M Dwarfs From Hubble Space Telescope Star Counts III: The Groth Strip

We analyze the disk M dwarfs found in 31 new fields observed with the Wide Field Camera (WFC2) on the Hubble Space Telescope (HST) together with the sample previously analyzed from 22 WFC2 fields and 162 prerepair Planetary Camera (PC1) fields. The new observations, which include the 28 high-latitude fields comprising the Large Area Multi-Color Survey (``Groth Strip''), increase the total sample to 337 stars, and more than double the number of late M dwarfs (M_V>13.5) from 23 to 47. The mass function changes slope at M~0.6 Msun, from a near-Salpeter power-law index of \alpha=-1.21 to \alpha=0.44. In both regimes the mass function at the Galactic plane is given by ${d^3 N / d\log M d M_V d V} = 8.1\times 10^{-2}\pc^{-3} ({M / 0.59 M_\odot})^{\alpha}$. The correction for secondaries in binaries changes the low-mass index from \alpha=0.44 to \alpha\sim 0.1. If the Salpeter slope continued to the hydrogen-burning limit, we would expect 500 stars in the last four bins (14.5<M_V<18.5), instead of the 25 actually detected. The explanation of the observed microlensing rate towards the Galactic bulge requires either a substantial population of bulge brown dwarfs or that the disk and bulge mass functions are very different for stars with M~< 0.5 Msun.