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
21 pages, 9 figures, 3 tables. Submitted to ApJ. Posted after referee report; comments very welcome