Fourier analysis of the light curves of W UMa-type stars

The light curves of 30 well observed W UMa-type systems are analysed according to Kopal's method for the study of the light changes of eclipsing variables by using frequencydomain techniques. New geometric and photometric elements are derived and new values for the gravity-darkening coefficients are also given. Finally, an answer to the problem of whether or not these are contact systems is attempted.     

Fourier analysis of the light curves of eclipsing variable stars

The aim of the present paper is to establish the explicit forms of the photometric perturbations, in the frequency-domain, of close binaries, whose components are distorted by axial rotation and mutual tidal action.Following a brief introduction, Section 2 describes the light changes and the photometric perturbations within eclipses in the frequency-domain. In Section 3 the explicit forms of the perturbations for occultation eclipses terminating in totality are given; while in Section 4 analogous results are established for transit eclipses terminating in annular phases. In this latter case the results can be expressed in terms of the photometric perturbations for total eclipses and in terms of some series. To facilitate applications to actual stars these series have been computed and their results are represented in Table I and by the Graphs. Finally, Section 5 gives a discussion of the results.An extension of the photometric perturbations to the case of partial eclipses will be given in a subsequent communication.     

Fourier analysis of the light curves of eclipsing variable stars

The aim of the present paper is to find the eclipse perturbations, in the frequency-domain, of close eclipsing systems exhibiting partial eclipses.After a brief introduction, in Section 2 we shall deal with the evaluation of thea _n ^(l) integrals for partial eclipses and give them in terms ofa ₀ ⁰ ,a ₀ ⁰ (of the associated -functions) and integrals; while Section 3 gives the eclipse perturbations arising from the tidal and rotational distortion of the two components. The are given for uniformly bright discs (h=1) as well as for linear and quadratic limb-darkening (h=2 and 3, respectively).Finally, Section 4 gives a brief discussion of the results and the way in which they can be applied to practical cases.     

Fourier analysis of light curves of eclipsing variable stars

The photometric perturbationsB _h ^(l) arising from both tidal and rotational distortion of a close eclipsing binary have been given in two previous papers (Livaniou, 1977; Rovithis-Livaniou, 1977). The aim of the present paper will be to find the eclipse perturbationsB _2m =B _{2m, tid} +B _{2m, rot} of a close binary exhibiting partial eclipses. This will be done giving the suitable combinations of theB _h ^(l) 's and will make easier the application to real stars. After a very brief introduction, Section 2 gives both theB _{2m, tid} andB _{2m, rot} for uniformly bright discs; while in Sections 3 and 4 they are given for linear and quadratic limb-darkening, respectively. Finally, Section 5 gives a brief discussion of the results.     

W UMa-type stars BV Dra conis and BW DRa conis: Photoelectric observations

Photoelectric UBV observations of two W UMa-type stars, BV Dra (ADS 9537A) and BW Dra (ADS 9537B), are presented. New periods and epochs of minima are given for both variables, and magnitudes at maximum light are determined from standard star observations. It is concluded that these variables are quite normal W UMa stars.The two variables are members of the visual binary star ADS 9537, for which the angular separation and the position angle are determined from the photographic observations.On leave of absence from Dept. of Earth Science and Astronomy, College of General Education University of Tokyo.     

Rosat X-ray light curves of early-type stars

We have investigated ROSAT X-ray data of OB stars to search for evidence of time variability in the X-ray emission from early-type stars. As an example for such studies we present a detailed variability analysis for our two program stars Ori and Ori which have been multiply observed with ROSAT. The long-term analysis of both stars now covers a time range of 2.5 years and includes six pointed PSPC observations, an additional pointed HRI observation of Ori and the ROSAT all-sky survey data of both stars. Over a long time range the X-ray light curves of Ori and Ori show no evidence for variability. In the case of Ori we detected a moderate increase in X-ray count rate during a period of 2 days which can be explained as a strong shock propagating in the wind of an O-type star.     

CCD photometric analysis of the W UMa-type binary V376 Andromeda

This study presents the absolute parameters of the contact binary system V376 And. CCD photometric observations were made at the Çanakkale Onsekiz Mart University Observatory in 2004. The instrumental magnitudes of all observed stars were converted into standard magnitudes. New BV light curves of the system were analysed using the Wilson–Devinney method supplemented with a Monte Carlo type algorithm. Since there are large asymmetries between maxima (i.e., O’Connell effect) in these light curves, two different models (one with a cool spot and one with a hot spot) were applied to the photometric data. The best fit, which was obtained with a large hot spot on the secondary component, gives V376 And as an A sub-type contact binary in poor thermal contact and a small value of the filling factor (f ≈ 0.07). Combining the solutions of our light curves and Rucinski et al. (2001)’s radial velocity curves, the following absolute parameters of the components were determined: M₁ = 2.44 ± 0.04 M_⊙, M₂ = 0.74 ± 0.03 M_⊙, R₁ = 2.60 ± 0.03 R_⊙, R₂ = 1.51 ± 0.02 R_⊙, L₁ = 40 ± 4 L_⊙ and L₂ = 5 ± 1 L_⊙. We also discuss the evolution of the system, which appears to have an age of 1.6 Gyr. The distance to V376 And was calculated as 230 ± 20 pc from this analysis, taking into account interstellar extinction.     

An observational study of a spotted W UMa-type binary star CK Bootis

New photoelectric observations of CK Bootis (a binary star suspected of a spot activity) obtained in 1988 at Mt. Suhora Observatory are presented. On the basis of the spectroscopic observations made in May 1990 at the Toru University Observatory the spectral class F6V of the primary component was estimated. The physical parameters of the system with a circular spot were derived making use of the Wilson-Devinney code.     

