The Galactic disk mass function:: Reconciliation of the Hubble Space Telescope and nearby determinations

We derive and parameterize the Galactic mass function (MF) below 1 M-circle dot characteristic of both single objects and binary systems. We resolve the long-standing discrepancy between the MFs derived from the Hubble Space Telescope (HST) and from the nearby luminosity functions, respectively. We show that this discrepancy stemmed from two cumulative effects, namely, (1) incorrect color-magnitude-determined distances, due to 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 (2) unresolved binaries. We show that both the nearby and HST MF for unresolved systems are consistent with a fraction similar to50% of M dwarf binaries, with the mass of both the primaries and the companions originating from the same underlying single MF. This implies that similar to30% of M dwarfs should have an M dwarf companion and similar to20% should have a brown dwarf companion, in agreement with recent determinations. The present calculations show that the so-called "brown dwarf desert" should be reinterpreted as a lack of high mass ratio(m(2)/m(1) less than or similar to 0.1) systems and does not preclude a substantial fraction of brown dwarfs as companions of M dwarfs or for other brown dwarfs.