Analysis of the light curves of SZ Cam using automatized fourier techniques

UBV light curves of the early type close eclipsing binary system SZ Cam have been investigated using recently developed frequency-domain techniques. The combination of both minima in the analysis results in a distinct methodological improvement over the single minimum method discussed hitherto. This improvement has two aspects: (i) increased accuracy of the determined elements, (ii) agreement of the results of the two-minimum method with those of the single-minimum method provides a criterion whereby the self-consistency of the underlying model with its representation of the light curve in the regions between minima by a cosine series and the empirically determined coefficients of such a series may be assessed. Such a self-consistent solution is found, and a further step towards a realistic representation is made by including the photometric perturbations. It is confirmed from these three light curves that the less massive star is overluminous. A probable tendency for the limb-darkening coefficient of the more massive star to increase with decreasing wavelength is also noted.     

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.     

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.     

The semi-detached system RT Persei and its light curve

The observedV light curve of the eclipsing binary RT Persei has been analysed by four different methods of solution to get the geometrical and photometric elements of the system. The results show a good agreement within about 6%.The system shows a variable light curve and a tentative hypothesis is made to explain this behaviour by considering a dynamical instability that may be the cause of circulating matter through the system and of the variability of the period.     

A reanalysis of the light curve of RT Persei with the W-D code

The UBV photometric observations of RT Per, from Sanwal and Chaubey (1981), were analyzed by the Wilson and Devinney code (1971). The light curves include reflection effects that for the first time has been suggested by Dugan (1911). RT Per has a semi-detached configuration where the lower-mass component is in contact with its respective Roche surface. The higher-mass component very nearly fills its Roche lobe. It has the characteristic of an Algol type system. The absolute dimensions for the primary and secondary of this system were calculated from its spectral types and by combining the photometric solution with inferred component radial velocities (Lu, 1990).     

UBV photometry of RT Persei

Photoelectric and absolute elements of the system RT Per have been determined inU, B, andV filters. It is suggested that the primary star may be surrounded by a gaseous disk.     

On the period variations of RT Persei

The observed minima of RT Persei up to 1971 are collected and treated by the method of least squares to establish periodic terms with a fundamental period of 40^y0 and, furthermore, a quadratic term. It is shown that the periodic terms might be explained by the presence of a third body, but this hypothesis seems unlikely, and could be definitively ruled out by new spectroscopic observations. A dynamical instability of the system may constitute a more likely explanation of the observed period changes.     

Photoelectric light curves of RT coronae borealis and their analysis

The first photoelectric light curves of the RS CVn-type eclipsing binary RT CrB are presented. There is no indication about the existence of wave like distortion on its light curve. The light curves were analyzed by using Wood's and Nelson, Davis, and Etzel's methods. The radii of the components are nearly identical. The solutions indicate that the cooler component has a later spectral type between K0 and K2.     

A spectroscopic orbit for the two—Spectrum eclipsing binary RT Persei

Intensified Reticon spectra have been obtained at a high dispersion for the Algol system, RT Persei. They were measured by the cross-correlation technique. The spectroscopic elements, revised for the primary component and determined for the secondary for the first time, are: T₀ = HJD 2,446,038.9332, K₁ = 55.0, K₂ = 194.7, V₀ = −8.3 km/s. A mass ratio q = m₂/m₁ = 0.282 is deduced. A circular orbit is adopted. The spectrum of the primary is F5V, and the secondary is a subgiant. With the elements determined here and the published photometric parameters, the absolute dimensions of the binary are: A = 4.20, R₁ = 1.20, R₂ = 1.08 R; M₁ = 1.08, M₂ = 0.30 M.     

An optimization technique for the fourier analysis of the light curves of totally-eclipsing systems of algol-type

A fully automatized technique for the evaluation of geometric and photometric elements of Algol-type systems exhibiting total eclipses is presented. The method requires observations in at least two wavelengths and enables us to choose the most probable solution from a grid of solutions performed with various possible phase angles of the first contact of the eclipse.     

Fourier techniques for an analysis of eclipsing binary light curves. V

An integral transform called the momentsA _2m of the light curves has been introduced by Kopal (1975) and utilized in the subsequent papers for an analysis of the light curves of eclipsing variables. The aim of the present paper is to generalize this integral transform by two distinct ways: (i) by introducing an exponential factor, and (ii) a Jacobi polynomial as multiplicative factor into the integrand of the transformA _2m. Observational values of these general transforms are likewise obtainable. They have been expressed in terms of eclipse elementsr _1,2,i andL ₁. These expressions can be used to solve the eclipse elements in terms of observed quantities. Free parameters in the expressions increase the flexibility in applications and may be utilized to improve the determinacy of the elements.     

