Astron. Astrophys. 354, 193-215 (2000)

8. Conclusions and future work

We have presented the spectra of seven Galactic luminous O stars, that have been analysed by means of non-LTE, plane-parallel, hydrostatic model atmospheres, including line-blocking, and by means of spherical, mass-losing models. We have used these analyses to study some additional effects (physical as well as due to applied approximations) that have an influence on the results.

We have shown that line-blocking has to be taken into account when analysing very hot stars, in plane-parallel as well as in spherical models with mass-loss. Line-blocking indirectly affects the spectral-line diagnostics through changes in the level populations of He. Although for the spherical models with mass-loss we only made simulations, this is clearly one direction for future model improvements. In particular, we obtained very interesting results concerning the He II 4686 line and the blue wing of (actually, concerning the corresponding He II blend).

One of the conclusions of the present paper is that around 50 000 K (the exact value depending on gravity) we reach the limit of applicability of plane-parallel, hydrostatic models to real massive stars. This conclusion can be further refined, if we take into account the fact that line-blanketed models could give lower temperatures, or if we consider that spherical models with mass-loss will demand larger gravities. The final result would be models less affected by radiation pressure, larger masses and a cooler temperature scale.

Spherical models with mass-loss are thus needed to analyse these stars. We had to correct the gravities of all stars (except HD 5 689) when using these models, sometimes with increments as large as 0.25 dex. Part of the differences in the stellar parameters derived from both sets of models are due to a change in the preferred temperature indicator.

Our spherical models with mass-loss are also still not free from internal inconsistencies. For some models with strong winds, we see that He II 4200, 4541 give different temperatures, although we expect that inclusion of line-blocking will reduce this discrepancy, and will strongly improve the fits of He II 4686 and the blue wing of . We have also found that for stars with strong winds there is a difference in the mass-loss rates derived from and , that can reach a factor of two. We do not find good agreement with the two cases for which we have mass-loss rates from radio fluxes, although it is not possible to derive any firm conclusion from this fact.

The helium and mass discrepancies found here are in agreement with the findings of Paper I. The only difference is that we find a mass discrepancy also for luminosity class V stars, but this is actually misleading. What we find is that the luminosity class V stars analysed here have gravities lower than usual for their spectral classification. The conclusion of Paper I should then be changed to state that we do not find the mass discrepancy for stars with high gravities. At least a part of this effect is attributed to the fact that the intense radiation field affects the wings of the Balmer lines also for these stars. An additional possibility is that they actually never reach the zero-age main sequence (see, for example, Hanson 1998).

Spherical models with mass-loss largely reduce the mass discrepancy. Without solving it completely, the problem lies now in the systematic trend of spectroscopic values to be lower than evolutionary ones, but most of the individual values now agree within the formal error bars. We have also shown that the spectroscopic masses agree better with the predictions from the radiatively driven wind theory, because they give ratios of the terminal wind velocity to the escape velocity (or equivalently, values of the line force parameter) that are in the range predicted by that theory.

From the point of view of individual stars, we have analysed some of the most massive and luminous stars in the Milky Way. We have found that three of them (Cyg OB2 7, HD 15 570 and HD 15 558) have particularly large initial masses, around or in excess of 100 (depending on the technique used for the mass derivation). Cyg OB27, HD 14 947 and HD 210 839 have so extreme mass-loss rates that the wings of are strongly affected, and in HD 15 570 the wind is so strong that the exercise of deriving the gravity from the wings of results in highly uncertain values. On the other hand, we find that HD 5 689, the less luminous object in our sample, could have been wrongly assigned to Cas OB7, and might be a runaway star.

© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000
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