The Origin of Molecular Clouds in Central Galaxies

We present an analysis of 55 central galaxies in clusters and groups with molecular gas masses and star formation rates lying between ${10}^{8}\,\mathrm{and}\,{10}^{11}\ {M}_{\odot }$ and 0.5 and 270 ${M}_{\odot }\ {\mathrm{yr}}^{-1}$, 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 (${t}_{\mathrm{cool}}/{t}_{\mathrm{ff}}$) falls below ~10. We find that (1) molecular gas-rich systems instead lie between $10\lt \min ({t}_{\mathrm{cool}}/{t}_{\mathrm{ff}})\lt 25$, where ${t}_{\mathrm{cool}}/{t}_{\mathrm{ff}}=25$ corresponds approximately to cooling time and entropy thresholds of 1 Gyr and $35\,\mathrm{keV}\,{\mathrm{cm}}^{2}$, respectively; (2) $\min ({t}_{\mathrm{cool}}/{t}_{\mathrm{ff}}$) is uncorrelated with molecular gas mass and jet power; and (3) the narrow range $10\lt \min ({t}_{\mathrm{cool}}/{t}_{\mathrm{ff}})\lt 25$ 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 ${t}_{\mathrm{cool}}/{t}_{\mathrm{ff}}\lesssim 10$. 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).