2018ApJ...853..177P

We present an analysis of 55 central galaxies in clusters and groups with molecular gas masses and star formation rates lying between 10⁸ and 10¹¹ M_☉ and 0.5 and 270 M_☉ yr^–1, respectively. Molecular gas mass is correlated with star formation rate, Hα line luminosity, and central atmospheric gas density. Molecular gas is detected only when the central cooling time or entropy index of the hot atmosphere falls below ∼1 Gyr or ∼35 keV cm², respectively, at a (resolved) radius of 10 kpc. These correlations indicate that the molecular gas condensed from hot atmospheres surrounding the central galaxies. We explore the origins of thermally unstable cooling by evaluating whether molecular gas becomes prevalent when the minimum of the cooling to free-fall time ratio (t_cool/t_ff) falls below ∼10. We find that (1) molecular gas-rich systems instead lie between 10 {min}(t_cool/t_ff) 25, where t_cool/t_ff=25 corresponds approximately to cooling time and entropy thresholds of 1 Gyr and 35 keV cm², respectively; (2) {min}(t_cool/t_ff) is uncorrelated with molecular gas mass and jet power; and (3) the narrow range 10 {min}(t_cool/t_ff) 25 can be explained by an observational selection effect, although a real physical effect cannot be excluded. These results and the absence of isentropic cores in cluster atmospheres are in tension with models that assume thermal instability ensues from linear density perturbations in hot atmospheres when t_cool/t_ff 10. Some of the molecular gas may instead have condensed from atmospheric gas lifted outward by buoyantly rising X-ray bubbles or by dynamically induced uplift (e.g., mergers, sloshing).