RR Lyrae Variables in Two Fields in the Spheroid of M31

We present Hubble Space Telescope observations taken with the Advanced Camera for Surveys Wide Field Channel of two fields near M32 - between four and six kpc from the center of M31. The data cover a time baseline sufficient for the identification and characterization of 681 RR Lyrae variables of which 555 are ab-type and 126 are c-type. The mean magnitude of these stars is <V>=25.29 +/- 0.05 where the uncertainty combines both the random and systematic errors. The location of the stars in the Bailey Diagram and the ratio of c-type RR Lyraes to all types are both closer to RR Lyraes in Oosterhoff type I globular clusters in the Milky Way as compared with Oosterhoff II clusters. The mean periods of the ab-type and c-type RR Lyraes are <P(ab)>=0.557 +/- 0.003 and <P(c)>=0.327 +/- 0.003, respectively, where the uncertainties in each case represent the standard error of the mean. When the periods and amplitudes of the ab-type RR Lyraes in our sample are interpreted in terms of metallicity, we find the metallicity distribution function to be indistinguishable from a Gaussian with a peak at <[Fe/H]>=-1.50 +/- 0.02, where the quoted uncertainty is the standard error of the mean. Using a relation between RR Lyrae luminosity and metallicity along with a reddening of E(B-V) = 0.08 +/- 0.03, we find a distance modulus of (m-M)o=24.46 +/- 0.11 for M31. We examine the radial metallicity gradient in the environs of M31 using published values for the bulge and halo of M31 as well as the abundances of its dwarf spheroidal companions and globular clusters. In this context, we conclude that the RR Lyraes in our two fields are more likely to be halo objects rather than associated with the bulge or disk of M31, in spite of the fact that they are located at 4-6 kpc in projected distance from the center.