Revealing environmental dependence of molecular gas content in a distant X-ray cluster at z=2.51

We present a census of the molecular gas properties of galaxies in the most distant known X-ray cluster, CLJ1001, at z=2.51, using deep observations of CO(1-0) with JVLA. In total 14 cluster members with $M_{*} > 10^{10.5} M_{\odot}$ are detected, including all the massive star-forming members within the virial radius, providing the largest galaxy sample in a single cluster at $z > 2$ with CO(1-0) measurements. We find a large variety in the gas content of these cluster galaxies, which is correlated with their relative positions (or accretion states), with those closer to the cluster core being increasingly gas-poor. Moreover, despite their low gas content, the galaxies in the cluster center exhibit an elevated star formation efficiency (SFE=SFR/$M_{\rm gas}$) compared to field galaxies, suggesting that the suppression on the SFR is likely delayed compared to that on the gas content. Their gas depletion time is around $t_{\rm dep} \sim 400$ Myrs, comparable to the cluster dynamical time. This implies that they will likely consume all their gas within a single orbit around the cluster center, and form a passive cluster core by $z\sim2$. This result is one of the first direct pieces of evidence for the influence of environment on the gas reservoirs and SFE of $z > 2$ cluster galaxies, thereby providing new insights into the rapid formation and quenching of the most massive galaxies in the early universe.