Issue |
A&A
Volume 371, Number 3, June I 2001
|
|
---|---|---|
Page(s) | 1084 - 1096 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361:20010440 | |
Published online | 15 June 2001 |
Opacity distribution in static and moving media
1
Institut für Theoretische Astrophysik, Tiergartenstrasse 15, 69121 Heidelberg, Germany
2
Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany
3
Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany
Corresponding author: R. Wehrse, wehrse@ita.uni-heidelberg.de
Received:
11
January
2001
Accepted:
21
March
2001
The use of the conventional opacity distribution function
(ODF) to deal with very many
spectral lines is restricted to static media. In this paper,
its generalization to differentially moving media is derived
from the analytical solution of the comoving-frame radiative transfer
equation. This generalized ODF depends on only two parameters,
on the wavelength position (as in the static case) and in addition
on a wavelength interval Δ over which the line extinction
is averaged.
We present two methods for the calculation of the generalized
ODF:
(i) in analogy to the static case, it is derived from the mean
values of the extinction coefficients over wavelength intervals
Δ,
(ii) it is calculated under the assumption that the lines
follow a Poisson point process.
Both approaches comprise the conventional static case as the
limit of vanishing velocities, i.e. of .
The averages of the extinction for all values of Δ
contain the necessary information about the Doppler shifts and
about the correlations between the extinction at different
wavelengths.
The flexible statistical approximation of the lines by a Poisson point
process as an alternative to calculating the averages over all Δ
from a deterministic "real"spectral line list, has the advantage
that the number of parameters is reduced, that analytical expressions
allow a better insight into the effects of the
lines on the radiative transfer, and that the ODFs and their
corresponding characteristic functions can be calculated efficiently
by (fast) Fourier transforms.
Numerical examples demonstrate the effects of the relevant parameters
on the opacity distribution functions, in particular that with increasing
line density and increasing Δ the ODF becomes narrower
and its maximum is shifted to larger extinction values.
Key words: radiative transfer / spectral lines / opacity distribution function / stellar atmospheres / radiation hydrodynamics
© ESO, 2001
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