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

Abstract

We derive and parameterize the Galactic mass function (MF) below 1 M ☉ 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 ~50% of M dwarf binaries, with the mass of both the primaries and the companions originating from the same underlying single MF. This implies that ~30% of M dwarfs should have an M dwarf companion and ~20% 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 ≲ 0.1) systems and does not preclude a substantial fraction of brown dwarfs as companions of M dwarfs or for other brown dwarfs.