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
Article
  • 34 Downloads

Abstract

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.

Keywords

Radiation Energy Transfer Binary System Mathematical Formulation Radiative Energy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chandrasekhar, S.: 1933,Monthly Notices Roy. Astron. Soc. 93, 539.Google Scholar
  2. Chandrasekhar, S.: 1934,Monthly Notices Roy. Astron. Soc. 94, 444.Google Scholar
  3. Chandrasekhar, S.: 1944,Astrophys. J. 99, 180.CrossRefGoogle Scholar
  4. Chandrasekhar, S.: 1945,Astrophys. J. 101, 95.CrossRefGoogle Scholar
  5. Chandrasekhar, S.: 1950,Radiative Transfer, Clarendon Press, Oxford.Google Scholar
  6. Eddington, A. S.: 1926,The Internal Constitution of the Stars, Cambridge University Press, Cambridge, Ch. XII.Google Scholar
  7. Gratton, L.: 1937,Mem. Soc. Astron. Ital. 10, 309.Google Scholar
  8. Hopf, E.: 1934,Mathematical Problems of Radiative Equilibrium, Cambridge University Press, Cambridge.Google Scholar
  9. Kopal, Z.: 1980,Astrophys. Space Sci. 70, 407.CrossRefGoogle Scholar
  10. Kopal, Z.: 1989,The Roche Problem, Kluwer Academic Publishers, Dordrecht, Holland.Google Scholar
  11. Kopal, Z.: 1990,Mathematical Theory of Stellar Eclipses, Kluwer Academic Publishers, Dordrecht, Holland.Google Scholar
  12. Kopal, Z. and Zafiropoulos, F.: 1983,Astrophys. Space Sci. 91, 299.CrossRefGoogle Scholar
  13. Kourganoff, V.: 1952,Basic Methods in Transfer Problems, Clarendon Press, Oxford.Google Scholar
  14. Kozyrev, N. A.: 1934,Monthly Notices Roy. Astron. Soc. 94, 430.Google Scholar
  15. Menzel, D. H. and Pekeris, C. L.: 1935,Monthly Notices Roy. Astron. Soc. 96, 77.Google Scholar
  16. Milne, E. A.: 1926,Monthly Notices Roy. Astron. Soc. 87, 43.Google Scholar
  17. Rosseland, S.: 1926,Astrophys. J. 63, 342.CrossRefGoogle Scholar
  18. Schwarzschild, K.: 1906,Göttingen Nachr., Math.-Phys. Klasse, p. 41.Google Scholar
  19. Schuster, A.: 1905,Astrophys. J. 21, 1.CrossRefGoogle Scholar
  20. Sobolev, V. V.: 1975,Light Scattering in Planetary Atmospheres, Pergamon Press, Oxford.Google Scholar
  21. Stebbins, J.: 1910,Astrophys. J. 32, 213.Google Scholar
  22. Unsöld, A.: 1938,Physik der Sternatmosphären, Julius Springer Verlag, Berlin, p. 89.Google Scholar
  23. von Zeipel, H.: 1924,Monthly Notices Roy. Astron. Soc. 84, 702.Google Scholar
  24. Wilsing, J. L.: 1890,Astron. Nachr. 124, 121.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

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

Personalised recommendations