Synthesizing Stellar Populations in South Pole Telescope Galaxy
  Clusters: I. Ages of Quiescent Member Galaxies at 0.3 < z < 1.4
  Using stellar population synthesis models to infer star formation histories
(SFHs), we analyse photometry and spectroscopy of a large sample of quiescent
galaxies which are members of Sunyaev-Zel'dovich (SZ)-selected galaxy clusters
across a wide range of redshifts. We calculate stellar masses and mass-weighted
ages for 837 quiescent cluster members at 0.3 < z < 1.4 using rest-frame
optical spectra and the Python-based Prospector framework, from 61 clusters in
the SPT-GMOS Spectroscopic Survey (0.3 < z < 0.9) and 3 clusters in the SPT
Hi-z cluster sample (1.25 < z < 1.4). We analyse spectra of subpopulations
divided into bins of redshift, stellar mass, cluster mass, and velocity-radius
phase-space location, as well as by creating composite spectra of quiescent
member galaxies. We find that quiescent galaxies in our dataset sample a
diversity of SFHs, with a median formation redshift (corresponding to the
lookback time from the redshift of observation to when a galaxy forms 50% of
its mass, t$_{50}$) of $z=2.8\pm0.5$, which is similar to or marginally higher
than that of massive quiescent field and cluster galaxy studies. We also report
median age-stellar mass relations for the full sample (age of the Universe at
$t_{50}$ (Gyr) = $2.52 (\pm0.04) - 1.66 (\pm0.11)$ log$_{10}(M/10^{11}
M\odot))$ and recover downsizing trends across stellar mass; we find that
massive galaxies in our cluster sample form on aggregate $\sim0.75$ Gyr earlier
than lower mass galaxies. We also find marginally steeper age-mass relations at
high redshifts, and report a bigger difference in formation redshifts across
stellar mass for fixed environment, relative to formation redshifts across
environment for fixed stellar mass.
