Global Properties of M31's Stellar Halo from the SPLASH Survey: II.
  Metallicity Profile
  We present the metallicity distribution of red giant branch (RGB) stars in
M31's stellar halo, derived from photometric metallicity estimates for over
1500 spectroscopically confirmed RGB halo stars. The stellar sample comes from
38 halo fields observed with the Keck/DEIMOS spectrograph, ranging from 9 to
175 kpc in projected distance from M31's center, and includes 52 confirmed M31
halo stars beyond 100 kpc. While a wide range of metallicities is seen
throughout the halo, the metal-rich peak of the metallicity distribution
function becomes significantly less prominent with increasing radius. The
metallicity profile of M31's stellar halo shows a continuous gradient from 9 to
~100 kpc, with a magnitude of -0.01 dex/kpc. The stellar velocity distributions
in each field are used to identify stars that are likely associated with tidal
debris features. The removal of tidal debris features does not significantly
alter the metallicity gradient in M31's halo: a gradient is maintained in
fields spanning 10 to 90 kpc. We analyze the halo metallicity profile, as well
as the relative metallicities of stars associated with tidal debris features
and the underlying halo population, in the context of current simulations of
stellar halo formation. We argue that the large scale gradient in M31's halo
implies M31 accreted at least one relatively massive progenitor in the past,
while the field to field variation seen in the metallicity profile indicates
that multiple smaller progenitors are likely to have contributed substantially
to M31's outer halo.
