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 play a key role in shaping their star formation histories over cosmic time, yet such environmental effects remain elusive at high redshifts. We update this environmental process by adopting an advanced measure for cluster in-fall time using kinematics and reveal that galaxies experience a gradual decline of star formation after they fall into cluster environments up to $z \sim 1$. This conclusion is drawn from a uniform analysis of a remarkably large sample of 105 clusters and 1626 spectroscopically-confirmed member galaxies from the SPT and ACT Sunyaev-Zel'dovich surveys at 0.26 $< z <$ 1.13. Intriguingly, we find clear evidence for a gradual increase in the mean age ($\sim$ 0.71 $\pm$ 0.4 Gyr based on a 4000 Angstrom break, $\rm D_{\rm n}4000$) of the galaxy's stellar populations 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 effect. 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 strangulation. Thus, 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.