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Astron. Astrophys. 326, 287-299 (1997)

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4. Conclusion

The predicted [FORMULA] of the Ly [FORMULA] emission line is strongly reduced, and that of the H [FORMULA] emission line in active (dMe) stars is strongly enhanced by the inclusion of line blanketing in the background opacity in the non-LTE hydrogen calculation. In less active stars only Ly [FORMULA] is significantly affected. Furthermore, to calculate [FORMULA] for Ly [FORMULA] accurately, the calculation of [FORMULA] must be consistent in that it must reflect the chromospheric and transition region temperature rise. The calculated Pa [FORMULA] line is negligibly affected by the inclusion, and particular treatment, of [FORMULA]. We conclude that a careful teatment of background opacity is important when using H [FORMULA] to model relatively active dM stars and flares, or when using Ly [FORMULA] emission relative to the local continuum as a diagnostic.

The inclusion of [FORMULA] raises [FORMULA] in the Lyman continuum in the lowest pressure models, and raises [FORMULA] in the Balmer continuum for [FORMULA] in the highest pressure models, by a factor of [FORMULA]. In both cases, line blanketing directly causes a slight rise in [FORMULA] in the region where [FORMULA] is maximal. This, combined with a partial decoupling of [FORMULA] from [FORMULA], leads to the increase in [FORMULA]. This suggests that, in these spectral regions, [FORMULA] is a net source of emission and contributes positively to [FORMULA]. Furthermore, the thermal treatment of [FORMULA] strengthens the coupling of [FORMULA] to [FORMULA] in the upper chromosphere where [FORMULA] is increasing rapidly and this also causes the value of [FORMULA] to be larger in the case of line blanketing.

We confirm two of the most important results of Houdebine et al. (1996 ): the photometrically detectable influence of the highest pressure chromospheres on the U band flux, and the dominance of the continuum in the radiative cooling of the chromosphere. We disagree with the results of Houdebine et al. (1996 ) in detail in that we find that the continuum dominates the cooling for all models with [FORMULA] in the 2600 to 3000 K range, whereas they find that the continuum dominates only in the case of models at the hot end of the range. In either case, this result has important implications for the general problem of chromospheric heating because it greatly changes the estimated energy budget of the outer atmosphere. If this result is correct, and comparison with the observational analysis of Amado & Byrne (1997 ) suggest that it is, then proposed heating mechanisms must supply at least an order of magnitude more non-radiative heating to the chromosphere than would be needed in the case of an energy analysis based only on lines.

An important caveat to these conclusions is that the emergent UV flux in late type stars in known to be sensitive to non-LTE effects in the background opacity of both lines and continua. We have estimated the size of the expected effect in both cases for one of the models in our grid, crudely for the case of [FORMULA] continua. These non-LTE effects must be calculated more accurately for the entire grid of models before the role of continuum emission in the chromospheric energy budget can be assessed precisely.

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998
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