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Astron. Astrophys. 320, 920-928 (1997)

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Radiation hydrodynamics with many spectral lines

Analytical expressions for a differentially moving slab

B. Baschek 1, 2, C. Grüber 1, W. von Waldenfels 3 and R. Wehrse 1, 2

1 Institut für Theoretische Astrophysik, Tiergartenstraße 15, D-69121 Heidelberg, Germany
2 Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany
3 Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany

Received 21 May 1996 / Accepted 5 September 1996


An analytical solution of the comoving frame radiative transfer equation for a differentially moving slab is obtained and written in terms of the wavelength-integrated extinction coefficient [FORMULA], the spectral thickness. It is shown that [FORMULA] is much smoother than the extinction coefficient [FORMULA] itself and that it can be well approximated e.g. by a simple piecewise linear function. Compared to conventional algorithms it allows speed-ups of factors [FORMULA] in the calculation of wavelength-integrated quantities such as e.g. the total flux, the radiative force, or the energy balance with an accuracy of [FORMULA]. The total number of lines which can be taken into account is essentially unlimited. A simple expression for the total flux in the diffusion limit is derived and the dependencies on the velocity gradient are discussed.

Key words: radiative transfer – hydrodynamics – methods: analytical

Send offprint requests to: B. Baschek, Heidelberg; E-mail: baschek@ita.uni-heidelberg.de

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998