THE THEORETICAL MASS-MAGNITUDE RELATION OF LOW-MASS STARS AND ITS METALLICITY DEPENDENCE

We investigate the dependence of theoretically generated mass-absolute magnitude relations on stellar models. Using up-to-date physics we co mpute models of stars in the mass range 0.1 < m less than or equal to 1 M.. We compare the solar-metallicity models with our older models an d also with recent models computed by others. We further compare them with an empirical mass-absolute magnitude relation that best fits the observed data. At a given mass below 0.6 M. the effective temperatures differ substantially from model to model. However, taken individually , each set of models is in good agreement with observations in the mas s-luminosity plane. A minimum in the derivative dm/dM(v) at M-v approx imate to 11.5, which is due to H-2 formation and the establishment of a fully convective stellar interior, is present in all photometric ban ds, for all models, but its position changes from model to model. This minimum leads to a maximum in the stellar luminosity function for Gal actic disc stars at M-v approximate to 11.5, M-bol approximate to 9.8. Precise stellar models should locate this maximum in the stellar lumi nosity function at the same magnitude as observations. This is an extr a constraint on low-mass stellar models. Models which incorporate the most realistic theoretical atmospheres and the most recent equation of state and opacities can satisfy this constraint. These models are als o in best agreement with the most recent luminosity-effective temperat ure and mass-luminosity data. Each set of our models of a given metall icity (in the range 0.2 > [Fe/H] > -2.3) shows a maximum in -dm/dM(bol ), which moves to brighter bolometric magnitudes with decreasing metal licity. The change in location of the maximum, as a function of [Fe/H] , follows the location of structure in luminosity functions for stella r populations with different metal abundances. This structure, seen in all observed stellar populations, can be accounted for by the mass-lu minosity relation and does not require a maximum in the stellar mass f unction at m approximate to 0.3 M..