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 compute models of stars in the mass range 0.1 < m ≤ 1 M⊙. We compare the solar-metallicity models with our older models and 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 differsubstantially from model to model. However, taken individually, each set of models is in good agreement with observations in the mass-luminosity plane. A minimum in the derivative dm/dMv at Mv ≈ 11.5, which is due to H2 formation and the establishment of a fully convective stellar interior, is present in all photometric bands, for all models, but its position changes from model to model. This minimum leads to a maximum in the stellar luminosity function for Galactic disc stars at Mv ≈ 11.5, Mbol ≈ 9.8. Precise stellar models should locate this maximum in the stellar luminosity function at the same magnitude as observations. This is an extra 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 also in best agreement with the most recent luminosity-effective temperature and mass-luminosity data. Each set of our models of a given metallicity (in the range 0.2 > [Fe/H] > −2.3) shows a maximum in — dm/dMbol, which moves to brighter bolometric magnitudes with decreasing metallicity. The change in location of the maximum, as a function of [Fe/H], follows the location of structure in luminosity functions for stellar populations with different metal abundances. This structure, seen in all observed stellar populations, can be accounted for by the mass-luminosity relation and does not require a maximum in the stellar mass function at m ≈ 0.3 M⊙.