We have conducted a wide-field CCD-mosaic study of the resolved red-giant branch (RGB) stars of M31, in a field located 20 kpc from the nucleus along the SE minor axis. In our (I, V-I) color-magnitude diagram, RGB stars in the top three magnitudes of the M31 halo are strongly present. Photometry of a more distant control field to subtract field contamination is used to derive the `cleaned luminosity function and metallicity distribution function (MDF) of the M31 halo field. From the color distribution of the foreground Milky Way halo stars, we find a reddening E(V-I)= 0.10 +/- 0.02 for this field, and from the luminosity of the RGB tip, we determine a distance modulus (m-M)_o = 24.47 +/- 0.12 (= 783 +/- 43 kpc). The MDF is derived from interpolation within an extensive new grid of RGB models (Vandenberg et al. 2000). The MDF is dominated by a moderately high-metallicity population ([m/H]~ -0.5) found previously in more interior M31 halo/bulge fields, and is much more metal-rich than the [m/H]~ -1.5 level in the Milky Way halo. A significant (~30% - 40%, depending on AGB star contribution) metal-poor population is also present. To first order, the shape of the MDF resembles that predicted by a simple, single-component model of chemical evolution starting from primordial gas with an effective yield y=0.0055. It strongly resembles the MDF recently found for the outer halo of the giant elliptical NGC 5128 (Harris et al. 2000), though NGC 5128 has an even lower fraction of low-metallicity stars. Intriguingly, in both NGC 5128 and M31, the metallicity distribution of the globular clusters in M31 does not match the halo stars; the clusters are far more heavily weighted to metal-poor objects. We suggest similarities in the formation and early evolution of massive, spheroidal stellar systems.
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