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.     

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.     

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

The Fourier techniques developed so far for an analysis of eclipsing binary light curves have been re-discussed. The Fourier coefficients for the analysis have been derived in a simple form of series expansions, in terms of eclipse elements, valid for any type of eclipse (regardless of whetherr ₁r ₂).These coefficients may be utilized to solve the eclipse elements in terms of the observed characteristics of the light curves. A general relation between the observed quantitiesl and , and the eclipse elementsr _1,2,i andL ₁ has also been given in the form of series expansions which can be used for the synthesis of the light curves.     

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

The aim of the present paper will be to present a new approach to the light changes of eclipsing binary systems. The light changes have been expanded into the Fourier-Bessel and Dini series. The coefficients of these expansions which are the Hankel transforms of the order of the loss of light (1–l) have been expressed in terms of the eclipse elements. These discrete Hankel transformsH (j _m ) andH ( _m ) valid for only the positive real zerosj _m and _m of the functionsJ and [xJ(x)+J (x)] have been generalized for any positive value of andy. Thus, these general expressions for the Hankel transforms of the light curves which are valid for all types of eclipses, for any arbitrary degree of the adopted limb-darkening law and, moreover, for any positive value of the free parameters andy, may be used for the solution of the elements of eclipsing binary systems.     

Fourier techniques for an analysis of eclipsing binary light curves. VIa

The aim of the present paper is to deduce relations between the integral transformsA _2m, B_2m,andF _1,2 of the light curves of eclipsing binary systems. The integral transformsA _2m, B_2m,andF _1,2 have been related to one another by means of finite or rapidly converging infinite summations obtained by integrations of the series expansions of trigonometric functions.     

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

This is a continuation of a previous paper which appeared in this journal (Demircan, 1980b) and aims at ascertaining some other relations between the integral transforms of the light curves of eclipsing binary systems. The appropriate use of these relations should facilitate the numerical computations for an analysis of eclipsing binary light curves by different Fourier techniques.     

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.     

Analysis of selected Kepler Mission planetary light curves

We have modified the graphical user interfaced close binary system analysis program CurveFit to the form WinKepler and applied it to 16 representative planetary candidate light curves found in the NASA Exoplanet Archive (NEA) at the Caltech website http://exoplanetarchive.ipac.caltech.edu, with an aim to compare different analytical approaches. WinKepler has parameter options for a realistic physical model, including gravity-brightening and structural parameters derived from the relevant Radau equation. We tested our best-fitting parameter-sets for formal determinacy and adequacy. A primary aim is to compare our parameters with those listed in the NEA. Although there are trends of agreement, small differences in the main parameter values are found in some cases, and there may be some relative bias towards a 90^° value for the NEA inclinations. These are assessed against realistic error estimates. Photometric variability from causes other than planetary transits affects at least 6 of the data-sets studied; with small pulsational behaviour found in 3 of those. For the false positive KOI 4.01, we found that the eclipses could be modelled by a faint background classical Algol as effectively as by a transiting exoplanet. Our empirical checks of limb-darkening, in the cases of KOI 1.01 and 12.01, revealed that the assigned stellar temperatures are probably incorrect. For KOI 13.01, our empirical mass-ratio differs by about 7 % from that of Mislis and Hodgkin (Mon. Not. R. Astron. Soc. 422:1512, 2012), who neglected structural effects and higher order terms in the tidal distortion. Such detailed parameter evaluation, additional to the usual main geometric ones, provides an additional objective for this work.     

Analysis of light curves produced by surface inhomogeneities on magnetic CP stars

The problem of the determination of surface brightness distribution parameters from the observed CP2-star variability, usually explained with the “oblique rotator model”, is discussed. A simple geometrical model of the surface brightness distribution is derived from the common properties of the observed light curves of these stars. This “spot model” which is supported from the known facts concerning the magnetic field structure and the surface distributions of chemical elements serves as a basis of the special inverse problem: the determination of the number of large scale inhomogeneities, their locations and extents and further parameters, from all the observed light curves of a given star. A suitable technique for solving the special inverse problem is explained. The problem of ambiguity which even arises for the proposed simple model and, in connection with that, the remaining possibilities to win the relevant information on the inhomogeneities of surface brightness are discussed. For the purpose of illustration, the result of the light curve analysis of the CP2 star HD 8441 is given.