Determination of the Low-Mass Star Mass Function in the Galactic Disk

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Abstract
We use the theoretical mass-luminosity relationship derived recently for low-mass stars (Chabrier, Baraffe, & Plez) to determine the lower end of the stellar mass function in the Galactic disk from observed luminosity functions. The age and metallicity spreads characteristic of the disk population are carefully examined. The mass function (MF) is shown to rise monotonically with decreasing mass and is reasonably well described by a power law n(m) ∝ m-α with α ≈ 2 ± 0.5 from ~0.6 M☉ down to the hydrogen-burning limit. Bimodal MFs, as derived in previous studies, are shown to be due to unresolved binaries in the photometric luminosity function, as suggested previously by Kroupa and coworkers. Such a rising MF suggests a substantial amount of brown dwarfs in the Galactic disk. The local density of main-sequence stars is found to be ρ* = 4.2 ± 0.8 × 10-2 M☉ pc-3, which corresponds to a surface density Σ* = 28.5 ± 6 M☉ pc-2, including the thick-disk contribution. The expected number of brown dwarfs is examined within the context of the OGLE and MACHO microlensing experiments. Although the contribution of brown dwarfs to the disk-mass budget is likely to be larger than previously thought, it still lacks in reproducing the observed optical depth.