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We report the results of a pilot program to use the Magellan/M2FSspectrograph to survey the galactic populations and internal kinematics ofgalaxy clusters. For this initial study, we present spectroscopic measurementsfor $223$ quiescent galaxies observed along the line of sight to the galaxycluster Abell 267 ($z\sim0.23$). We develop a Bayesian method for modeling theintegrated light from each galaxy as a simple stellar population, with freeparameters that specify redshift ($v_\mathrm{los}/c$) and characteristic age,metallicity ($\mathrm{[Fe/H]}$), alpha-abundance ($[\alpha/\mathrm{Fe}]$), andinternal velocity dispersion ($\sigma_\mathrm{int}$) for individual galaxies.Parameter estimates derived from our 1.5-hour observation of A267 have medianrandom errors of $\sigma_{v_\mathrm{los}}=20\ \mathrm{km\ s^{-1}}$,$\sigma_{\mathrm{Age}}=1.2\ \mathrm{Gyr}$, $\sigma_{\mathrm{[Fe/H]}}=0.11\\mathrm{dex}$, $\sigma_{[\alpha/\mathrm{Fe}]}=0.07\ \mathrm{dex}$, and$\sigma_{\sigma_\mathrm{int}}=20\ \mathrm{km\ s^{-1}}$. In a companion paper,we use these results to model the structure and internal kinematics of A267.

Magellan/M2FS Spectroscopy of Galaxy Clusters: Stellar Population Model and Application to Abell 267