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Fourier analysis of the light curves of eclipsing variables, III

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Abstract

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.

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References

  1. Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. G.: 1953,Higher Transcendental Functions, McGraw Hill Co., London and New York, Vol. 1.

  2. Kopal, Z.: 1942,Proc. Am. Phil. Soc. 85, 399 (Harvard Reprint Ser. II, No. 2).

  3. Kopal, Z.: 1947, Harvard Obs. Circ., No. 450.

  4. Kopal, Z.: 1959,Close Binary Systems, Chapman-Hall and John Wiley, London and New York.

  5. Kopal, Z.: 1975a,Astrophys. Space Sci. 34, 431 (Paper I).

  6. Kopal, Z.: 1975b,Astrophys. Space Sci. 35, 159 (Paper II).

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Kopal, Z. Fourier analysis of the light curves of eclipsing variables, III. Astrophys Space Sci 35, 171–183 (1975). https://doi.org/10.1007/BF00644831

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Keywords

  • Binary System
  • Fourier Analysis
  • Closed Form
  • Light Curf
  • Practical Case