Astron. Astrophys. 327, 1039-1053 (1997)

5. Conclusion

In this paper, we have presented new calculations aimed at describing the structure and the evolution of low mass stars, from solar masses down to the hydrogen burning limit, for a wide range of metallicities. These calculations include the most recent physics aimed at describing the mechanical and thermal properties of these objects - equation of state, screening factors for the nuclear reaction rates, non-grey atmosphere models -. The Saumon-Chabrier hydrogen-helium EOS gives the most accurate description of the internal properties of these objects over the entire afore-mentioned mass range. Given their negligible number abundance, metals play essentially no role on the EOS itself and their presence is mimicked adequately by an effective helium fraction. Of course they do play a role as electron donors for the opacities and must be included in the appropriate ionization equilibrium equations when opacities are concerned. Note that, for the densest stars ( , , ), departure from ideality at (resp. ) in the atmosphere is found to represent (resp. ) on the adiabatic gradient (as obtained from a comparison between the complete SC EOS vs an ideal gas EOS). Thus, under LMS conditions, an ideal (Saha) EOS can be safely used over the entire atmosphere, for metallicities . Note that an (incorrect) grey approximation yield denser atmospheric profiles (cf Sect.  2.4) and thus will overestimate non-ideal effects.

We show that under LMS conditions, the responsive electron background participates to the screening of the nuclear reactions, and must be included for an accurate determination of the various minimum burning masses and of the abundances of light elements along evolution. We show that, near the bottom of the main sequence, the deuterium lifetime against proton capture in the PPI chain is order of magnitudes smaller than the convective mixing time. Instantaneous mixing is thus no longer satisfied. This yields the presence of a deuterium gradient in the burning core, which bears substantial consequences on the determination of the luminosity near the brown dwarf regime.

We have examined carefully the effect of various grey-like approximations on the evolution and the mass-calibration of LMS. Under LMS conditions, these prescriptions are incorrect, or at best unreliable, and yield inaccurate mass-luminosity and mass-effective temperature relationships, which in turn yield inaccurate mass functions from observed luminosity functions. We examine the behaviour of the different stellar macroscopic quantities, radius, temperature, luminosity, as functions of mass, time and metallicity. We link the general behaviour of these quantities to intrinsic physical properties of stellar matter, in particular the transition from classical to quantum objects and the onset of convection or radiation in the stellar interior and atmosphere. We derive new limits for the hydrogen-burning minimum mass, effective temperature and luminosity, for each metallicity. These limits are smaller than the values determined previously, a direct consequence of non-grey effects in the atmosphere.

We believe the present calculations to represent a significant improvement in low-mass star theory and in our understanding of the properties of cool and dense objects. This provides solid grounds to examine the structure and the evolution of substellar objects, brown dwarfs and exoplanets.

At last the present models provide reliable mass-luminosity relationships, a cornerstone for the derivation of accurate mass functions (Méra, Chabrier & Baraffe, 1996; Chabrier & Méra, 1997). The comparison with observations has already been presented in different Letters (see references), and is examined in detail in two companion papers, namely Baraffe et al. (1997) for metal-poor globular cluster and halo field stars and in Allard et al. (1997a) for solar-like abundances.

Tables 2-7 are available by anonymous ftp:

© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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