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1.
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.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
A part of the light curves of two detached (CD Tau and V909 Cyg) and one semi-detached (Algol) binaries have been analysed with the emphasis on the determinacy of the parameters of different systems from a part of their eclipse curves. A model light curve for whichr 1=0.050,r 2=0.150,i=90°, andL 1=0.800 were chosen, has also been considered for a further clarification of the determinacy problem of the eclipse parameters. Some insight into the determinacy is gained by varying one parameter and adjusting the others for the best fit to the light curves in the considered eclipse phases. It was realised that the determinacy problem of the unknown parameters is stored in the determinacy of the type of the eclipse minima. The attempts of the solutions with a false choice of initial elements result in finding (i) no minimum of 2 to give any acceptable solution, (ii) rapid departure from the false start and convergence on the correct solution, or (iii) a false solution mostly with a true inclinationi, but wrong sense of the ratio of the radii.  相似文献   

6.
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.  相似文献   

7.
The practical procedures for the solutions of the elements of any eclipsing system in the frequency-domain have been described in a previous paper of this series (Kopal and Demircan, 1978, Paper XIV). The fundamental quantities from which we depart in quest of our solution are twog-functions defining by the momentsA 2m (see Equations (2.13)–(2.16) in Paper XIV, or Equations (3.2)–(3.6) in Paper XV: Demircan, 1978b). If we establish the observational values for these functions, they constitute two independent relations between the unknown parametersa andc o, and can be numerically solved for them with the aid of the general expressions for the respective moments. However, the determinacy of these parameters depends on not only the accuracy of observations but also the employedg-functions. For better understanding of the geometrical determinacy of the eclipse parametersa andc o, different combinations of the momentsA 2m have been worked out asg-functions. For the index 2m, the values between 0 and 6 were applied. It has been noted that the behaviour of these functions vary but very little with applied different combinations of the moments. A choice of the most convenient moments to obtain a good determinacy for the eclipse elements were discussed. In this connection, (i) them-dependence of the moments, and the errors in their observational values have been considered, (ii) different practical procedures for the solution of eclipse elements were introduced, and (iii) different type of moments were tested.  相似文献   

8.
The Behlen observatory 0.76 m telescope CCD photometer is used to obtain 347 observations of the short period (P0d.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.  相似文献   

9.
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.  相似文献   

10.
The system EE Aqr has been observed inUBV colours. A consistent set of orbital elements and a slightly improved period of 0 . d 5089954 have been obtained. The eclipse is partial and variability is of Lyrae-type. The colour of the components has been determined.  相似文献   

11.
UBV photometric observations and elements of TT Hydrae obtained by Kulkarni and Abhyankar (1980) are combined with the radial velocity curve of Popper (1979, personal communication) to derive the absolute dimensions and. a model of this important Algol system. While the photometric ratios of radii inV andB are in agreement givingk = 0.3812 for a limb darkening coefficient ofx = 0.6, application of Irwin’s (1947) method givesx = 0.4 forU. The primary is found to be a main sequence Al V star of mass 2.61M ⊙ and radius 2.01 R⊙, and the secondary is classified as a Kl III star of mass 0.70M ⊙ and radius 5.33R ⊙. The observed Fourier coefficients for the light outside the eclipse agree with those calculated from theory for the reflection and ellipticity effects. The system shows an ultraviolet excess of 0.5 to 0.6 magnitudes during primary eclipse, which is attributed to an asymmetric circumstellar distribution of matter around the primary. The evolutionary status of the secondary, which does not appear to fill its Roche lobe completely, is discussed.  相似文献   

12.
The aim of the present paper is to deduce some further properties of the fundamental quantities inherent in the frequency-domain approach-such as the fractional loss of light l 0 and momentsA 2m of the light curves of eclipsing variables; and also to develop an iterative method for the solution of two key eclipse parametersa andc 0 in terms of the observed quantities. This should facilitate practical applications of the methods developed in the preceding papers of this series for the frequency-domain light curve analysis of eclipsing variables.  相似文献   

13.
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   

14.
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.  相似文献   

15.
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   

16.
We perform a Monte Carlo analysis of the eclipse probabilities of short-period binary systems in an attempt to estimate the distribution of ellipsoidal variable system with Main-Sequence components. Our results suggest that possibly as many as one in four of the non-eclipsing, spectroscopic binaries withP(d)10, and Main-Sequence components withM v 10 could be ellipsoidal variable systems. This result, while an upper limit, would seem to hold irrespective of primary spectral type (B5 to G5).  相似文献   

17.
R and I band CCD observations of the nova V1494 Aql during July-November 2002 are reported and the V, R, and I light curves are analyzed. The orbital light curve of this nova has an eclipse-like form with two unequal humps before and after the eclipse. The approach to the eclipse lasts twice as long as the emergence from it. The overall duration of the eclipse is about 0.45P orb. The depth of eclipse increases with wavelength and averages 0m.3 (V), 0m.5 (R), and 0m.7 (I). The secondary, shallow minimum has an average depth of 0m.1 in R and I and about 0m.03 in V. The hump at phase 0.65 is higher than the one at phase 0.17. The most probable explanation for the observed variations in the light with the phase of the orbital period may be self eclipsing of the accretion column in the magnetic exploding variable (white dwarf) together with partial eclipsing of the accretion region by the secondary component.  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.
Recently Kopal (1975a, b, c, d) initiated a new approach to the analysis of the light curves of eclipsing binary systems in which the solution is based on transforming the problem from the conventional time-domain into the frequency-domain. Irrespective of the type of eclipse, the present formulation of the frequency approach requires that a set of quantitiesA 2m, called moments, be determined from the observations.It is the purpose of the present paper to describe a data interpolation and smoothing technique based on a version of the Kalman filter to pre-process observations and to determine the quantitiesA 2m in an optimal sense.  相似文献   

20.
This is a third paper dealing with the numerical evaluation of the light changes exhibited by close binary systems; for previous communications, Lanzano, 1976a, b.TheJ-integrals which were introduced by Kopal for the purpose of this numerical evaluation can be expanded in terms of the Appell hypergeometric series of the first kind. This relationship has been instrumental in establishing a number of recursion formulae for theJ-integrals applicable to the case of an annular eclipse. It was found that some recursion formulae hold both for the case of a partial and annular eclipse.The appropriate use of these recursion formulae should facilitate any numerical computation for eclipsing binaries.  相似文献   

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