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Low-mass eclipsing binaries have unveiled that stellar models do not reproduce the radii and effective temperatures of its components while luminosities are correctly predicted. The magnetic activity due to the rapid rotation of these stars has been proposed as the cause of these differences between models and observations and corrections to the models have already been suggested. One of the theoretical scenarios is considering that stars could be more spotted than it is deduced from light curves. Therefore, tests to the amount of spot coverage needed in the models to reproduce observations are implemented on well-known eclipsing binary systems and consistency checks between these corrections and observations are presented.

We have developed a new EOS for hydrogen in a temperature and density domain relevant to low mass stars, giant planets, and the outer layers of DA white dwarfs, using the most sophisticated tools presently available in statistical physics. We believe that this EOS incorporates significant improvements over existing equations of state, especially in the intermediate density regime (-3 < log p < 0) and the partial ionization zone (Saumon, Chabrier and Van Horn 1988). Using two sophisticated free energy models, we calculated a critical transition line and a critical point and found that a plasma phase transition might occur in the interior of giant planets (Saumon and Chabrier 1988).

We briefly summarize our present knowledge of the theory of low-mass stars and substellar objects and their contribution to the Galactic population.

Accurate modeling of the mechanical and thermal properties of very-low-mass stars (VLMS), Brown Dwarfs (BD) and Extra-solar Giant Planets (EGP) is of prior importance for a wide range of physical and astrophysical problems, from the fundamental physics point of view to the astrophysical and cosmological implications. They provide natural laboratories to test the different theories, equations of state, nuclear reaction rates, model atmospheres aimed at describing the physics of dense and cool objects. They represent the largest stellar population in the Galaxy, and thus provide a substantial contribution to the Galactic (disk) mass budget. Finally they represent one of the most intriguing questions in our understanding of the formation of star-like objects: are planet and star formation processes really different ? Is there, and if so what is, a minimum mass for the formation of star-like objects ? This field has blossomed recently with the discovery of several brown dwarfs (Nakajima et al. 1995; Rebolo et al., 1995) and numerous exoplanets since 51 Pegasi (Mayor and Queloz 1995; Mayor, this conference), which provide important information to challenge the theory.

If the unseen matter in our Galaxy is provided by very low-mass star-like objects, we show that the halo infrared luminosity is dominated by 0. 1M ⊙ objects. In this case, the halo IMF must be much steeper than in the disk, so that most of the unseen matter consists of brown dwarfs. We show that a halo made-up of low-mass star-like objects is consistent with present day observations, in particular with recent data from the HST.