Astrophysics and Space Science

, Volume 186, Issue 2, pp 253–276 | Cite as

Radiative energy transfer in extended photospheres of the components of close binary systems

  • Zdeněk Kopal


The aim of the present paper will be to set up, and solve, the equations governing transfer of radiation in semi-transparent envelopes of the stars; and, in order to do so, to employ a system of curvilinear (non-orthogonal) three-dimensional coordinates in which the radial coordinate has been identified with equipotential surfaces. Such coordinates are particularly suitable to a treatment of the problems arising in close binary systems, which render the outcome more than any other amenable to observable tests, but which has so far received but very scant attention.

The introductory section of this paper will contain a statement of the problem; and its mathematical formulation in terms of Clairaut coordinates (cf. Kopal, 1980, 1989, Chapter V) will be outlined in Section 2; their methods in Section 3. Section 4 will then contain an application to the problem of distribution of surface brightness (‘limb-darkening’) over the apparent discs of distorted components of close binary systems; while in Section 5 we shall do the same for radiative flux of distorted stars as a function of the phase (‘gravity darkening’).

The concluding Section 6 will then contain an outline of additional problems arising in this connection, to which we shall turn in successive parts of this series.


Radiation Energy Transfer Binary System Mathematical Formulation Radiative Energy 
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Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Zdeněk Kopal
    • 1
  1. 1.Department of AstronomyUniversity of ManchesterEngland

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