E. Brocato, S. Cassisi and V. Castellani
Osservatorio Astronomico di Collurania, Via M. Maggini, I-64100
Teramo, Italy
Dipartimento di Fisica, Universitá de L'Aquila, Via Vetoio, I-67100 L'Aquila, Italy
Dipartimento di Fisica, Universitá di Pisa, Piazza Torricelli 2, I-56100 Pisa, Italy
--0.093
and the metallicity ranges from
[Fe/H]
to [Fe/H]
.
By adopting updated molecular
opacities, as provided by Alexander & Ferguson (1994), and by relying on
the Saumon & Chabrier (1992) equation of state, we show that our models
allow an
impressive fitting of HST observations of metal poor very low mass stars (VLM)
in the galactic globular cluster NGC6397. We also extend the investigation
to a sample of nearby field VLM stars with known parallaxes suggesting that the
observed color spread is due to differences in the metallicity between the
stars. The theoretical scenario concerning solar metallicity
VLM is also briefly discussed.
Keywords: very low mass stars,globular cluster
The improved efficiency of the Hubble Space Telescope discloses the opportunity to investigate the still largely unexplored field of very faint stars in galactic globular clusters. This occurrence offers an excellent test to the stellar evolution theory of metal poor VLM stars and, in the meantime, allows a comparison between VLM stars in globular cluster and similar stars observed in the solar neighborhood.
In the recent past, large efforts have been performed to improve our knowledge of the physical conditions, opacity and equation of state, expected in VLM stars (Alexander & Ferguson 1994, Saumon & Chabrier 1992 and references therein).
For both these reasons, we extended the set of evolutionary tracks previously available (see e.g., Cassisi, Castellani & Straniero 1994) to VLM models, these evolutionary computations for VLM stellar structures are presented in this report. In the next section, we discuss briefly the models and the adopted physical inputs. In the following section, we discuss the result of the comparison between our models and observational data for main sequence stars in the globular cluster NGC6397. The comparison between data for VLM stars in NGC6397 and similar stars with known parallaxes in the solar neighborhood is shown in section 3, where we also briefly discuss the agreement between the theoretical sequence of models and the observations for solar composition VLM stars. A short discussion on the future developments of this research closes the paper.
As well known in the literature (see, for instance, Dorman et al. (1989)), the theoretical evaluations about the very low mass stars are critically dependent on the evaluations of both the opacity and the equation of state for a low temperature high density gas.
Recently, large improvements have been performed both in the computations of low temperature opacities including molecules and grains (Alexander & Ferguson 1994) and in the evaluations of the thermodynamical behavior of the matter in cool and dense objects as presented by Saumon & Chabrier (1992) and by Saumon et al. (1995). These physical inputs have been adopted in computing the VLM stellar models presented here.
Selected sequences of stellar models in the range of mass:
0.8
--0.093
, have been computed for metallicities ranging from
[Fe/H]
to [Fe/H]
, assuming an Helium content
everywhere. All computations have been performed assuming a
mixing length parameter as given by 
, obtained by the solar
model calibration (Salaris & Cassisi 1996). For more details
on the evolutionary computations and/or on the internal structures
of the models, the interested reader is referred to Alexander et al. (1996).
Figure: The location in the HR diagram
for the 10Gyr old models, for different assumptions on the stellar metallicity.
In fig. 1, the HR diagram locations of the 10Gyr old models, for the labeled assumptions on the metallicities, are shown. In the following comparison to observational data we adopted bolometric corrections and color temperature relation by Kurucz (1993) implemented for effective temperature lower than 4000K by using Allard & Hauschildt (1995) and Allard et al. (1996). The Holtzman et al. (1995) prescriptions have been used to map the theoretical models in the HST observational plane.
The recent Hubble Space Telescope observations of the galactic globular cluster
NGC6397 as presented by Paresce et al. (1995) and by Cool et al. (1996) (see
also the paper by King et al., in this volume, p. 
) have disclosed the presence of a
very tight and well populated sequence of VLM stellar objects. These results
show a very high accuracy providing strong constraints to check the
reliability of the present theoretical scenario on the VLM star.
