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

1. Introduction

Accurate modelling of the mechanical and thermal properties of very-low-mass stars (VLMS), or M-dwarfs, defined hereafter as objects with masses below 0.8 , is of prior importance for a wide range of physical and astrophysical reasons, from the understanding of fundamental problems in basic physics to astrophysical and cosmological implications. VLMS are compact objects, with characteristic radii in the range . Their central densities and temperatures are respectively of the order of g cm^-3 and K, so that correlation effects between the particles dominate the kinetic contribution in the interior stellar plasma. Effective temperatures of VLMS are below K, and surface gravities are in the range . These conditions show convincingly that the modelling of VLMS requires a correct description of non-ideal effects in the equation of state (EOS) and the nuclear reaction rates, and a derivation of accurate models for dense and cool atmospheres, where molecular opacity becomes eventually the main source of absorption. Several ground-based and space-based IR missions are now probing the VLMS wavelength range () down to the end of the main-sequence (MS), reaching sometimes the sub-stellar domain. These existing or future surveys will produce a substantial wealth of data, stressing the need for accurate theroretical models. Indeed the ultimate goal of VLMS theory is an accurate calibration of observations, temperature, luminosity and above all the mass, with the identification of genuine brown dwarfs. At last, VLMS represent the major component () of the stellar population of the Galaxy. A correct determination of the contribution of these objects to the Galactic mass budget, both in the central parts and in the outermost halo, requires the derivation of reliable mass functions for VLMS, and thus accurate theoretical mass-luminosity relationships for various metallicities.

Tremendous progress has been realized within the past decade in the field of VLMS, both from the observational and theoretical viewpoints. From the theoretical point of view, the most recent benchmarks in the theory, without being exhaustive, have been made by D'Antona & Mazzitelli (1985, 1994), who initiated the research in the field, the MIT group (Dorman, Nelson & Chau 1989; Nelson, Rappaport & Joss 1986, 1993) and the Tucson group (Lunine et al. 1986; Burrows, Hubbard & Lunine 1989; Burrows et al. 1993). So far, all these models, however, failed to reproduce the observations at the bottom of the VLMS sequence, predicting substantially too large temperatures for a given luminosity (see e.g. Monet et al. 1992). This shortcoming of the theory made a reasonable identification of the observational HR diagram elusive. Such a discrepancy stemed from incorrect stellar radii (and adiabatic gradients), a consequence of inaccurate EOS, but most importantly from the use of grey atmosphere models. These points will be largely examined in Sect. 2.4 and Sect. 2.5. A significant breakthrough in the structure and evolution of VLMS was made recently by the Tucson group, who first derived evolutionary models based on non-grey atmosphere models (Saumon et al. 1994), although for zero-metallicity, and by the Lyon group (Baraffe et al. 1995, BCAH95; 1997, BCAH97; Chabrier et al. 1996) who derived evolutionary models based on the Allard-Hauschildt (1995a, AH95; 1997, AH97) non-grey model atmospheres for various finite metallicities. The BCAH95 models were shown to improve significantly the afore-mentioned discrepancy at the bottom of the MS. These initial calculations have now been improved substantially. The aim of the present paper is to present a complete description of the physics entering the theory of VLMS and to relate the properties of these objects to well understood physical grounds. Extensive comparisons with available observations, color-magnitude diagrams and mass-magnitude relationships, will be presented in companion papers (BCAH97; Allard et al. 1997a).

The present paper is organized as follows. In Sect.  2, we describe the input physics which enters the present theory, EOS, enhancement factors of the nuclear reaction rates, atmosphere models and boundary conditions. Evolutionary models are presented in Sect.  3, together with the prediction of the abundances of light elements (⁷ Li,⁹ Be,¹¹ B) along evolution and the burning minimum masses for these elements. We also derive a new limit for the hydrogen burning minimum mass (HBMM), i.e. the brown dwarf limit, which is found to be lower than previous estimates, a direct consequence of non-grey effects. The mass-dependence of photospheric quantities is examined in Sect. 4. Section 5 is devoted to the concluding remarks.

© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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