Using stellar population synthesis models to infer star formation histories (SFHs), we analyze photometry and spectroscopy of a large sample of quiescent galaxies that 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 three clusters in the SPT Hi-z cluster sample (1.25 < z < 1.4). We analyze 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 data set 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 ± 0.5, 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 (±0.04)-1.66 (±0.12) log10(M/1011 M ⊙)) and recover downsizing trends across stellar mass; we find that massive galaxies in our cluster sample form on aggregate ∼0.75 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.
