The Mass-Function of Low Mass Halo Stars: Limits on Baryonic Halo Dark Matter

We derive mass functions for halo red dwarfs (stars just massive enough to burn hydrogen) with varying assumptions about metallicity and about possible unresolved binaries in the sample. 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). We find that the mass function for halo red dwarfs cannot rise more quickly than $1/m^2$ as one approaches the hydrogen burning limit. We also find a more accurate estimate (than in our previous work) of the local halo density for red dwarfs: $2 \times 10^{-5} \msun/{\rm pc}^3$, i.e., roughly $0.3\%$ of the mass of the halo. We extrapolate these mass functions into the brown-dwarf regime. Using star formation theory of Adams and Fatuzzo (1996), we show 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).