M Dwarfs, Microlensing, and the Mass Budget of the Galaxy
  We show that faint red stars do not contribute significantly to the mass budget of the Galaxy or to microlensing statistics. Our results are obtained by analyzing two long exposures of a high-latitude field taken with the Wide Field Camera on the newly repaired {\it Hubble Space Telescope}. Stars are easily distinguished from galaxies essentially to the limiting magnitudes of the images. We find five stars with $2.0<V-I<3.0$ and $I<25.3$ and no stars with $V-I>3.0$. Therefore, main-sequence stars with $M_I>10$ that are above the hydrogen-burning limit in the dark halo or the spheroid contribute $<6%$ of the unseen matter. Faint red disk stars, M-dwarfs, contribute at most $ 15%$ to the mass of the disk. We parameterize the faint end of the cumulative distribution of stars, $\Phi$, as a function of luminosity $L_V$, $d\Phi/d \ln L_V \propto L_V^{-\gamma}$. For spheroid stars, $\gamma<0.32$ over the range $6<M_V<17$, with 98% confidence. The disk luminosity function falls, $\gamma<0$, for $15\lsim M_V\lsim 19$. Faint red stars in the disk or thick disk, and stars with $M_V<16$ in the spheroid contribute $\tau< 10^{-8}$ to the optical depth to microlensing toward the Large Magellanic Cloud. 
John N. Bahcall, Chris Flynn, Andrew Gould, and Sofia Kirhakos