Determination of the globular cluster and halo stellar mass functions and stellar and brown dwarf densities

We use recent low-mass star models, which reproduce accurately the observed sequences of various globular clusters, to convert the observed luminosity functions into bolometric luminosity functions and mass functions down to the bottom of the main sequence. These mass functions are well describedby a slowly rising power-law $dN/dm\propto m^{-\alpha}$, with $0.5\wig < \alpha \wig < 1.5$, down to $\sim 0.1 \msol$, independently of the metallicity, suggesting a rather universal behaviour of the cluster initial mass functions. We predict luminosity functions in the NICMOS filters in the stellar and in the brown dwarf domains for different mass functions and metallicities. We apply these calculations to the determination, slope and normalization, of the mass function of the Galactic halo (spheroid and dark halo). The spheroid mass function is well described by the afore-mentioned power-law function with $\alpha \sim 1.7\pm 0.2$ down to 0.1 $\msol$, although a slowly decreasing mass function below $\sim 0.15 \msol$ can not be excluded with the data presently available. Comparison with the Hubble Deep Field star counts is consistent with such a mass function and excludes a significant stellar population in the dark halo. Consistent analysis with recent microlensing experiments towards the LMC shows that the spheroid and the dark-halo stellar+brown dwarf populations represent at most $\sim$ 1% of the Galactic dark matter density. This clearly excludes brown dwarfs and low-mass stars as significant dark matter candidates.