## 4. Results## 4.1. Individual stars## 4.1.1. Gl 212
Alonso (1996) used the Infrared Flux Method and
ATLAS9 (Kurucz 1990) models to measure
and found 3832 K. He adopted values of
and equal to 5.0 and 0.0,
respectively. Spectral types of dM1, dM2.5, and dM2 have been reported
by Poveda et al. (1994), Eggen (1996), and Rutten et al. (1989),
respectively. Measured emission fluxes in well known chromospheric
lines such as Ca II
We measure to be -0.40, which is stronger by
than the value of Stauffer & Hartmann
(1986). From Table 4 we see that the predicted value of
of H in
From Fig. 6 we see that models of Series
give rise to line profiles in which the core is
wider than those of Series . Also, within each
Series, the three models of lowest chromospheric pressure all give
rise to line profiles that are almost identical. Therefore, we cannot
expect the Na I
Both lines can be fit approximately with a model of Series
with a value of between
-5.2 and -5.6. Series models are ruled out by
the width of the Na I ## 4.1.2. Gl 382
Mathioudakis & Doyle (1991) give K and a spectral type of dM2. Eggen (1996) also reports a spectral type of dM2. Panagi & Mathioudakis (1993), Giampapa et al. (1989), and Mathioudakis & Doyle (1991) report integrated flux values for various chromospheric emission lines. Stauffer & Hartmann (1986) and Mathioudakis & Doyle (1991) give (H) equal to -0.37 and , respectively.
We measure to be , in close agreement with the value of of -0.37 measured by Stauffer & Hartmann (1986), but higher than the value of -0.23 measured by Mathioudakis & Doyle (1991). From Table 4 we see that, like Gl 212, all three of these measured values of indicate either between -5.6 and -5.2, or between -4.8 and -4.6. From Fig. 7, we see that the observed line profile is similar to that of Gl 212, but slightly weaker. Again, the closest fit is provided by a model of either series with between -5.6 and -5.2. However, in this case, models of both series with greater than -5.2 are ruled out by the narrowness of the observed line core. The measured temperature of Gl 382 is almost 300 K lower than that of our model (Mathioudakis & Doyle 1991). From the perturbation analysis of Fig. 3, we expect a model that is too hot to overpredict the strength of H in the low chromospheric pressure regime. Therefore, the values of derived here are lower limits.
From Fig. 8 we see that, for the low pressure models, the
model that is fit most closely by the shape of the inner wings and
that which is fit most closely by the contrast of the inner wing to
the core are even more discrepant than was the case for Gl 212.
However,
The closest fit value of found from the
Na I ## 4.1.3. Gl 388
Gl 388 (AD Leo) is a well known flare star (Pettersen 1991).
Giampapa et al. (1989) and Malyuto et al. (1997) report spectral types
of dM4Ve and dM4.5Ve, respectively. Fleming et al. (1995) report solar
metallicity, while Naftilan et al. (1992) found
from spectrum synthesis. Caillault & Patterson (1990) found
. Panagi & Mathioudakis (1993), Rutten et
al. (1989), Giampapa et al. (1989), Doyle et al. (1990), Pettersen
& Hawley (1989), Herbst & Miller (1989), and Elgaroy et al.
(1990) give measured flux values in a variety of chromospheric
emission lines including, variously, H,
Ly, Ca II The most extensive atmospheric modelling effort to date is that of
Mauas & Falchi (1996), who performed two component,
chromospheric/TR modelling in the
approximation of the
We measure to be ,
which falls between the values of 2.7 and 4.0 found by MacMillan &
Herbst (1991) and Pettersen & Hawley (1989), respectively. From
Table 4 we see that this range in can be
accommodated by a very narrow range of models in the grid as result of
the large sensitivity of
(H) to changes in
. Our observed value and that of MacMillan &
Herbst (1991) may be fit by a model of either series with
between -4.2 and -4.0. We measure the
The theoretical profiles have been rotationally broadened with a
value of equal to 5.6 km s
In Fig. 10, for models that have emission cores, the
Na I
Both lines have emission cores and, therefore, require high
pressure chromospheres. However, the value of
required by the H line is 0.4 dex lower in column
mass density than that required to fit Na I
. The discrepancy may in part be due to the high
sensitivity of the emission strength to small changes in
, especially in the case of
H, and in part due to the inaccuracy of the value
of used in the model, which limits the fit to a
derivation of an upper limit only on the value of
. The greater sensitivity of Na I
Mauas & Falchi (1994) derived a semi-empirical atmospheric
model of the quiescent state of AD Leo (henceforth the MF model) by
fitting several spectral features observed by Pettersen & Hawley
(1989) with synthetic spectra calculated with the
PANDORA (Avrett & Loeser 1992) model atmosphere
code: the over all continuum, the profiles of the first four members
of the Balmer series, Na I The chromospheric structure of their model is more general than ours in that it deviates from a straight line. However, the mean slope is close to that of our Series models. The location of in the MF model is close to that of our highest pressure model. The value of falls within the range spanned by our closest fit models, but the TR temperature rise of the MF model is much more gradual than that of ours. One possible reason for the discrepancies between the MF model and
ours is the difference in the spectral resolution of the data being
fit. We fit fully resolved profiles of emission cores, whereas the
data of Pettersen & Hawley (1989) have a resolution,
, of , which is not
sufficient to resolve the detailed shape of the line profile. For
example, the central absorption reversal of the H
emission core in dMe stars is a diagnostic of the TR slope (Houdebine
et al. 1995), and our Series model fits the
reversal approximately. By contrast, the observed
