  We present HST/ACS observations of 19 nearby M subdwarfs in a search for
binary systems. Other than the wide common proper motion pair LHS 2140/2139,
none of our sdM and esdM targets are found to be binaries. Our survey is
sensitive to equal-luminosity companions at close (2-8 AU) separations, while
sub-stellar secondaries could have been detected at separations in the range of
6-30 AU. To check for wide binaries, we have compared the POSS I and II images
in a field of view as large as 10'x10', but could not detect a single co-moving
star for any of the targets. Combining our results with those from Gizis &
Reid, we have a binary fraction of 3% (1/28). Detection of a small number of M
subdwarf binaries reported in the literature suggests a higher fraction than
the one obtained here, probably comparable to that found for the more massive
solar-type stars in the halo (13-15%). Comparison with the disk M dwarf
fraction (25%) however suggests multiplicity to be rare among the lowest mass
halo stars, implying the two populations formed under different initial
conditions. The low binary fraction in our survey could be explained by
selection biases. A decrease in multiplicity has been observed in the disk for
masses below 0.1Msun, the peak in the disk mass function (MF). The globular
cluster MF is found to peak at about 0.33Msun, with a decrease in the number of
stars per unit mass below the peak mass. Our sample being composed of stars
with masses between ~0.2 and 0.085 Msun suggests that a decrease in
multiplicity similar to the disk may also be true for the halo stars, but
perhaps below a mass of ~0.3Msun. A higher M subdwarf binary fraction may be
obtained if the selected primaries have masses near or higher than the peak in
the MF.
