Disk M dwarf luminosity function from Hubble Space Telescope star counts

We study a sample of 257 Galactic disk M dwarfs (8 less than or equal to M(V) less than or equal to 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 (PC1) 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(.)), decreasing by a factor greater than or equal to 3 by M(V) similar to 14 (M similar to 0.14 M(.)). 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(.) < M < 1.6 M(.) by log(phi) = -1.35 - 1.33 log (M/M(.)) - 1.82[log(M/M(.))](2), where phi is the number density per logarithmic unit of mass. The total column density of M stars is only Sigma(M) = 12.4 +/- 1.9 M(.) pc(-2), implying a total ''observed'' disk column density of Sigma(obs) similar or equal to 40 M(.) 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 tau less than or similar to 1 x 10(-8), compared to the observed optical depth found in ongoing experiments tau(obs) similar to 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 nu(z) proportional to 0.80 sech(2) (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.