Galactic Stellar and Substellar Initial Mass Function

We review recent determinations of the present day mass function (PDMF) and initial mass functions (IMF) in various components of the Galaxy, disk, spheroid, young and globular clusters and in conditions characteristic of early star formation. As a general feature, the IMF is found to depend weakly on the environment and to be well described by a power-law form for m & 1M⊙ and a lognormal form below, except possibly for early star formation conditions. The disk IMF for single objects has a characteristic mass around mc ∼ 0.08M⊙ and a variance in logarithmic mass σ ∼ 0.7, whereas the IMF for multiple systems has mc ∼ 0.2M⊙ and σ ∼ 0.6. The extension of the single MF into the brown dwarf regime is in good agreement with present estimates of Land T-dwarf densities and yields a disk brown dwarf number density comparable to the stellar one nBD ∼ n⋆ ∼ 0.1 pc. The IMF of young clusters is found to be consistent with the disk field IMF, providing the same correction for unresolved binaries, confirming the fact that young star clusters and disk field stars represent the same stellar population. Dynamical effects, yielding depletion of the lowest-mass objects, are found to become consequential for ages & 130 Myr. The spheroid IMF relies on much less robust grounds. The large metallicity spread in the local subdwarf photometric sample, in particular, remains puzzling. Recent observations suggest that there is a continuous kinematic shear between the thick-disk population, present in local samples, and the genuine spheroid one. This enables us to derive only an upper limit for the spheroid mass density and IMF. Within all the uncertainties, this latter is found to be similar to the one derived for globular clusters, and is well represented also by a lognormal form with a characteristic mass slightly larger than for the disk, mc ∼ 0.2-0.3 M⊙, excluding a significant population of brown dwarfs in globular clusters and in the spheroid. The IMF characteristic of early star formation at large redshift remains undetermined, but different observational constraints suggest that it does not extend below ∼ 1M⊙. These results suggest a characteristic mass for star formation which decreases with time, from conditions prevailing at large redshift to conditions characteristic of the spheroid (or thick-disk), to present-day conditions. These conclusions, however, remain speculative, given the large uncertainties in the spheroid and early star IMF determinations. These IMFs allow a reasonably robust determination of the Galactic present-day and initial stellar and brown dwarf contents. They also have important galactic implications beyond the Milky Way in yielding more accurate mass-to-light ratio determinations. The mass-to-light ratios obtained with the disk and the spheroid IMF yield values 1.8 to 1.4 smaller than for a Salpeter IMF, respectively, in agreement with various recent dynamical determinations. This general IMF determination is examined in the context of star formation theory. None of the theories based on a Jeans-type mechanism, where fragmentation is due only to gravity, can fulfill all the observational constraints on star formation and predict