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Deep three band ($B_J < 27.5, R < 26.4, I < 25 mag$) CCD images of 12 high galactic latitude fields covering a total of $144 arcmin^2$ on the sky have been obtained as part of a 4-m survey done at CTIO over the past decade. Together with a single $2048^2$ CCD field covering 48 sq. arcmin on the sky obtained at KPNO, these data have been analyzed to search for M dwarfs near the halo and disk hydrogen burning limits. Our color data have been carefully calibrated using stars of different luminosities which have spectroscopically determined metallicities, in order to separate out the different population types. We find no evidence for a population of very low mass M dwarfs sufficient to account for an important fraction of the halo dark matter.
For the least luminous halo M subdwarfs ($M_V \approx 15$) our survey is complete out to 3000 pc, covering a volume of approx. 205,000 $pc^3$. We detect 6 objects having colors consistent with M subdwarfs of $M_V = 13.5 -- 15$, though this sample may be contaminated by 1--2 misclassified compact high redshift galaxies of similar color which appear stellar. Our finding is consistent with the halo luminosity function determined in the solar neighborhood by Dahn and Liebert (1994 Proceedings of the ESO workshop: "The Bottom of the Main Sequence and Beyond"). They predict that we should find $5 \pm 3$ of the least luminous subdwarfs within our volume. By comparison, the halo luminosity function of Richer and Fahlman (1992, Nature 358, 383) would predict over five times as many low mass M subdwarfs than we find in our surveys.
Moreover, with a completeness limit of 500 pc, we find no excess of the least luminous disk M dwarfs (dM8-9, $M_V \approx 18 -- 19$) beyond that predicted by the luminosity function determined from a large area CCD Transit Instrument Survey (Kirpatrick et al 1994, ApJS 94, 749). Our data similarly suggest that the latest M dwarfs have a scale height much smaller than the 350 pc. value widely used for earlier M dwarfs.
