Star formation activity and cold gas contents. Left: Galaxy star formation rate as a function of halo mass, at z = 0. A quiescent threshold of sSFR < 10⁻¹¹yr⁻¹ is indicated as the gray triangular region, adopting the stellar mass to halo mass relation of TNG-Cluster. Black crosses mark those clusters identified as strong cool-cores with the fiducial criterion of (Lehle et al. 2024). The vast majority of central galaxies in clusters are quenched, and only a small number have non-negligible levels of residual star formation. Right: total cold (HI) mass in the halo as a function of mass, compared to observations stacking ALFALFA data on SDSS groups and clusters (Obuljen et al. 2019).