1 Introduction

New winds are blowing from hot massive stars. The development of new model atmosphere codes during recent years (Hubeny & Lanz 1995; Santolaya-Rey et al. 1997; Hillier & Miller 1998; Pauldrach et al. 2001) employing improved numerical techniques and detailed atomic models offers the opportunity to derive more realistic stellar parameters that can be used for the research of astrophysical problems. Thus very recently Martins et al. (2002) have presented a new temperature scale for massive O dwarfs that lowers considerably the previous one given by Vacca et al. (1996) as a result of strong metal line blanketing. The effect should be even larger for supergiants, where strong mass-loss should add to metal line opacity to yield even smaller effective temperatures. First indications of this behaviour were obtained for example by Crowther & Bohannan (1997), Herrero et al. (2000) or Fullerton et al. (2000). More recently, Crowther et al. (2002) have presented an analysis of 4 supergiants in the LMC and the SMC with similar trends and Bianchi & García (2002) obtain comparable results for O6-O7 stars in the Milky Way.

The stellar masses of O stars are still a subject of debate. A large part of the uncertainty originates from the so-called mass-discrepancy (Herrero et al. 1992): masses derived from a spectroscopic analysis using hydrostatic, plane-parallel model atmospheres are systematically lower than those predicted by non-rotating evolutionary models. Unified model atmospheres are expected to reduce the discrepancy, especially if new evolutionary models account for rotationally induced mixing in stars (Herrero et al. 2000; Meynet & Maeder 2000). To this end, considerable effort has been made in the last decade to account for the possibility of He enriched and CNO contaminated atmospheres in early type stars. Efforts to improve the derived abundances have lowered them, but without completely ruling out He enhancements (Villamariz et al. 2002).

On the other hand, the presence of a wind momentum-luminosity relation (WLR) for hot, massive stars offers the unique opportunity to derive stellar distances directly from the analysis of the observed spectra with an accuracy of about 10$\%$ (Kudritzki et al. 1999). For this purpose, the coefficients in the relation

$$\begin{eqnarray*}{\rm log} (\dot M V_\infty R^{0.5}) \approx \frac{1}{\alpha^\prime} {\rm log} L + C = x~ {\rm log} (L/L_\odot) + {\rm log} D_0 \end{eqnarray*}$$

have to be calibrated as function of metallicity and spectral type. For O-stars, this has been done by Puls et al. (1996) for Galactic and MC objects. However, their WLR shows a large scatter, especially for non-supergiants. It is reasonable to assume that part of this scatter results from uncertainties in the individual stellar distances, as their sample was mainly taken from Herrero et al. (1992), aiming at targets with large apparent brightness.

Following this idea, we started a programme to calibrate the WLR using a more homogeneous sample of OB supergiants, all of them belonging to the same OB association. From this approach we expected to reduce the scatter in the derived WLR. The OB association chosen was Cyg OB2, and the optical observations and first analysis using plane-parallel, hydrostatic models were presented in Herrero et al. (1999). The required wind terminal velocities were obtained from HST STIS observations and are discussed in Herrero et al. (2001).

By means of spherical, mass-losing models we will derive here an improved WLR for those Cyg OB2 supergiants that were observed with the HST. (One of the stars, Cyg OB2 #4, is actually a luminosity class III object, but we will refer to our sample as Cyg OB2 supergiants. When required, we will emphasize the difference.)

This effort is being complemented in our group by other studies to calibrate the WLR in the Local Group (see McCarthy et al. 1997; Urbaneja et al. 2002; Bresolin et al. 2002 for M 31 and M 33).

The remainder of this paper is organized as follows. In Sect. 2 we describe the characteristics of the code we have used, and in Sect. 3 we present an analysis of the O9 V star 10 Lac as a test case. The analyses of our targets is given in Sect. 4, and we end with a discussion of our results in Sect. 5 and the conclusions in Sect. 6.