Substellar mass function and maximum baryonic mass in the halo of the Galaxy

We use recently observed luminosity functions of halo M-dwarfs and an accurate mass-luminosity relationship to derive the mass function of Pop II low-mass stars in the galactic spheroid. All these luminosity functions yield rising mass functions near the hydrogen-burning limit (with alpha approximate to 2). Connecting the microlensing and star count constraints, we show that the mass function in the dark halo steepens significantly (alpha greater than or similar to 4). The minimum mass is found to be m(inf) approximate to 0.02M., which corresponds to an average mass (m) over bar approximate to 0.03M., strongly suggesting that the dark objects responsible for the microlensing events are genuine brown dwarfs. We determine the expected spheroid and halo brown-dwarf density in the solar neighbourhood. The mass fraction under the form of substellar objects in the halo of the Galaxy is likely to represent only 5 to 15% of the total dynamic mass.