Disk M Dwarf Luminosity Function from Hubble Space Telescope Star Counts

Abstract

We study a sample of 257 Galactic disk M dwarfs (8 ≤ M_v ≤ 18.5) found in images obtained using the Hubble Space Telescope (HST). These include 192 stars in 22 fields imaged with the repaired Wide Field Camera (WFC2) with mean limiting mag I = 23.7 and 65 stars in 162 fields imaged with the prerepair Planetary Camera (PC 1) with mean limiting mag V = 21.3. We find that the disk luminosity function (LF) drops sharply for M_v > 12 (M < 0.25 M_sun), decreasing by a factor ≥ 3 by M_v ∼ 14 (M ∼ 0.14 M_sun). This decrease in the LF is in good agreement with the ground-based photometric study of nearby stars by Stobie, Ishida, & Peacock, and in mild conflict with the most recent LF measurements based on local parallax stars by Reid, Hawley, & Gizis. The local LF of the faint Galactic disk stars can be transformed into a local mass function using an empirical mass-M_v relation. The mass function can be represented analytically over the mass range 0.1 M_sun < M < 1.6 M_sun by log (φ) = -1.35 - 1.33 log (M/M_sun) - 1.82[log (M/M_sun)]², where φ is the number density per logarithmic unit of mass. The total column density of M stars is only Σ_M = 12.4±1.9 M_sun pc^-2, implying a total "observed" disk column density of Σ_obs ≃ 40 M_sun pc^-2, lower than previously believed, and also lower than all estimates with which we are familiar of the dynamically inferred mass of the disk. The measured scale length for the M-star disk is 3.0±0.4 kpc. The optical depth to microlensing toward the Large Magellanic Cloud (LMC) by the observed stars in the Milky Way disk is τ ≤ 1 x 10^-8, compared to the observed optical depth found in ongoing experiments τ_obs ∼ 10^-7. The M-stars show evidence for a population with characteristics intermediate between thin disk and spheroid populations. Approximating what may be a continuum of populations by two separate components, we find a vertical density profile v(z) ∝ 0.80 sech² (z/323 pc) + 0.20 exp (- |z|/656 pc). If we combine the HST data with ground-based measurements of the local density of M dwarfs, then a traditional double-exponential vertical density profile is strongly excluded.