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Using stellar population synthesis models to infer star formation histories(SFHs), we analyse photometry and spectroscopy of a large sample of quiescentgalaxies which are members of Sunyaev-Zel'dovich (SZ)-selected galaxy clustersacross a wide range of redshifts. We calculate stellar masses and mass-weightedages for 837 quiescent cluster members at 0.3 < z < 1.4 using rest-frameoptical spectra and the Python-based Prospector framework, from 61 clusters inthe SPT-GMOS Spectroscopic Survey (0.3 < z < 0.9) and 3 clusters in the SPTHi-z cluster sample (1.25 < z < 1.4). We analyse spectra of subpopulationsdivided into bins of redshift, stellar mass, cluster mass, and velocity-radiusphase-space location, as well as by creating composite spectra of quiescentmember galaxies. We find that quiescent galaxies in our dataset sample adiversity of SFHs, with a median formation redshift (corresponding to thelookback time from the redshift of observation to when a galaxy forms 50% ofits mass, t$_{50}$) of $z=2.8\pm0.5$, which is similar to or marginally higherthan that of massive quiescent field and cluster galaxy studies. We also reportmedian 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 thatmassive galaxies in our cluster sample form on aggregate $\sim0.75$ Gyr earlierthan lower mass galaxies. We also find marginally steeper age-mass relations athigh redshifts, and report a bigger difference in formation redshifts acrossstellar mass for fixed environment, relative to formation redshifts acrossenvironment for fixed stellar mass.

Synthesizing Stellar Populations in South Pole Telescope Galaxy Clusters: I. Ages of Quiescent Member Galaxies at 0.3 < z < 1.4