Origins of molecular clouds in early-type galaxies
  We analyze $Chandra$ observations of the hot atmospheres of 40 early spiral
and elliptical galaxies. Using new temperature, density, cooling time, and mass
profiles, we explore relationships between their hot atmospheres and cold
molecular gas. Molecular gas mass correlates with atmospheric gas mass and
density over four decades from central galaxies in clusters to normal giant
ellipticals and early spirals. The mass and density relations follow power
laws: $M_{\rm mol} \propto M_{\rm X}^{1.4\pm0.1}$ and $M_{\rm mol} \propto
n_{\rm e}^{1.8\pm0.3}$, respectively, at 10 kpc. The ratio of molecular gas to
atmospheric gas within a 10 kpc radius lies between $3\%$ and $10\%$ for
early-type galaxies and between $3\%$ and $50\%$ for central galaxies in
clusters. Early-type galaxies have detectable levels of molecular gas when
their atmospheric cooling times falls below $\sim \rm Gyr$ at a radius of 10
kpc. A similar trend is found in central cluster galaxies. We find no
relationship between the ratio of the cooling time to free fall time, $t_{\rm
c}/t_{\rm ff}$, and the presence or absence of molecular clouds in early-type
galaxies. The data are consistent with much of the molecular gas in early-type
galaxies having condensed from their hot atmospheres.
