The Structure and Evolution of Stars of Very Low Mass

Both an "idealized" and a "detailed" approach are employed to calculate pre-main-sequence evolutionary tracks and main-sequence models for stars of essentially solar composition (X = 0.739, Y = 0.240) in the mass range 0.20-0.02 Mo. The idealized approach is based on the assumption that the interior structure may be represented by a polytrope of index n = 1.5. This assumption is tested through the construction of detailed evolutionary models at 0. t and 0.07 Mo in which the effects due to electrostatic interactions between particles are investigated. The outer boundary condition for both sets of model calculations is obtained from approximate model atmospheres. It is concluded that the polytropic representation for main-sequence objects of very low mass should be adequate and that the lower limiting mass for main-sequence stars is near 0.1 Mo. Comparison of the main-sequence models with observational data on the masses, radii, and luminosities of low-mass stars in the solar neighborhood reveals considerable discrepancy between the theoretical and the empirical mass-luminosity and mass-radius relations, although we find fair agreement with the adopted empirical mass-luminosity relation for masses below 0.3 Mo. A possible effect of the main-sequence limiting mass on the observed mass function for nearby stars is discussed.