Disk M Dwarf Luminosity Function from Hubble Space Telescope Star Counts

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Abstract
We study a sample of 257 Galactic disk M dwarfs (812 (M<0.25 ms), decreasing by a factor gsim 3 by M_V~14 (M~0.14ms). This decrease in the LF is in good agreement with the ground-based photometric study of nearby stars by Stobie et al. (1989), and in mild conflict with the most recent LF measurements based on local parallax stars by Reid et al. (1995). 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 0.1ms<M<1.6ms by log(phi)=-1.35-1.34log(M/ms)-1.85 [log(M/ms)]^2 where phi is the number density per logarithmic unit of mass. The total column density of M stars is only Sigma_M=11.8pm 1.8mspc^{-2}, implying a total `observed' disk column density of Sigma_obs~=39mspc^{-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 3.0pm 0.4 kpc. The optical depth to microlensing toward the LMC by the observed stars in the Milky Way disk is au~1x10^{-8}, compared to the observed optical depth found in ongoing experiments au_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 component, we find characteristic exponential scale heights of ~210 pc and ~740 pc.
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