Astron. Astrophys. 359, 788-798 (2000)

The diffusion of radiation in moving media

II. Limits for large and small velocity gradients for deterministic lines

R. Wehrse ^1,3, B. Baschek ^1,3 and W. von Waldenfels <sup>2,3

1</sup> Institut für Theoretische Astrophysik, Tiergartenstrasse 15, 69121 Heidelberg, Germany
² Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany
³ Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany

Received 18 January 2000 / Accepted 27 April 2000

Abstract

The general formulae for radiative quantities in the diffusion limit for a differentially moving 3D medium which have been derived in Paper I of this series, are evaluated for the limiting cases of very large and very small velocity gradients . The extinction coefficient is specified by the continuum and the contribution of spectral lines which is formulated deterministically. For large w all radiative quantities can conveniently be calculated in terms of the spectral thickness, i.e. of the wavelength-integrated extinction coefficient, which can be well approximated by a piecewise linear function. For small w the radiative quantities are developed to the second order in w. The coefficients are essentially determined by the first two wavelength derivatives of the mean free path of the photons, i.e. of the reciprocal extinction coefficient. Since these depend on temperature, density and chemical composition only, they can be precalculated resulting in convenient expressions for hydrodynamic calculations. Examples are given for selected extinction coefficients such as a power-law continuum, a spectral edge, a single narrow line, and many, isolated as well as overlapping lines. In the non-overlapping case the lines contribute only in second order of w and the motions always lead to a decrease of the total flux whereas the radiative acceleration is unaffected. On the other hand, the effect of overlapping lines can only be determined by a detailed calculation for any specific extinction distribution. Furthermore, it is shown that the flux vector has components perpendicular to the temperature gradient if the latter is not parallel to the velocity vector.

Key words: diffusion radiative transfer stars: interiors stars: novae, cataclysmic variables stars: supernovae: general

Send offprint requests to: R. Wehrse (wehrse@ita.uni-heidelberg.de)

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Contents

• 1. Introduction
• 2. Basic expressions
  • 2.1. Monochromatic radiation flux
  • 2.2. Extinction coefficient
• 3. Limit of large w
• 4. Limit of small w
  • 4.1. Wavelength-integrated radiative quantities
  • 4.2. Effects of various extinction distributions
    • 4.2.1. Power-law continuum
    • 4.2.2. Spectral edge
    • 4.2.3. Single narrow line
    • 4.2.4. Many spectral lines
• 5. The flux vector in moving 3D media
• 6. Conclusions and outlook
• Acknowledgements
• References

© European Southern Observatory (ESO) 2000

Online publication: July 7, 2000
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