Elemental abundances in M31: Individual and Coadded Spectroscopic [Fe/H] and [{\alpha}/Fe] throughout the M31 Halo with SPLASH

We present spectroscopic chemical abundances of red giant branch (RGB) stars in Andromeda (M31), using medium resolution ($R\sim6000$) spectra obtained via the Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo (SPLASH) survey. In addition to individual chemical abundances, we coadd low signal-to-noise ratio (S/N) spectra of stars to obtain a high enough to measure average [Fe/H] and [$\alpha$/Fe] abundances. We obtain individual and coadded measurements for [Fe/H] and [$\alpha$/Fe] for M31 halo stars, covering a range of 9--180 kpc in projected radius from the center of M31. With these measurements, we greatly increase the number of outer halo ($R_{\mathrm{proj}} > 50$ kpc) M31 stars with spectroscopic [Fe/H] and [$\alpha$/Fe], adding abundance measurements for 45 individual stars and 33 coadds from a pool of an additional 174 stars. We measure the spectroscopic metallicity ([Fe/H]) gradient, finding a negative radial gradient of $-0.0050\pm0.0003$ for all stars in the halo, consistent with gradient measurements obtained using photometric metallicities. Using the first measurements of [$\alpha$/Fe] for M31 halo stars covering a large range of projected radii, we find a positive gradient ($+0.0026\pm0.0004$) in [$\alpha$/Fe] as a function of projected radius. We also explore the distribution in [Fe/H]--[$\alpha$/Fe] space as a function of projected radius for both individual and coadded measurements in the smooth halo, and compare these measurements to those stars potentially associated with substructure. These spectroscopic abundance distributions highlight the substantial evidence that M31 has had an appreciably different formation and merger history compared to our own Galaxy.