H spectrum used by Mauas & Falchi does not
resolve the central reversal. Similarly, the slope,
of the chromospheric temperature rise is
distinguished in our fitting by the presence or absence of a central
absorption reversal in the Na I Another reason for discrepancies in the chromospheric/TR structure
between our model and the MF model is the difference in the
photospheric structure of the two models. The photospheric temperature
structure of the MF model is flatter than ours, and we have already
seen from the perturbation analysis presented in Figs. 3 and
4 that the calculated profiles of chromospheric features depend
sensitively on the structure of the underlying photosphere. Because
Mauas & Falchi derived the structure of the Fig. 15 also shows the model of AD Leo of Hawley & Fisher
(1992) (henceforth the HF model). The photospheric base is provided by
a model of Mould (1976) that corresponds to
equal to 3500 K, equal to 4.75, and
equal to 0.0. The temperature structure of the
chromosphere and upper photosphere of this model was computed
theoretically by adopting a model for the overlying corona and
assuming that coronal X-ray illumination is the source of excess
heating in the outer atmosphere during quiescence. The energy
equilibrium structure is computed by balancing the coronal X-ray
heating against the radiative losses in the H I
spectrum and the Mg II The value of in the HF model is 0.2 dex less
than that of the lowest pressure model that approximately fits either
of our diagnostics. Also, the location of is
almost 0.3 dex deeper than our well fitting model with the deepest
. Furthermore, the slope, ,
of the chromospheric temperature rise is similar to that of our Series
models, which are clearly ruled out by the lack
of a central absorption reversal in the observed Na I
## 4.1.4. Gl 494
Alonso (1996) finds K by the Infrared Flux
Method, having adopted values of and
equal to 5.0 and 0.0, respectively. Rutten et
al. (1989) give a spectral type of dM2e and Henry et al. (1994) find a
type of dM3V. Panagi & Mathioudakis (1993), Rutten et al. (1989),
Doyle et al. (1990), Pettersen & Hawley (1989), Herbst &
Miller (1989), and Panagi et al. (1991) give measured flux values in
various chromospheric emission lines, including the
Na I
We measure to be ,
which is just below the range of the previous measurements of 2.12,
1.48, and (Stauffer & Hartmann 1986,
Panagi et al. 1991, Pettersen & Hawley 1989). From Table 4, a
model with between -4.4 and -4.2 provides a fit
to our measured value and those of Stauffer & Hartmann (1986) and
Panagi et al. (1991). We measure the The synthetic profiles have been rotationally broadened with a
value of of 10.0 km s
Unlike the synthetic H profiles, the synthetic
Na I
The value of that is found from a fit to the
H line is 0.4 dex smaller in column mass density
than that found from a fit to the Na I
core. Indeed, the value found from the
H profile corresponds to a model in which the
Na I ## 4.1.5. Gl 900
Gl 900 is unique in our sample because it is the only "zero H" (dM(e)) star. There are no measured values of reported in the literature. Byrne & Doyle (1989) report fluxes in a variety of FUV lines that form in the TR and find that they are intermediate between those of quiescent dM and active dMe stars. From high resolution spectroscopy, Robinson & Cram (1989) find that the Ca II core flux is intermediate between that of dM and dMe stars. They also find that the H profile has emission wings and an absorption core. Rutten et al. (1989) give a spectral type of dM1. Panagi &
Mathioudakis (1993), Rutten et al. (1989), Giampapa et al. (1989),
Herbst & Miller (1989), and Robinson et al. (1990) give measured
flux values in a a variety of chromospheric emission lines. Stauffer
& Hartmann (1986) give
(H).
Fleming et al. (1989), from moderate resolution spectroscopy, measure
km s
Although Gl 900 has been found to be a zero H star, we detect a distinct absorption line, although it is much weaker than that of Gl 212 or Gl 382. We measure to be , which is smaller than the values of 0.01 and 0.08 found by (Stauffer & Hartmann 1986, Robinson et al. 1990). The latter two values correspond to slight emission, rather than absorption. From Table 4 we see that in Series all three measured values may be fit with a model with between -4.8 and -4.6. Among Series models, our value corresponds to a model with between -4.8 and -4.6 and those of Stauffer & Hartmann (1986) and Robinson et al. (1990) indicate a model with between -4.6 and -4.4. In Fig. 13 the depth and width of the observed line profile is approximately fit by a model of Series with equal to -4.6. However, this model has small but significant emission wings that are not present in the observed line profile. A model with a value between -4.6 and -4.8, which would be deeper but have weaker or absent emission wings may provide a better fit, in agreement with the results of the fit. The Series profiles of the same range are slightly narrower and, therefore, provide a slightly worse fit.
In Fig. 14 we can see that a model of Series with equal to -4.2 provides a very close fit to the shape of the entire inner line profile. None of the models of Series is able to provide even an approximate fit.
The Na I line profile is
almost perfectly fit by a model in which the value of
is larger by at least 0.4 dex in column mass
density than that needed to fit H. The usual
caveats about inaccuracies in the stellar parameters of the model
apply, although we cannot provide a quantitative assessment due to the
lack of measured values of the parameters in the literature. In the
case of Gl 900, the ability to simultaneously fit both lines is
complicated by another consideration: the
"zero-H" stars of intermediate chromospheric
pressure exist in a regime where both H and the
Na I © European Southern Observatory (ESO) 1998 Online publication: July 20, 1998 |