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 Å ) across a wide spectral range ( 4500 Å < \lambda < 9100 Å ) .
By applying our technique to low-resolution spectra of \deleted 135 \added 170 \deleted red giant branch ( RGB ) \added giant stars in \deleted 4 \added 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 \deleted 0.040.09 dex in [ Fe/H ] and [ \alpha /Fe ] , respectively .
We apply our method to deep , low-resolution spectra of \deleted 14 \added 11 \deleted RGB \added 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 \deleted 0.31 \added 0.29 dex and \langle [ Fe/H ] \rangle = - \deleted 1.53 \added 1.59 \pm \deleted 0.52 \added 0.56 dex for our sample .
This implies that \added —much like the Milky Way—the smooth halo field \added of M31 is likely composed of disrupted dwarf galaxies with truncated star formation histories that were accreted early in \deleted the formation history of M31 \added the halo ’ s formation .