The Galactic disk mass-budget : II. Brown dwarf mass-function and density

In this paper, we extend the calculations conducted previously in the stellar regime to determine the brown dwarf IMF in the Galactic disk. We perform Monte Carlo calculations taking into account the brown dwarf formation rate, spatial distribution and binary fraction. Comparison with existing surveys seems to exclude a power-law MF as steep as the one determined in the stellar regime below 1 $\msol$ and tends to favor a more flatish behaviour. Comparison with methane-dwarf detections tends to favor an eventually decreasing form like the lognormal or the more general exponential distributions determined in the previous paper. We calculate predicting brown dwarf counts in near-infrared color diagrams and brown dwarf discovery functions. These calculations yield the presently most accurate determination of the brown dwarf census in the Galactic disk. The brown dwarf number density is comparable to the stellar one, $n_{BD}\simeq n_\star\simeq 0.1$ pc$^{-3}$. The corresponding brown dwarf mass density, however, represents only about 10% of the stellar contribution, i.e. $\rho_{BD}\simle 5.0\times 10^{-3} \mvol$. Adding up the local stellar density determined previously yields the density of star-like objects, stars and brown dwarfs, in the solar neighborhood $\rho_\odot \approx 5.0\times 10^{-2} \mvol$.