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 et al . 1995 ) .
We use stellar models of Alexander et al . ( 1996 ) and make varying assumptions about metallicity and about possible unresolved binaries in the sample .
We find that the MF for halo red dwarfs can not 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 .