Elemental Abundances in M31: A Comparative Analysis of Iron and Alpha
  Element Abundances in the Outer Disk, Giant Stellar Stream, and Inner Halo of
  M31
  We measured [Fe/H] and [$\alpha$/Fe] using spectral synthesis of
low-resolution stellar spectroscopy for 70 individual red giant branch stars
across four fields spanning the outer disk, Giant Stellar Stream (GSS), and
inner halo of M31. Fields at M31-centric projected distances of 23 kpc in the
halo, 12 kpc in the halo, 22 kpc in the GSS, and 26 kpc in the outer disk are
$\alpha$-enhanced, with $\langle$[$\alpha$/Fe]$\rangle$ = 0.43, 0.50, 0.41, and
0.58, respectively. The 23 kpc and 12 kpc halo fields are relatively
metal-poor, with $\langle$[Fe/H]$\rangle$ = $-$1.54 and $-$1.30, whereas the 22
kpc GSS and 26 kpc outer disk fields are relatively metal-rich with
$\langle$[Fe/H]$\rangle$ = $-$0.84 and $-$0.92, respectively. For fields with
substructure, we separated the stellar populations into kinematically hot
stellar halo components and kinematically cold components. We did not find any
evidence of an [$\alpha$/Fe] gradient along the high surface brightness core of
the GSS between $\sim$17$-$22 kpc. However, we found tentative suggestions of a
negative [$\alpha$/Fe] gradient in the stellar halo, which may indicate that
different progenitor(s) or formation mechanisms contributed to the build up of
the inner versus outer halo. Additionally, the [$\alpha$/Fe] distribution of
the metal-rich ([Fe/H] $>$ $-$1.5), smooth inner stellar halo (r$_{\rm{proj}}$
$\lesssim$ 26 kpc) is inconsistent with having formed from the disruption of
progenitor(s) similar to present-day M31 satellite galaxies. The 26 kpc outer
disk is most likely associated with the extended disk of M31, where its high
$\alpha$-enhancement provides support for an episode of rapid star formation in
M31's disk, possibly induced by a major merger.
