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Astron. Astrophys. 317, 90-98 (1997)

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4. Metal poor VLM main sequences

Tables 2 to 5 give selected theoretical quantities for models with [FORMULA] for four selected choices about the heavy metal content (Z=0.0001, Z= 0.0003, Z=0.0006, Z=0.001) and for the labeled assumptions about star masses and ages. In the same tables, there are also the expected location in the (V, V-I) observational plane, as evaluated adopting bolometric correction and color temperature relation from Kurucz (1993) implemented for effective temperatures lower than 4000K with similar evaluations given by Allard & Hauschildt (1995) shifted to overlap Kurucz evaluation at the fitting point ( [FORMULA] ) (see the discussion in D'Antona & Mazzitelli 1996, hereafter DM96).

[TABLE]

Table 2. Luminosity, effective temperature, surface gravity, central density and temperature and the expected location in the ( [FORMULA],V-I) observational plane, for stellar models with [FORMULA] with metallicity [FORMULA] and Y=0.23 , at ages equal to 10 Gyr and 20 Gyr.

[TABLE]

Table 3. As in Table 1, but for a metallicity [FORMULA].

[TABLE]

Table 4. As in Table 1, but for a metallicity [FORMULA].

[TABLE]

Table 5. As in Table 1, but for a metallicity [FORMULA].

[FIGURE]Fig. 4. The HR diagram location of the 10 Gyr old models for the assumed metallicities Z=0.0001, 0.0003, 0.0006 and 0.001. Masses of the models as reported in Tables 2 to 5 with the addition of [FORMULA] and [FORMULA] structures. The tentative location of the sequence with Z=0.006 is also reported (see text).

Fig. 4 reports the location of the 10 Gyr sequences in the theoretical HR diagram for the four choices on the star metallicity. From this figure it is possible to recognize the already known sinuous shape of the VLM sequence together with the effect of metallicity on the HR diagram location, so by increasing the metallicity for each given value of the mass, cooler and moderately less luminous structures are being expected. For the sake of comparison, in the same figure the location of a Z=0.006 sequence has been added, which however has to be regarded with caution, since it is difficult to evaluate if metals begin to play a not marginal role in the EOS of such a moderately metal rich mixture. According to the discussion given in Sect. 2, the same figure shows at [FORMULA] =3.60 or 3.65 the lower temperature limit for the validity of the adopted treatment of stellar atmospheres either in the solar or in the zero metal case, respectively.

[FIGURE]Fig. 5. Comparison of locations in the theoretical HR diagram of the 10 Gyr old models from present paper and from D'Antona & Mazzitelli (1996). Metallicity as labeled.

Present results can be usefully compared with similar results recently presented by DM96 for Z=0.0001, Z=0.001. This comparison is shown in Fig. 5 for both the quoted values of metallicity. For the larger masses in the sample one finds a good, and, sometime, an excellent agreement. However, going toward lower masses DM96 models appear progressively hotter until, below about 0.12 [FORMULA], the disagreement is eventually reduced and sometime reversed. To discuss the origin of such a behavior, let us notice that DM96 use a similar, but not identical, treatment of the atmosphere. According to their indication, the atmosphere integration is stopped at [FORMULA] =2/3 in all cases, without investigating the onset of convection. However, numerical experiments performed adopting DM96 procedure show that in that assumptions our models became "cooler", as expected from the evidence that similar models allow larger temperature gradient in the atmosphere. Thus the origin of the differences is probably to be found either in the adopted EOS or in the not complete coverage of opacity tables reported by DM96. Since both papers adopt quite similar procedures to evaluate bolometric corrections and V-I color, the difference in the theoretical HR diagram are plainly transferred into the (M [FORMULA],V-I) CM diagram disclosed by Fig. 6. As for the general shape of the low main sequence, it appears that the two results differ in the sense of DM result foreseeing a larger slope of the branch below M [FORMULA] 0.4 [FORMULA]. Note that both sequences in present paper or in DM96 keep, hopefully, full validity only for temperature larger or of the order of [FORMULA], cooler models being affected by a not-appropriate treatment of the atmosphere, overestimating the effective temperature of the stars.

[FIGURE]Fig. 6. Comparison of predicted distribution in the (M [FORMULA], V-I) CM diagram of the 10 Gyr old models from present paper and from D'Antona & Mazzitelli. Metallicity as labeled.

An estimate of such an effect can be obtained on the basis of the discussion given in Baraffe et al. (1995) for the solar metallicity. According to these Authors, it appears that the use of a [FORMULA] relation sizably affects the main sequence models between about [FORMULA] 3.42 and 3.58, with a maximum effect at [FORMULA] = 3.52 where the Eddington approximation produce models hotter than about 200 K . However, we lack similar indication for the metal poor models we are dealing with. Thus let us directly compare present results with recent observations of low main sequence stars. Hubble Space Telescope observation of the galactic globular cluster NGC6397, as recently presented by Paresce, De Marchi & Romaniello (1995) and by Cool, Piotto & King (1995), already disclosed a tight sequence of cluster VLM stars which represents a new fundamental test for the theory of VLM structures. According to the current literature, the metallicity of this cluster is evaluated around [Fe/H]= -2.0 (Webbink 1985) whereas evidences have been reported for a reddening in the range [FORMULA] (Alcaino et al. 1987) and for a visual distance modulus ranging from 12.5 (Alcaino et al. 1987) to 12.3 (Fahlman et al. 1989). Adopting from Taylor (1986) [FORMULA], [FORMULA] is obtained.

[FIGURE]Fig. 7. (V, V-I) CM diagram for lower main sequence stars in the globular cluster NGC6397 (Cool, Piotto & King 1995). The comparison with theoretical sequences for t=10 Gyr and for the two labeled assumptions about the star metallicity has been performed adopting for the cluster [FORMULA], E(V-I)=0.19 (see text)

Fig. 7 shows the observational HST/WFPC2 data for NGC 6397 by Cool, Piotto & King (1995) as mapped in the (V,V-I) plane according to Holtzman et al. (1995) prescriptions. The same Fig. 7 shows our best fitting with theoretical (V,V-I) data, as obtained assuming for the cluster a distance modulus [FORMULA] and E(V-I)=0.19 , a couple of values which appear compatible with the quoted evaluations. The agreement of theoretical predictions for Z=0.0003 ( [Fe/H] =-1.91) with the observed distribution of cluster stars can be obviously regarded as largely satisfactory. It may be noticed that the agreement has been achieved for a value of metallicity only marginally larger than expected on observational ground, without invoking the [FORMULA] -enhancement required by DM96 to reconcile their theoretical results with the observation. However, a more detailed discussion will be possible as soon as the effect of the [FORMULA] will be better understood and improved theoretical color- [FORMULA] transformations (Allard 1996) suitable for metal poor stellar structures will become available.

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