Evolutionary state of W UMa-type systems

The evolutionary status of a sample of 31 W UMa-type systems (20 of W, 9 of A, and 2 of A/W sub-class) is examined and discussed on the basis of their positions in the H-R, mass-radius and mass-luminosity diagrams. The absolute elements of these systems have been evaluated by use of their spectroscopic and photometric data as they were found in the literature. Since different analysis methods have been used by the various investigators this gives the opportunity to make different H-R, mass-radius and mass-luminosity diagrams, according to the method used, and compare the results.Moreover, from the spectral type-period diagram of those systems that have spectral types from O to G2 it was found that all of them lie in the evolved region. Finally, the log (L _l/L _s) log (M _l/M _s) diagrams are presented and discussed.     

Finding outlier light curves in catalogues of periodic variable stars

We present a methodology to discover outliers in catalogues of periodic light curves. We use a cross-correlation as the measure of 'similarity' between two individual light curves, and then classify light curves with lowest average 'similarity' as outliers. We performed the analysis on catalogues of periodic variable stars of known type from the MACHO and OGLE projects. This analysis was carried out in Fourier space and we established that our method correctly identifies light curves that do not belong to those catalogues as outliers. We show how an approximation to this method, carried out in real space, can scale to large data sets that will be available in the near future such as those anticipated from the Panoramic Survey Telescope & Rapid Response System (Pan-STARRS) and Large Synoptic Survey Telescope (LSST).     

Periodic phenomena in Ae / Be Herbig stars light curves

Light curves of 78 Herbig Ae/Be stars were studied by digital analysis methods. Twenty-five thousand photoelectricUBVR observations of these stars were made by the authors in 1978–1990. A star was usually observed once a night. The stars were observed between 70 and 770 nights and on average each star was observed at more than 300 nights. The mean epoch for a star is 5 years. A morphologic classification of the light curves is suggested. The method of digital analysis are briefly described. To estimate the reliability of cyclic phenomena discovered in our study, a large number of them has been examined.     

Variation in the orbital period of W UMa-type contact systems

The secular variation in the orbital period P_orb is studied as a function of the mass ratio q of the components in a sample of 73 contact systems of class W UMa constructed from a survey of current (1991–2003) published photometric and spectroscopic data. Almost all the W UMa-systems (>93% of this sample) are found to have a variation in their orbital periods P_orb which alternates in sign independently of their division into A-and Wsubclasses. A statistical study of this sample in terms of the observed characteristics dP_orb/dt and q showed that on the average the numbers of increases (35 systems) and decreases (33 systems) in the periods are the same, which indicates the existence of flows directed alternately from one component to the other and illustrates the cyclical character of the thermal oscillations. An analysis of the behavior of dP_orb/dt as a function of the mass interval of the primary component yields a more accurate value for the mass ratio, q ≈ 0.4 ÷ 0.45 at which contact binaries are separated into A-and W-subclasses. No correlations were observed between the fill-out factor for the outer contact configuration, the total mass of the contact system, and the mass ratio of the components, on one hand, and the sign of the secular variation in the period. The physical properties and evolutionary features of these systems are discussed. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 419–432 (August 2006).     

The minimum mass ratio of W UMa-type binary systems

When the total angular momentum of a binary system   J _tot= J _orb+ J _spin  is at a certain critical (minimum) value, a tidal instability occurs which eventually forces the stars to merge into a single, rapidly rotating object. The instability occurs when   J _orb= 3 J _spin  , which in the case of contact binaries corresponds to a minimum mass ratio   q _min≈  0.071–0.078. The minimum mass ratio is obtained under the assumption that stellar radii are fixed and independent. This is not the case with contact binaries where, according to the Roche model, we have   R ₂= R ₂( R ₁, a , q )  . By finding a new criterion for contact binaries, which arises from  d J _tot= 0  , and assuming   k ²₁≠ k ²₂  for the component's dimensionless gyration radii, a theoretical lower limit   q _min= 0.094–0.109  for overcontact degree   f = 0–1  is obtained.     

The photometric solution of W UMa-type star BW draconis

The photometric solutions of W UMa-type binary BW Dra have been determined by applying the Wilson and Devinney Code toUBV observations of Rucinski and Kaluzny.It is shown that BW Dra is corresponding to a system with an overcontact configuration and smaller mass ratioq=0.392 andUBV light curves give the converging solutions with non-zero third light.It is proved that the components of BW Dra are older stars (the spectral types are G0 and G3, respectively). They could come into contact later stage of evolution. The photometric solution is similar to the results of Kaluzny and Rucinski. According to the photometric solution and spectroscopic results of Batten and Lu, the absolute parameters are presented too.     

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.     

Investigations into the thermal non-equilibrium of W UMa-type contact binaries

Traditionally, some physical details(e.g., magnetic braking, energy transfer, angular momentum loss, etc.) have to be taken into consideration during investigations into the evolution of contact binaries. However, the real evolutionary processes which usually contain several of these physical mechanisms are very complicated as a result of strong interaction between components. To avoid dealing with these factors, a linear relationship is applied to the temperatures of components. It is found that the higher the mass ratio(M_2/M_1) of a contact system, the weaker the deviation from thermal equilibrium.On this basis, a variation trend of fill-out factor(f) changing with mass ratio can be inferred, which is consistent with observations. Moreover, if we stick to this point of view, it should be natural that the number of semi-detached binaries in the predicted broken-contact phase of relaxation oscillations is less than the number in the contact phase.