Cluster candidates with massive quiescent galaxies at $z\sim2$

Galaxy clusters are crucial to understanding role of the environment in galaxy evolution. However, due to their rarity, only a limited number of clusters have been identified at $z\gtrsim2$. In this paper, we report a discovery of seven cluster candidates with massive quiescent galaxies at $z\sim2$ in the $3.5\,\mathrm{deg}^{2}$ area of the XMM-LSS field, roughly doubling the known cluster sample at this frontier redshift if confirmed. We construct a photometric redshift catalog based on deep ($i\sim26$, $K\mathrm{s}\sim24$) multi-wavelength photometry from $u^*$-band to $K$-band gathered from the Hyper Suprime-Cam Subaru Strategic Program and other collaborative/public surveys. We adopt a Gaussian kernel density estimate with two different spatial scales (10" and 60") to draw a density map of massive ($\log(M{*}/M{\odot})>10.5$) and quiescent ($\log(\mathrm{sSFR\, [\mathrm{yr^{{-1}}]})<-10$)} galaxies at $z\sim2$. Then, We identify seven prominent overdensities. These candidates show clear red sequences in color-magnitude diagrams ($z-H$ vs. $H$). Moreover, one of them shows an extended X-ray emission with $L\mathrm{X}=(1.46\pm0.35)\times10^{44}$ erg s$^{-1}$, suggesting its virialized nature. There is no clear evidence of enhancement nor suppression of the star formation rate of the main sequence galaxies in the clusters. We find that cluster galaxies have a higher fraction of transition population with $-10.5<\log(\mathrm{sSFR\, [\mathrm{yr^{{-1}}]})<-10$} ($12\%$) than the field ($2\%$), which implies the ongoing star formation quenching. The quiescent fraction in the cluster candidates also exceeds that in the field. We confirm that the excess of a quiescent fraction is larger for higher-mass galaxies. This is the first statistical evidence for the mass-dependent environmental quenching at work in clusters even at $z\sim2$.