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Astron. Astrophys. 326, 249-256 (1997)

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1. Introduction

Two thirds of the stars in the Milky Way are M dwarfs. Altough their individual masses are small, they account, due to their large number, for half the total mass of main-sequence stars, or about 20% of the luminous mass of the galaxy. Apart from their intrinsic interest, the similarity between solar activity and M dwarf activity suggests that a comparative study can be very valuable for our understanding of phenomena like chromospheric and coronal heating, stellar activity and dynamos.

Generally, dwarf M stars are divided in two subclasses according to whether the Balmer lines are in emission or not. This distinguishes the emission dMe stars from the non-emission dM stars. The presence, in both types, of many atomic lines and molecular bandheads in absorption, proves the existence of a cool photosphere, whereas the fact that M dwarfs show an emission core in the Ca II resonance lines implies that they have a chromosphere. The difference between the spectra of dM and dMe stars is most likely due to a different chromospheric structure as occurs in quiet and active regions on the Sun.

For a thorough understanding of the atmospheric structure of these stars, complete chromospheric models are needed. Grid of photospheric models for dM stars (from the deep photosphere up to approximately the temperature minimum) were computed by Mould (1976) and more recently by Brett (1995) and Allard and Hauschildt (1995).

The first attempts to model the chromosphere of dM stars where those by Cram & Mullan (1979), who assumed very schematic chromospheric models and studied the response of the emitted Balmer lines to changes of different atmospheric parameters. They found that, as the temperature gradient in the chromosphere increases, the very weak [FORMULA] line predicted for a star with an isothermal chromosphere first becomes an increasingly strong absorption line, then gradually fills in and eventually goes into emission as the chromospheric temperature increases further.

Giampapa et al. (1982) constructed homogeneous models in a similar way, to explain the profiles of the Ca II K line for some representative dMe and dM stars. They found that their models did not predict the right flux for the Mg II resonance lines, and concluded that the assumption of a homogeneous chromosphere was unrealistic.

Houdebine and Doyle (1994a), and Doyle et al. (1994) recently presented grids of atmospheric models, which were merged in Houdebine et al. (1995). They studied the influence of the atmospheric structure on the hydrogen and Ca II line profiles. Houdebine and Doyle (1994b) applied this modelling to the dM2.5e star AU Mic. They obtained very good agreement with the observed profiles for [FORMULA] and [FORMULA], but they had to add an arbitrary constant to their computed profiles, in order to match them with the observations. In their model, the position of the transition region is fixed to obtain a ratio between the [FORMULA] and the [FORMULA] flux of about 1.1, as was found by Doyle et al. (1990). However, they treated [FORMULA] assuming Complete Redistribution, which has been shown to be a rather poor approximation (e.g. Vernazza et al. 1981).

Hawley & Fisher (1992) computed a theoretical model of the quiescent atmosphere of AD Leo (Gl 388) from the photosphere to the corona. The structure of the corona and the transition region is computed for a loop of length L = 1010 cm and an apex coronal temperature of 3 106 K, in hydrostatic and thermal equilibrium. The photosphere is taken from the grid of models by Mould (1976). The chromosphere is a linear log T - log m interpolation (where m is the column mass) joining the transition region and the photosphere. They use this model only to determine the quiescent heating rate necessary for the computation of flare models and their results do not fit very well the observed spectral features of the quiet star.

In Paper I of this series (Mauas & Falchi 1994) we presented a semiempirical model for the dM3.5e star AD Leo, computed to match a wide set of observations. We obtained very good agreement for the continuum level, the first four Balmer lines, the Na D and infrared lines and the Mg II flux. However, the agreement was not so good for the Ca II K line profile, and for the [FORMULA] flux, for which we found a difference between the observed and computed features of about a factor of two. The resulting model was used in Paper II (Mauas & Falchi 1996a) as the base for modelling a large flare on the same star.

We believe the approach of semi-empirical modelling, where an atmospheric model is constructed to find the best possible agreement between the computed profiles and a large number of observations, is the one that gives the best results to eliminate the uncertainties found when only a few lines (generally [FORMULA] or Ca II K) are matched. In a future paper (Mauas & Falchi 1997, Paper IV), we will discuss this problem in detail.

In this paper we present models for two other dM stars, Gl 588 and Gl 628, with photospheric characteristics similar to AD Leo, resulting in very similar colours for the three stars, and we compare the results with the model obtained for AD Leo in Paper I, slightly modified to account for a new set of atomic parameters for the hydrogen model atom.

As Gl 588 and Gl 628 are non-emission stars we expect that the comparison between the chromospheres of the three stars can help understand the mechanisms of chromospheric heating. In particular, we want to understand whether different levels of activity are related to a different chromospheric structure, and/or to different filling factors by a "plage" component, embedded in the same chromosphere (Robinson et al. 1990).

In Sect. 2. we give the stellar parameters of the sample stars, and discuss the observations. In Sect. 3. we explain how the modelling was done, and in Sect. 4. we present the computed models, and compare the predicted and observed spectral features. In Sect. 5. we discuss the energy requirements of the models. Finally, in Sect. 6. we discuss the results.

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998