Deep UBRI images of a 15 ^ { \prime } \times 15 ^ { \prime } field in the outer spheroid of the M31 galaxy obtained using the Kitt Peak National Observatory 4-meter telescope , and I band images obtained with the Keck 10-meter telescope and Low Resolution Imaging Spectrograph , are used to isolate a sample of candidate red giant branch stars located at a projected radial distance of 19 kpc along the minor axis . These stars are distinguished from the more numerous distant field galaxies on the basis of broadband U - B , B - R , and R - I colors and image morphology : We isolate objects whose colors are consistent with the long , but relatively narrow locus occupied by red giants in UBRI color space ( as observed in Galactic globular cluster giants and predicted by models spanning a wide range of metallicities and ages ) , and those whose angular sizes are consistent with the stellar point spread function , FWHM = 0 \hbox { $\ > . ^ { \prime \prime } $ } 6 – 0 \hbox { $\ > . ^ { \prime \prime } $ } 9 ( Keck ) and FWHM = 0 \hbox { $\ > . ^ { \prime \prime } $ } 9 – 1 \hbox { $\ > . ^ { \prime \prime } $ } 5 ( Kitt Peak ) . We carry out the same analysis of data on a comparison field with a similar Galactic latitude to the M31 halo field . The color-magnitude diagram of objects in the comparison field is well described by a superposition of foreground Galactic dwarf stars ( in keeping with a standard empirical model of the Galaxy ) against a backdrop of contaminating faint blue field galaxies ( I \ga 21 , B - I \sim 1 \ > – \ > 2.5 ) , while the M31 halo field contains a clear excess of faint red objects ( I \sim 20 \ > – \ > 23 , B - I \sim 2 \ > – \ > 3.5 ) in addition to these two components . The location of this population of faint red objects in the color-magnitude diagram is as would be expected for red giant stars at the distance of M31 . The surface density of red giant candidates in the R = 19 kpc M31 halo field is consistent with the findings of two recent Hubble Space Telescope studies . The data indicate that M31 ’ s stellar halo is much denser and/or larger than that of the Galaxy : ( \rho _ { M 31 } ^ { RGB } / \rho _ { MW } ^ { RGB } ) ( \Lambda / 1.5 ) ^ { - \nu } \sim 10 , where \Lambda is the ratio of the radial scale lengths of M31 and the Galaxy and \nu = -3.8 is the assumed power law index of the density profile ; in fact , M31 ’ s profile may be steeper than this ( \nu < -3.8 ) . The color and slope of the red giant branch in M31 ’ s outer halo are suggestive of a relatively metal-rich population , [ Fe / H ] \ga - 1 , in agreement with the Hubble Space Telescope measurements .