The Mass-Function of Low Mass Halo Stars: Limits on Baryonic Halo Dark   Matter
  We derive mass functions (MF) for halo red dwarfs (the faintest hydrogen burning stars) and then extrapolate to place limits on the total mass of halo brown dwarfs (stars not quite massive enough to burn hydrogen). The mass functions are obtained from the luminosity function of a sample of 114 local halo stars in the USNO parallax survey (Dahn \etal 1995). We use stellar models of Alexander \etal (1996) and make varying assumptions about metallicity and about possible unresolved binaries in the sample. We find that the MF for halo red dwarfs cannot rise more quickly than $1/m^2$ as one approaches the hydrogen burning limit. Using recent results from star formation theory, we extrapolate the MF into the brown-dwarf regime. We see that likely extrapolations imply that the total mass of brown dwarfs in the halo is less than $\sim 3\%$ of the local mass density of the halo ($\sim 0.3\%$ for the more realistic models we consider). Our limits apply to brown dwarfs in the halo that come from the same stellar population as the red dwarfs. 
David S. Graff and Katherine Freese