Lettre de l'OHP - No.14

Chromospheres of cool main-sequence stars

E.R. Houdebine
Space Science Department, ESA-ESTEC

The solar outer atmosphere (chromosphere, transition region, corona) has been extensively investigated, observationally and theoretically, but it is however only one star. One must understand the "chromosphere-corona'' phenomenon as a whole; an ambitious endeavour which comes through the study of its closest equivalents, the main-sequence dwarfs.

Recently, we performed NLTE-radiation transfer calculations of chromospheric spectral lines for M-G type stars that have lead to a number of theoretical predictions. Those results can easily be tested with high resolution spectroscopic observations. We carried out such observations at Observatoire de Haute Provence with the Elodie echelle spectrograph. They successfully confirm our models and further show that surface magnetic activity is directly dependent on the stellar luminosity, an important constraint for stellar dynamo models.

Magnetic activity gives rise to a number of variable phenomena in pre-main sequence stars, main sequence stars and binary systems for instance. Notably, flares and hot and dense outer atmospheres are most commonly observed. In fact, Heidmann & Thomas (1980) showed that there are spectral evidence for non-thermally generated atmospheres on stars of all spectral types, and that we must understand the nonthermal "mass-flux/energy flux'' as a whole. For this, we need to investigate theoretically the formation of spectral lines in those atmospheres and compare to observations.

Among non-thermal mechanisms that sustain chromospheres, those of the so-called "magnetic activity'' type are the most widely spread after "acoustic heating''. Magnetic activity, most often of "solar type'', is also the most common source of stellar variability. It can affect stellar spectra throughout the wavelength range, from X-ray to radio emission, and on time scales varying from the second (flares) to the decade (magnetic cycles). It is common to a large variety of stars, including pre-main sequence stars, main sequence stars and binary systems. The most widely detected signature of magnetic activity is the chromospheric (and transition region) phenomenon. To progress along the lines commented above, here we report high resolution observations and the comparison to our models (Doyle et al. 1994; Houdebine & Doyle 1994abc, 1995; Houdebine et al. 1994, 1995).

Observations and results
Observations were obtained with the new Elodie echelle spectrograph mounted on the 1m93 telescope at OHP. This instrument covers a 3000Å spectral range from the near Ultra-Violet to the near Infra-Red at high resolution (R=45000), and is therefore ideally suited for the study of important spectral diagnostics such as the Balmer lines, the Ca II resonance doublet, Ca I 4227, 6572, He I 5875, 4026, 4471, Fe II~4233, Li I 6708, 6104 and Na I D1/D2.

We found the software very convivial and the spectrograph quite efficient. A significant advantage over other spectrographs of a similar class is the spectral coverage and the on line reduction procedure.

The formation of spectral lines in the outer atmosphere of stars is a quite complex problem because a number of parameters play simultaneously an important role;:e.g., magnetic activity, acoustic heating, surface gravity, metallicity, spectral type, binarity. So far, only quite inhomogeneous sets of observations have been gathered, which made it impossible to isolate and understand the effect of one given parameter. This also is responsible for the lack of discoveries of empirical correlations between various spectral signatures and not least, the important scatter in the correlation diagrams so far obtained. This is well illustrated in the Wilson-Bappu relationships, and it can be noted that the scatter increases sharply for the late type dwarfs, simply because magnetic heating becomes increasingly dominant.

Figure 1. H[[alpha]] profiles for a sample of stars in our program. This shows the effect of magnetic activity, from top to bottom: the line goes from strong emission to strong absorption and then weakens till almost zero equivalent width. This very successfully confirms our theoretical predictions.

To solve the problem, one needs a rigorous selection of objects in order to isolate the influence of only one parameter. Due to the relative faintness of M dwarfs, this is unfortunately not attainable with a 2m class telescope at all wavelengths, because there are too few targets of adequate magnitude. For this reason, we primarily selected stars with the same R-I color (R-I=0.875+/-0.05, M1 spectral type), which is the most precise color for M dwarfs, so as to isolate the effect of magnetic activity. In September 1994 we obtained high signal to noise spectra for 16 stars. We show a sample of these spectra at about H[[alpha]] in Fig.1.

Our sample is still rather inhomogeneous in the sense that we have so far not isolated various domains in metallicity nor surface gravity (luminosity). However, the former parameter is known to have little influence on the H[[alpha]] line (Houdebine & Doyle 1994), and the effect of surface gravity will be isolated when our observations are completed.

