The Galactic Disk Mass Function: Reconciliation of the [ITAL]Hubble Space Telescope[/ITAL] and Nearby Determinations

We derive and parametrize the Galactic mass function (MF) below 1 $\msol$ characteristic of both single objects and binary systems. We resolve the long standing discrepancy between the MFs derived from the HST and from the nearby luminosity functions, respectively. We show that this discrepancy stemmed from {\it two} cumulative effects, namely (i) incorrect color-magnitude determined distances, due a substantial fraction of M dwarfs in the HST sample belonging to the metal-depleted, thick-disk population, as corrected recently by Zheng et al. and (ii) unresolved binaries. We show that both the nearby and HST MF for unresolved systems are consistent with a fraction $\sim $50% of M-dwarf binaries, with the mass…