Stellar models and luminosity functions for the Population II main sequence down to its lower end

We have computed new sets of stellar models, for masses from similar to 0.8 M. down to the lower termination of the main sequence, for metallicities and helium contents adequate to represent the halo and globular cluster populations, with the most updated opacity tables. By means of theoretical color-T-eff transformations by Kurucz and by Allard, we have derived M(I) versus V-I data to be compared with globular clusters and nearby subdwarf data. We show that the characteristic ''double kink'' shape of the M(I) versus V-I diagram is well reproduced by the models, although better agreement would have been obtained if the V-I theoretical colors were redder by similar to 0.1 mag. We then discuss the mass-luminosity relation, particularly in correspondence with the kinks, since they turn out to be critical in establishing the luminosity functions (LFs) of the observed sets of stars. We present tables of the mass-M(I)-V-I relations, which can be used for comparisons with observed LFs. We also discuss the general features of the luminosity functions obtained from these models assuming simple analytic mass functions of different power-law slope. We find that all the LFs peak in the range 8 less than or equal to M(I) less than or equal to 10, the magnitude of the maximum increasing both with Z and with the power-law exponent in the mass function. As an example, we compare our results with the recent Hubble Space Telescope observational results by Paresce et al. for the globular cluster NGC 6397.