With those observations we have confirmed our theoretical predictions and further made additional discoveries. So as to give more statistical significance to our findings, we have searched the litterature for additional data (see Houdebine et al. 1995). Although it makes the whole set much less homogeneous it is still satisfying for the present investigation.We plotted the U-B, B-V, R-I colors (Eggen 1974; Upgren & Lu 1986; Bessel 1990; Weis 1991ab, 1993; Gliese 1991 catalogue from the IDL database library) against the H[[alpha]] equivalent widths in Fig. 2. Each parameter is plotted into two sub-diagrams, for H[[alpha]] in emission and absorption, and with the ordinate axis organised as suggested by our calculations in Paper~III (Houdebine & Doyle 1995). In these figures, the level of activity increases from left to right (not linearly).

Figure 2. Broad-band U-B, B-V and R-I colors versus H[[alpha]] equivalent width for a selected sample of M1 dwarfs with R-I=0.875+/-0.05. One can depict a significant UV excess for active stars with H[[alpha]] in emission only.

U-B decreases with increasing activity level which agrees with our calculations (Paper V, Houdebine et al. 1995). Absorption line stars have colors at about U-B=1.2 whereas for emission line stars it is centered at about 1.1, 0.1 magnitudes below. On the contrary, B-V and R-I colors do not exhibit such trend: for B-V, the averages are 1.47 and 1.48 respectively for emission and absorption line stars. Moreover, the scatter in U-B is much larger than those in B-V and R-I, and higher than measurement uncertainties. This is in agreement with the variable nature of surface magnetic activity.

We show in Fig. 3 the H[[alpha]] FWHM and the stellar visual luminosity versus the H[[alpha]] equivalent width. There is a good correlation of the FWHM with Ha EW (activity level) that confirms our numerical calculations (Papers I and III). We can recall that for these stars (dM1 and a narrow spectral domain), this effect should be due to radiation transfer (radiative damping, see Paper III) and not chromospheric turbulence nor rotation (see Paper I). There should also be little or no dependence on metallicity and spectral type, which explains the tighter correlation. Instead, the main sources of the scatter here are surface inhomogeneities and surface gravity.

In Paper III, our model chromospheres gave H[[alpha]] equivalent widths from 0.60Å to -40Å for Series I and from 0.52 to -29Å for Series II. If one excludes the three rather peculiar stars MCC 169, MCC 69 and Gl 153B, all observations except one star (Gl 134) give absorption equivalent widths smaller than 0.52Å. This is in excellent agreement with our calculations (we recall that Series~II models describe better absorption line stars). Emission line stars have H[[alpha]] equivalent widths up to -3.3Å. Along the same lines, the full widths half maximum (FWHM) agree also well with the predicted values. The larger scatter suggests increasing inhomogeneity at the chromospheric level.

Stellar luminosity - i.e. stellar size here - also increases with magnetic activity level. Although there is still a large scatter in the diagram we present, emission line stars are in average larger than absorption line stars. We obtain an average of Mv=9.26 and Mv=9.74 respectively, which is a significant difference of 0.5 magnitudes. This is an important constraint for dynamo mechanisms. From our own data, we suspect the same trend for absorption line stars only, although this needs to be confirmed with highly selected stars and good observations.

Figure 3. H[[alpha]] FWHM and visual absolute magnitude versus H[[alpha]] EW. The FWHM show a tight correlation with EW, in good agreement with our theoretical predictions (Paper I and III). Also, an interesting result for stellar dynamo is that surface magnetic activity increases with the stellar luminosity (proportional to its size here)

The rather large scatter is probably due to the non-homogeneous combinations of starspots and plages and intrinsic variability in the level of magnetic activity (photometric and spectroscopic observations were obtained years apart). The large variability in H[[alpha]] is well illustrated by Gl 908 which changed in equivalent width from 0.360Å in 1989 to 0.509Å in 1994. There is also some problems in defining the "continuum level'' in those stars and some photometric uncertainty. In addition, metallicity and surface gravity are not homogeneous in our sample and are significant respectively for the stellar broad-band colors and Balmer series formation.

Nevertheless, our observations confirm quite well our modelling of late type M dwarfs. They further emphasize that a rigorous approach in the observations of stellar spectroscopic signatures is the only way around the problem. One just has to make the correct observations and we believe this will yield tens of empirical relationships as important as that of Wilson-Bappu!

Acknowledgements. This work was supported by a Research Fellowship at the ESA Space Science Department at ESTEC.

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