclipse elements from the observed photometric data. The closed-form expressions for the functionsf ₂,f ₄ andf ₆ have also been derived (Section 3) in terms of Kopal'sI-integrals.The automated methods for obtaining the eclipse elements from one minimum alone have been tested on the light curves of YZ (21) Cassiopeiae under the spherical model assumptions. The results of these applications will be given in Section 5 which follows a brief introduction to the procedure we followed.     

Theory of the light curves of eclipsing systems with oscillating components: I

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.     

Photoelectric observations of BV Draconis

In this paper the twoB andV light curves of the close eclipsing binaryBV Draconis, obtained with the 48-in reflector of the National Observatory of Athens, are represented and discussed. Also, new period of the system is given.     

Fourier analysis of the light curves of eclipsing variables,III

The aim of the present paper will be to extend our new methods of analysis of the light curves, of eclipsing binary systems, consisting of spherical components, by Fourier approach to eclipses oftransit type — which arise when the eclipsing component happens to be smaller of the two. Our present principal concern will be transit eclipses, terminating in annular phase, of stars characterized by arbitrary radially-symmetrical distribution of brightness over their apparent discs — a phenomenon which will cause the light of the system to vary continuously during annular phase. In the first section which follows this abstract, an outline of the problem at issue will be given. Section 2 has been devoted to an analysis of light changes arising in the course of partial phases of transit eclipses; and the concluding Section 3 will contain an analysis of the corresponding light changes, during annular phase. Unlike for occultation eclipses considered in our previous paper (cf. Kopal, 1975b), the momentsA _2m of the light curves due to eclipses of transit type can again be expressed in terms of the geometrical elements of such eclipses in a closed form for limb darkening characterized by any value ofn; but the use of such functions will require auxiliary tables (now in preparation) for applications to practical cases. A parallel treatment of partial eclipses of the occultation or transit type — eclipses which stop short of totality or annular phase — is being postponed for a subsequent communication.     

The early-type eclipsing contact binary TY Puppis

In this paper we present theBV photoelectric light curves of the W UMa-type eclipsing binary TY Pup. We have gained ephemerides by means of the times of minima. The obtained light curves have been solved using Wilson-Devinney's synthetic code. The results indicate that TY Pup is a contact system with mass ratio 0.185 and a large degree of overcontact of 52%. Combined with spectroscopic material, absolute parameters of TY Pup are derived. It may be concluded that TY Pup is an evolved contact binary.     

UV Leo: The Binary with the Two Suns

BV light curves of the eclipsing binary UV Leo obtained at the Kryonerion Astronomical Station of the National Observatory of Athens, Greece, are analyzed. The analysis is based on a Roche configuration with two spots on the secondary surface. The elements of the two components of the system are calculated and the spot characteristics are given.     

Rotational dynamics of a deformable medium

The aim of the present investigation has been to derive from the fundamental Cauchy's first law of continuum mechanics the explicit form of the Eulerian general equation which governs the three-axial generalized rotation about the centre of mass of a self-gravitating deformable finite material continuum, viscolinear (i.e., Newtonian) or not, consisting of compressible fluid of arbitrary viscosity, in an external field of force. The generalized rotation is a superposition of the so-called rigid-body (i.e., time dependent only) rotation of the continuum plus a nonrigidbody (i.e., position-time dependent) rotation of its configurations.In Section 2, which follows brief introductory remarks outlining the problem, we develop a mathematical theory which describes the whole phenomenon in terms of two rotation tensors corresponding, respectively, to the rigid-body and nonrigid-body rotation modes. In Section 3, we derive the differmation vectors of velocity and acceleration. The equations we have obtained are a very general version of Navier Stokes' equations, which were not given in previous investigations. In Section 4, we perform integration of the left-hand side of Cauchy's first law, cross-multiplied by the position vector, without any restriction. In Section 6, integration of the right-hand side of the same law, cross-multiplied by the position vector, is carried out, by taking account of actually simplifying assumptions stated in Section 5. All the integral terms occurring in both sides are expressed explicitly by quantities evaluated in terms of components of properly defined moments.Finally, in Section 7, the system of the general Eulerian equations is set up; and some easy modifications are given, which describe nicely physical models of special interest; while the concluding Section 8 contains a general discussion of the results.     

The CCD photometric study of the newly identified RS CVn binary star V1034 Hercules

This paper presents a new CCD Bessell VR_cI_c light curves and photometric analysis of the newly discovered RS CVn type eclipsing binary star V1034 Her. The light curves were obtained at the Çanakkale Onsekiz Mart University Observatory in 2006. Variations of the orbital period of the system were firstly studied. The (O − C) diagram with a low range of observing time of about 20 years shows an upward parabola, which indicates a secular increase in the orbital period of the system. The light curves are generally those of detached eclipsing binaries; however, there are large asymmetries between maxima. The VR_cI_c light curves were analysed with two different fitting procedures: Wilson–Devinney method supplemented with a Monte Carlo type algorithm and Information Limit Optimization Technique (ILOT). Our general results find V1034 Her. as a well detached system, in which the components are filling 65% of their Roche lobes. Light curve asymmetries of the system are explained in terms of large dark starspots on the primary component. The primary star shows a long-lived spot distribution with active longitudes in the same hemisphere.     

B,V photometry of the active RS CVn system II Peg

In this work,B andV photometry of the RS CVn-type binary II Peg is presented. The light curves obtained in 1983 and 1984 display two unequal maxima. The light curves of the system have different amplitudes. The amplitude seems to vary with three different periods. 10, 6, and 4 years of periods may be attributed to those variations.     

Light and colour curve observations and analysis of the short period eclipsing binary system UV Psc

In the present work we have presented and analysedB andV light curves and the (B-V)-colour curve of the short period (RS CVn type) binary system UV Psc, and derived absolute information from the available data.x ² minimization procedures were utilized to a large extent in fitting light and colour curves.The solutions show the binary to be at a distance of about 90 pc with two detached components which are close to the main sequence (G2 and K0). The inclination of the orbit is close to 90°Photometric irregularities present in the light curve are briefly considered in relation to current ideas on RS CVn systems, and the colour information indicates a locally hotter (rather than cooler) region is responsible for the irregularities.     

Light curves analysis of AB Andromedae

The new B and V light curves of the eclipsing variable AB And obtained during 1979 are analysed. Frequency Domain techniques is used and new geometric and photometric elements are given.     

Photoelectric study of AW UMa

UBV photoelectric photometry of the eclipsing binary system AW UMa has been presented. A slightly improved period of 0 _. ^d 4387304 has been given. The colour of the system has been discussed. Eccentricity is present in the system. Light and colour curves show that intrinsic light variations may be present in the system. The presence of mass transfer is a possibility.