In fig. 2, the color-magnitude (CM) of NGC 6397 obtained with HST/WFPC2
by Cool et al. (1996) is
shown. In the same figure, we report also two isochrones for the same age: t=10Gyr,
but for two different metallicities: [Fe/H]
and 
. Our best
fitting is obtained assuming for the cluster a distance modulus 
and a reddening 
, a couple of values in reasonable agreement with
the evaluations reported in the literature (Webbink 1985, Alcaino et al. 1987,
Fahlman et al. 1989).
Figure: The CM diagram for the Main Sequence of NGC6397.
Two theoretical sequences of models for the labeled assumptions concerning
the metal content are also plotted (see text concerning the adopted distance
modulus and reddening).
Once a distance modulus and a reddening value are assumed,
the observed distribution of stars in the cluster is narrow enough
to recognize a better agreement for theoretical models
with [Fe/H]
. A metallicity value which agrees with previous
determination.
For long time, the fairly rich sample of stars with known parallaxes, in the solar neighborhood has provided a fundamental tool to test the theoretical approach to VLM structures. In recent times, observational effort has been devoted to make larger the sample of stellar objects with known parallaxes. For instance, Dahn et al. (1995) have carried out a program for the determination of parallaxes. Their data, together with the previous sample of Monet et al. (1992), appear as the most complete database presently available. Moreover, the new catalog of CCD parallaxes go deeper than the earlier result, increasing the statistic from a few to a few tens of stars for bin of magnitude.
The data of solar neighborhood VLM stars from Monet et al. (1992) and from Dahn et al. (1995) are plotted in figure 3, together with the data for NGC6397, as given by Cool et al. (1995). The distance modulus and the reddening are the same as in the previous section.
Figure: The CM diagram for the Main Sequence of NGC6397,
compared
with similar data for stars with known parallaxes.
It is interesting to notice that the lower main sequence of NGC6397 rank indeed along the blue boundary of the observed distribution of VLM objects with known parallaxes. Taking into account the low metallicity of NGC6397, this behavior supports the fundamental role of the metallicity in determining the subdwarf location in the CM diagram (see also figure 1).
The data from Monet et al. (1992) and from Dahn et al. (1995) discloses also the opportunity of comparing theoretical models of solar chemical composition to observations. This comparison is presented in fig. 4 where the agreement is not as satisfactory as for low metallicity. In the same figure we plot the recent computations presented by D'Antona & Mazzitelli (1994, 1996) and by Baraffe et al. (1995) as based just on the same zero metal EOS by Saumon & Chabrier (1992) and Saumon et al. (1995). We guess that a more adequate (solar chemical composition) assumption on the EOS, when available, could improve the agreement with observations for both Baraffe et al. (1995) and our theoretical models for solar metallicity.
Figure: (
) CM diagram for faint stars with known parallaxes
from Monet et al. (1992) and Dahn et al. (1995) with superimposed our theoretical
models for VLM stars of solar composition, the models presented by Baraffe et al. (1995)
and the ones of D'Antona & Mazzitelli (1994, 1996).
The differences between our sequence of models and the Baraffe et al. (1995)
one, which rapidly increases for lower effective temperature, reaching a
maximum around 
, is due to the different approaches to the
treatment of stellar envelope (for more details, we refer to Alexander et al.
(1996) and to Baraffe et al. (1995)).
In this report, we present theoretical computations which appear in fine agreement with new HST data for the low luminosity main sequence of a metal poor galactic globular cluster NGC6397. This agreement suggests that the present VLM stellar models and the adopted physical inputs (opacities and equation of state) for low metallicity provide a valuable theoretical scenario which, however, needs more constraints by observations. In particular, it is very important to observe more galactic globular clusters with the same accuracy that it has been recently attained in the HST observations of NGC6397. In this framework, the Hubble Space Telescope appears, obviously, as a primary tool.
We are grateful to I. King, G. Piotto and A. Cool for allowing us the use of their HST data on NGC6397, to G. Chabrier for providing his zero metal EOS and to F. Allard for making available to us her new color-temperature relation for solar metallicity.
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