  We have used Hubble Space Telescope Wide Field Planetary Camera 2
observations to construct a color-magnitude diagram (CMD) for the bulge of M31
at a location ~1.6 kpc from the galaxy's center. Using scaled-solar abundance
theoretical red giant branches with a range of metallicities, we have
translated the observed colors of the stars in the CMD to abundances and
constructed a metallicity distribution function (MDF) for this region. The MDF
shows a peak at [M/H]~0 with a steep decline at higher metallicities and a more
gradual tail to lower metallicities. This is similar in shape to the MDF of the
Milky Way bulge but shifted to higher metallicities by ~0.1 dex. As is the case
with the Milky Way bulge MDF, a pure closed box model of chemical evolution,
even with significant pre-enrichment, appears to be inconsistent with the M31
bulge MDF. However, a scenario in which an initial infall of gas enriched the
bulge to an abundance of [M/H] ~ -1.6 with subsequent evolution proceeding as a
closed box provides a better fit to the observed MDF. The similarity between
the MDF of the M31 bulge and that of the Milky Way stands in stark contrast to
the significant differences in the MDFs of their halo populations. This
suggests that the bulk of the stars in the bulges of both galaxies were in
place before the accretion events that occurred in the halos could influence
them.
