## Radiation hydrodynamics with many spectral lines## Analytical expressions for a differentially moving slab
^{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
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 , the spectral thickness. It is shown that is much smoother than the extinction coefficient 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 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 . 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.
## Contents- 1. Introduction
- 2. Radiative transport
- 3. Spectral thickness
- 4. Wavelength-integrated radiative quantities
- 5. Piecewise linear approximation of
- 5.1. Direct integration
- 5.2. Rational approximation
- 6. Basic effects of the motion upon radiative quantities
- 7. Discussion and outlook
- Acknowledgements
- Appendix
- References
© European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |