首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 31 毫秒
1.
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.  相似文献   

2.
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   

3.
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   

4.
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.  相似文献   

5.
The aim of the present paper will be to extend the Fourier methods of analysis of the light curves of eclipsing binaries, outlined in our previous communication (Kopal, 1975) in connection with systems whose components would appear as uniformly bright discs, to systems whose components exhibit discs characterized by an arbitrary radially-symmetrical distribution of brightness —i.e., an arbitrary law of darkening towards the limb — be it linear or nonlinear.In Section 2 which follows a few brief introductory remarks, fundamental equations will be set up which govern the light changes arising from the mutual eclipses of limb-darkened stars — be such eclipses total, partial or annular; and Section 3 will contain a closed algebraic solution for the elements of the occulation eclipses terminating in total phase. Such a solution proves to be no more complicated than it turned out to be for uniformly bright discs in our previous paper; and calls for no special functions for the purpose — as will be put in proper perspective in the concluding Section 4.The cases of transit eclipses terminating in an annular phase, of partial eclipses of occulation or transit type, will be similarly dealt with by Fourier methods in the next paper of the present series.  相似文献   

6.
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.  相似文献   

7.
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.  相似文献   

8.
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   

9.
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   

10.
In the present paper n 0 , for occulation and transit eclipses of partial phases, are evaluated numerically by means of the Runge-Kutta methods. Section 2 contains the required differential equations of n 0 with respect to the modulusX orC, and Section 3 includes the numerical method of the solutions of these differential equations. Theoretical values of 0 0 and 1 0 , with corresponding values ofC, are also added in this section.  相似文献   

11.
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   

12.
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.  相似文献   

13.
The aim of the present paper will be to pioneer a new approach to the analysis of the light changes of eclipsing binary systems in the frequency domain, and to point out its merits in comparison with a conventional treatment of the same problem in the time-domain which has been developed so far. Following an introductory section in which the broad features of our problem will be set forth, Section 2 will contain an outline, and critique, of the time-domain approach. Section 3 will give an explicit treatment of the light changes arising from total and annular eclipses in the frequency domain — a problem which we succeeded in solving in close algebraic form. Section 4 will extend this treatment to the case of partial eclipses; and in the concluding Section 5 the relative merits of our new results will be discussed in broader perspective. Sections 3 and 4 contain explicit results pertaining to mutual eclipses of spherical stars exhibiting uniformly bright discs. An extension of these results to the case of arbitrary limb-darkening, and taking account of mutual distortion of both components, will be given in subsequent communications.  相似文献   

14.
The theoretical values of the momentsA 2m for any type of eclipses, expressed in terms of the elementsL 1,a andc 0, have been derived in the simple forms of rapidly convergent expansions to the series of Chebyshev polynomials, Jacobi polynomials and KopalJ-integrals (Kopal, 1977c) and hold good for any real (not necessarily integral) value ofm0.The aim of the present paper has been to establish explicit expressions for the Jacobian and its fast enough computation in the light changes of close eclipsing systems, arising from the partial derivative of different pairs ofg-functions (Kopal and Demircan, 1978, Paper XIV) with respect toa andc 0 2 , for any type of eclipses (be these occultations or transit, partial, total or annular) and for any arbitrary degreel of the adopted law of limb-darkening. The functional behaviour of this Jacobian would determine the reasonable light curve in connection with geometrical determinacy of the parametersa andc 0. In the expansion of Jacobian, the terms consist of two polynomials which satisfy certain three-term recursion relations having the eclipse parametersa andc 0, as their arguments.Closed form expressions forf-functions, as well as of the Jacobian (e.g.,m=1, 2, 3), obtaining in the case of total eclipses, are given for a comparative discussion with the theoretical values of Jacobian derived from partial derivative of different pairs ofg-functions.The numerical magnitude of Jacobian would determine the best combination of the momentsA 2m in the different pairs ofg-functions and definite results would follow in the subsequent paper of this series (Edalati, 1978c, Paper XXIV).  相似文献   

15.
The aim of the present paper has been to generalize the methods previously developed for analysis of the light changes of eclipsing binary systems in the frequency-domain to cases in which the components of such systems revolve in eccentric orbits. It is shown that these methods can indeed be generalized to systems with eccentric orbits provided that the light momentsA 2m deduced from such eclipses are suitably re-defined in terms of the true, rather than mean, anomaly in the relative orbit; and that due attention is paid to the unit of length in terms of which the fractional radii of the two stars are expressed. When this is done the Fourier methods continue to be applicable to all types of eclipses exhibited by eccentric binary systems — whether these are occultations or transits; total, annular or partial.An application of these methods to practical cases has been postponed for a subsequent communication.  相似文献   

16.
A new method has been developed for the evaluation of the light momentsA 2m, required for a Fourier analysis of the light curves of eclipsing variables, in terms of the elements of the eclipsea method simpler and more straightforward than that previously developed in so far as it dispenses with the auxiliary coefficientsa n (l) andb n (l) used before at the intermediary stage. Our present method is applicable to an analysis of the eclipses of spherical stars of any type, arbitrarily darkened at the limb; and its results agree with those previously established in Papers III and IV of this series in less explicit form.  相似文献   

17.
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   

18.
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.  相似文献   

19.
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.  相似文献   

20.
The aim of the present paper will be to detail the procedure outlined in our previous investigations (Kopal, 1975; Kopalet al., 1976) for a solution of the elements of distorted eclipsing systems by a Fourier analysis of their light changes. This procedure—which constitutes an equivalent, in the frequency-domain, of rectification hitherto practised in the time-domain — should enable us to free the observed momentsA 2m of the light curves from all photometric effects of distortion (between minima as well as within eclipses) — a feat impossible in the time-domain except under very restricted conditions — and thus to make it possible to obtain the geometrical elements of the eclipses which should be free from any obvious source of systematic errors.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号