Elemental Abundances in M31: Alpha and Iron Element Abundances from
  Low-Resolution Resolved Stellar Spectroscopy in the Stellar Halo
  Measurements of [Fe/H] and [$\alpha$/Fe] can probe the minor merging history
of a galaxy, providing a direct way to test the hierarchical assembly paradigm.
While measurements of [$\alpha$/Fe] have been made in the stellar halo of the
Milky Way, little is known about detailed chemical abundances in the stellar
halo of M31. To make progress with existing telescopes, we apply spectral
synthesis to low-resolution DEIMOS spectroscopy (R $\sim$ 2500 at 7000
Angstroms) across a wide spectral range (4500 Angstroms $<$ $\lambda$ $<$ 9100
Angstroms). By applying our technique to low-resolution spectra of 170 giant
stars in 5 MW globular clusters, we demonstrate that our technique reproduces
previous measurements from higher resolution spectroscopy. Based on the
intrinsic dispersion in [Fe/H] and [$\alpha$/Fe] of individual stars in our
combined cluster sample, we estimate systematic uncertainties of $\sim$0.11 dex
and $\sim$0.09 dex in [Fe/H] and [$\alpha$/Fe], respectively. We apply our
method to deep, low-resolution spectra of 11 red giant branch stars in the
smooth halo of M31, resulting in higher signal-to-noise per spectral resolution
element compared to DEIMOS medium-resolution spectroscopy, given the same
exposure time and conditions. We find $\langle$[$\alpha$/Fe]$\rangle$ = 0.49
$\pm$ 0.29 dex and $\langle$[Fe/H]$\rangle$ = 1.59 $\pm$ 0.56 dex for our
sample. This implies that---much like the Milky Way---the smooth halo of M31 is
likely composed of disrupted dwarf galaxies with truncated star formation
histories that were accreted early in the halo's formation.
