2 The code

The analyses presented here have been performed by means of the latest version of FASTWIND (an acronym for Fast Analysis of STellar atmospheres with WINDs), a code which was originally described by Santolaya-Rey et al. (1997) and was recently updated to include an approximate treatment of metal line opacity effects, i.e., metal line blocking and blanketing.

The code follows the philosophy of using suitable physical approximations allowing for a fast computational time, thus enabling us to calculate a large number of models (which are necessary to analyze stellar atmospheres with winds), while being realistic enough to preserve their value as a tool for determining stellar parameters.

It assumes a $\beta$-velocity law in the wind and calculates a consistent photospheric structure; the temperature structure is approximated using "NLTE Hopf functions'' as described in Santolaya-Rey et al. (1997); the coupling between the radiation field and the rate equations is treated within an ALI scheme, using local ALOs following Puls (1991). The program allows for a solution of the rate equations using either Sobolev or comoving frame calculations, but all calculations presented here were done using comoving frame. The formal solution to calculate the emergent profiles utilizes a radial micro-grid to account for the different scales involved and includes Stark broadening, which is a prerequesite for the analysis of O stars by means of H and He lines.

The approximate treatment of metal line blocking/blanketing will be described in detail by Puls (2002), in the following we will give only a brief summary. The basic philosophy to calculate the required NLTE metal opacities (bound-bound, bound-free and free-free) follows the line of reasoning given by Abbott & Lucy (1985), Schmutz (1991), Schaerer & Schmutz (1994) and Puls et al. (2000), however applying significant improvements. In particular and most important for realistic results, we have reformulated the equations of approximate ionization equilibrium (e.g., Puls et al. 2000, Eq. (43)) to account for the actual radiation field (as function of depth) at all ionization edges (including those from excited levels) and employ a consistent coupling of rate-equations and mean intensity, in a way similar to the ALI approach, to avoid any kind of Lambda Iteration.

The underlying atomic data base has been described by Pauldrach et al. (1998). In order to save computational effort, the resulting metal line opacities are averaged in a suitable way (mean of inverse opacities, in analogy to Rosseland means) over a frequency interval of order wind terminal velocity before the radiation transport is performed. Finally, flux conservation (and thus line blanketing) is obtained by adapting the NLTE-Hopf parameters in a consistent way. The method has been carefully tested by comparing the results with up-to-date methods, in particular with calculations performed with TLUSTY (Hubeny & Lanz 1995) for the case of dwarfs (see also the next section) and with WMBasic (Pauldrach et al. 2001) for the case of stars with winds.