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

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1. Introduction

Strong spectral lines play a special role in the modelling of late-type stellar atmospheres because their cores are sensitive to the outer layers where poorly understood non-radiative heating processes affect the atmospheric structure (for a review, see Avrett 1990 ). The spectrum of H I plays a particularly important role, not only because it contains strong lines, but because the ionization balance of H I /H II in the outer atmosphere partly determines the atmospheric structure. In a recent series of papers, Doyle et al. (1994 ), Houdebine & Doyle (1994 ), Houdebine et al. (1995 ), and Houdebine et al. (1996 ) have explored the detailed line formation physics of the hydrogen spectrum in an extensive grid of chromospheric models of early M dwarfs. This monumental study includes an investigation of the response of the H I spectrum to atmospheric parameters and details of the chromospheric structure in models that span the entire range of observed activity level. This study provides a valuable guide to using H I lines as semi-empirical chromospheric diagnostics.

Among the modelling achievements and important results of the above study are the following: 1) the construction of low activity models that can reproduce the very weak H [FORMULA] absorption of the "zero H [FORMULA] " dM(e) stars and simultaneously reproduce the observed low surface flux of the Ca II HK and Mg II hk emission lines in these stars (Doyle et al. 1994 ); 2) the determination of constraints on the mass loading, ([FORMULA]), at the onset of the transition region at the top of the chromosphere (equivalent to determining the chromospheric pressure and the steepness of the chromospheric gradient or the thickness of the chromosphere for a given value of [FORMULA]), the temperature at the onset of the transition region (8500 K in most cases), and the thickness and functional form of the transition region that is required to simultaneously fit the self-reversed H [FORMULA] and H [FORMULA] emission line profiles and the ratio of Ly [FORMULA] to H [FORMULA] surface flux in the most active (dMe) stars (Houdebine & Doyle 1994 ); 3) the construction of a comprehensive grid of chromospheric models that successfully reproduces the observed morphology of the H [FORMULA] line in dM stars, from the lowest activity dM(e) stars to intermediate activity stars with either strong H [FORMULA] absorption or H [FORMULA] emission wings and an absorption core, to the highest activity dMe stars with strong H [FORMULA] emission. This grid has been used to derive chromospheric diagnostics by comparing the relative response of the various series of the H I spectrum (Lyman to Brackett) to changes in the structure of both the lower and upper chromosphere (Houdebine et al. 1995 ); and, 4) the modelling of the H emission continua and the hitherto unexpected realization that these continua, rather than the emission line spectrum, is the dominant coolant in the chromospheres of those stars with relatively hot [FORMULA] values, and that the excess H I continuum emission in the highest activity stars decreases the [FORMULA] colour to an extent that is observable (Houdebine et al. 1996 ).

In the present investigation, we refine the above study by including additional physics: line blanketing of the radiation field in the non-LTE treatment of hydrogen. In general, the cores of strong lines that form at relatively low gas densities high in the atmosphere differ greatly from those predicted by calculations done with the approximation of Local Thermodynamic Equilibrium (LTE) (see the review by Avrett 1990 ). As a result, the line under investigation may depend on radiative rates in other transitions of the atom, and these rates may be sensitive to the non-local radiation field. Therefore, a detailed description of the background radiation field may be important for an accurate solution of the non-LTE problem (see, for example, Mihalas (1978 )). The reduction of non-LTE over-ionization in the UV continua of Fe I in the Sun due to the inclusion of line veiling in the background radiation field is a particularly instructive example (Rutten 1988 ).

Many previous non-LTE calculations of chromospheric lines have ignored line blanketing in the background radiation field. Some have included photospheric line opacity only, as in the case of the H I and Na I study in chromospheric dM star models by Andretta et al. (1997 ) (ADB henceforth), or the non-LTE multi-line chromospheric modelling of g Her (M6 III) by Luttermoser et al. (1994 ). Because the Lyman and Balmer line series and the Lyman continuum form well above [FORMULA], the statistical equilibrium of hydrogen may be affected by blanketing due to lines that form in the chromosphere (and transition region in the case of Ly [FORMULA]) as well as blanketing due to photospheric lines. Therefore, we have used the recently developed PHOENIX model atmosphere code of Allard & Hauschildt (1995 ) to include line blanketing of the background radiation field throughout the entire outer atmosphere, taking into account the chromospheric and transition region temperature structure. We discuss the behavior of chromospheric and transition region line blanketing and assess its impact on the hydrogen equilibrium and line formation physics in chromospheric models.

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998