Elemental Abundances in M31: Gradients in the Giant Stellar Stream
  We analyze existing measurements of [Fe/H] and [$\alpha$/Fe] for individual
red giant branch (RGB) stars in the Giant Stellar Stream (GSS) of M31 to
determine whether spatial abundance gradients are present. These measurements
were obtained from low- ($R \sim 3000$) and moderate- ($R \sim 6000$)
resolution Keck/DEIMOS spectroscopy using spectral synthesis techniques as part
of the Elemental Abundances in M31 survey. From a sample of 62 RGB stars
spanning the GSS at 17, 22, and 33 projected kpc, we measure a [Fe/H] gradient
of $-$0.018 $\pm$ 0.003 dex kpc$^{-1}$ and negligible [$\alpha$/Fe] gradient
with M31-centric radius. We investigate GSS abundance patterns in the outer
halo using additional [Fe/H] and [$\alpha$/Fe] measurements for 6 RGB stars
located along the stream at 45 and 58 projected kpc. These abundances provide
tentative evidence that the trends in [Fe/H] and [$\alpha$/Fe] beyond 40 kpc in
the GSS are consistent with those within 33 kpc. We also compare the GSS
abundances to 65 RGB stars located along the possibly related Southeast (SE)
shelf substructure at 12 and 18 projected kpc. The abundances of the GSS and SE
shelf are consistent, supporting a common origin hypothesis, although this
interpretation may be complicated by the presence of [Fe/H] gradients in the
GSS. We discuss the abundance patterns in the context of photometric studies
from the literature and explore implications for the properties of the GSS
progenitor, suggesting that the high $\langle$[$\alpha$/Fe]$\rangle$ of the GSS
(+0.40 $\pm$ 0.05 dex) favors a major merger scenario for its formation.
