The GOGREEN Survey: Constraining the Satellite Quenching Timescale in Massive Clusters at $\boldsymbol{z} \gtrsim 1$

We model satellite quenching at $z \sim 1$ by combining $14$ massive ($10^{13.8} < M_{\mathrm{halo}}/\mathrm{M}_{\odot} < 10^{15}$) clusters at $0.8 < z < 1.3$ from the GOGREEN and GCLASS surveys with accretion histories of $56$ redshift-matched analogs from the IllustrisTNG simulation. Our fiducial model, which is parameterized by the satellite quenching timescale ($\tau_{\rm quench}$), accounts for quenching in our simulated satellite population both at the time of infall by using the observed coeval field quenched fraction and after infall by tuning $\tau_{\rm quench}$ to reproduce the observed satellite quenched fraction versus stellar mass trend. This model successfully reproduces the observed satellite quenched fraction as a function of stellar mass (by construction), projected cluster-centric radius, and redshift and is consistent with the observed field and cluster stellar mass functions at $z \sim 1$. We find that the satellite quenching timescale is mass dependent, in conflict with some previous studies at low and intermediate redshift. Over the stellar mass range probed ($M_{\star}> 10^{10}~\mathrm{M}_{\odot}$), we find that the satellite quenching timescale decreases with increasing satellite stellar mass from $\sim1.6~{\rm Gyr}$ at $10^{10}~\mathrm{M}_{\odot}$ to $\sim 0.6 - 1~{\rm Gyr}$ at $10^{11}~\mathrm{M}_{\odot}$ and is roughly consistent with the total cold gas (H{\scriptsize I}+H$_{2}$) depletion timescales at intermediate $z$, suggesting that starvation may be the dominant driver of environmental quenching at $z < 2$. Finally, while environmental mechanisms are relatively efficient at quenching massive satellites, we find that the majority ($\sim65-80\%$) of ultra-massive satellites ($M_{\star} > 10^{11}~\mathrm{M}_{\odot}$) are quenched prior to infall.