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Astron. Astrophys. 333, 678-686 (1998)

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5. Discussion

In this work we presented a thermo - radiative mechanism which is able to create steady state shells in optically thin stellar atmospheres. This mechanism is based on the Paper II analytical 2 - D solution and the analysis of CM for the thin radiative force. The shell is formed in the supersonic region of the outflow. The results show that early and late type superluminous supergiants are expected to create massive shells in their envelopes even if the opacity in thin lines is smaller than the continuum opacity. This happens because these stars are close to their Eddington limit. Stars which are closer to the main sequence can possess shells with the same mechanism but with larger line opacity.

This mechanism is insensitive to stellar rotation. So, the stars do not have to rotate close to the Keplerian-speed limit. The centrifugal force is negligible in most applications, so, the mechanism applies similarly to fast and slowly rotating objects.

The thermal driving used for early type stars does not produce enormous temperature close to the stellar surface. The corona-like region is very thin ([FORMULA] for the example of 4.2, [FORMULA] for the P Cyg example of 4.4) and the maximum temperatures are bounded by the value [FORMULA]. This is in accordance with Hearn (1975a,b), Lamers & Snow (1978), Cassinelli, Olson & Stalio (1978), Olson (1978), Cassinelli & Olson (1979) (Sect. 3). We note that possible incorporation of non-thermal driving mechanisms in the inner acceleration region will decrease the temperature values, and this will be a subject for future work.

Concerning the observed shell variabilities we have to note that they cannot be modeled by the present steady state solutions. On the other hand, the present shells depend upon the balance of the thin radiative force with gravity as well as the differential rotation of the fluid. If the radiative parameters change during the life of the star the shells may appear or disappear at several distances. The transition between these situations needs time - dependent HD, but, if the time periods between them are large enough the final stages of shell creation can be described by the present model as steady state. As seen in Sect. 4.2. this mechanism can either produce shells or double blobs beyond the poles. We note that the spectroscopic observations depend on the relative observer's direction. So, variabilities with periodicities correlated with the star's rotation may be appropriate to the present solutions. We also note that very massive shells with large opacity may cause deviations in the observed stellar mass and radius.

The adopted radiative force in this work decays monotonously with distance. If this force exhibit local maxima and minima the creation of multiple shells is also possible.

In the present work we study the dynamic nature of shells. The energetics of the outflow must also be studied. Just applying the [FORMULA] Law of Thermodynamics we find that the outflow must be heated very close to the stellar surface and it is cooled at all other distances (Paper II). The cooling is possibly radiative, so, emission lines are expected in the spectrum. The flow energetics as well as the spectrum formation, the thermodynamic conditions in the shell and ionization stages will be the subject of a forthcoming work. Another point for future work is the incorporation of the thick radiative force, using the Sobolev mechanism, in the inner acceleration region where the velocity gradients are significant. The inclusion of other driving mechanisms in the inner part of the envelope, such as magnetic driving, could also be considered.

Conclusively, steady shells are consistent with single fluid HD when the thin radiative force is important. This result concerns early and late type supergiants which usually exhibit shell characteristics and emission lines in their spectrum.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998