A Gradual Decline of Star Formation since Cluster In-fall: New Kinematic Insights into Environmental Quenching at 0.3 < z < 1.1

The environments where galaxies reside crucially shape their star formation histories. We investigate a large sample of 1626 cluster galaxies located within 105 galaxy clusters spanning a large range in redshift ($0.26 < z < 1.13)$. The galaxy clusters are massive (M$_{500} \gtrsim 2\times10^{14}$M$_{\odot}$), and are uniformly selected from the SPT and ACT Sunyaev-Zel'dovich (SZ) surveys. With spectra in-hand for thousands of cluster members, we use galaxies' position in projected phase space as a proxy for their in-fall times, which provides a more robust measurement of environment than quantities such as projected cluster-centric radius. We find clear evidence for a gradual age increase of the galaxy's mean stellar populations ($\sim$ 0.71 $\pm$ 0.4 Gyr based on a 4000 $\r{A}$ break, $\rm D_{\rm n}4000$) with the time spent in the cluster environment. This environmental quenching effect is found regardless of galaxy luminosity (faint or bright) and redshift (low-$z$ or high-$z$), although the exact stellar age of galaxies depends on both parameters at fixed environmental effects. Such a systematic increase of $\rm D_{\rm n}4000$ with in-fall proxy would suggest that galaxies that were accreted into hosts earlier were quenched earlier, due to longer exposure to environmental effects such as ram pressure stripping and starvation. Compared to the typical dynamical time scales of $1-3$ Gyr of cluster galaxies, the relatively small age increase ($\sim$ 0.71 $\pm$ 0.4 Gyr) found in our sample galaxies seems to suggest that a slow environmental process such as starvation is the dominant quenching pathway. Our results provide new insights into environmental quenching effects spanning a large range in cosmic time ($\sim 5.2$ Gyr, $z=0.26$--1.13) and demonstrate the power of using a kinematically-derived in-fall time proxy.