## 2. Static case and nomenclatureThe aim of our diffusion calculations is to derive simple expressions for the radiative flux and radiative acceleration at positions far away from the surface in a medium -
(i) that is optically very thick, -
(ii) in which the extinction coefficient hardly varies over a photon mean free path, and -
(iii) in which the variation of the source function can be approximated by a linear function in the neighborhood of the point where the radiative quantities are to be calculated.
For this purpose we start with the general form of the transfer
equation for a Here with (cf. Oxenius 1986). We introduce which are mostly used throughout this paper in place of the usual wavelengths in order to obtain Doppler shifts that depend only on spatial coordinates and angles. Then , . In the diffusion limit, the mean intensities are very close to the
In the following we need also the wavelength-integrated Planck function denoted by with being the Stefan-Boltzmann constant, the spatial derivatives of and , respectively, with , and the weighting function This weighting function, which enters the Rosseland mean opacity
(Eq. (19)), is normalized according to
and is
In terms of these quantities the source function in the neighborhood of can be written - see assumption (iii) above - as are sufficiently In order to clarify the nomenclature, we present the relevant
## 2.1. Radiative fluxis obtained by integration over all wavelengths from the vector of
the It is evident from Eq. (12) that the essential physics is contained
in the ## 2.2. Radiative accelerationThe vector of the net radiative acceleration (force per unit
volume) has the same direction as that of the flux so that the
being the ## 2.3. Static radiative quantities in the diffusion limitFor a static medium we find from the well-known solution of Eq. (1) along a ray at a position well inside the medium The wavelength-integrated flux can be expressed in terms of the
(static) with being the weighting function given in Eq. (8). Then we obtain from Eqs. (14) and (18) the classical result of Rosseland (1924). According to Eq. (17) the expressions for the radiative acceleration become and according to Eqs. (15) and (16) © European Southern Observatory (ESO) 2000 Online publication: July 7, 2000 |