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The halo mass–temperature (M–T) relation for a sample of 216 galaxy clusters, groups, and individual galaxies observed by the Chandra X-ray Observatory is presented. Using accurate spectral measurements of their hot atmospheres, we derive the M–T relation for systems with temperatures ranging between 0.4 and 15.0 keV. We measure the total masses of the clusters, groups, and galaxies at radius R 2500, finding that the M 2500 ∝ T α relation follows a power law with α = 1.65 ± 0.06. Our relation agrees with recent lensing studies of the M–T relation at R 200 and is consistent with self-similar theoretical predictions and recent simulations. This agreement indicates that the M–T relation is weakly affected by nongravitational heating processes. Using lensing masses within R 200 we find M 200–T follows a power law with a slope of 1.61 ± 0.19, consistent with the M 2500–T relation. No evidence for a break or slope change is found in either relation. Potential biases associated with sample selection, evolution, and the assumption of hydrostatic equilibrium that may affect the scaling are examined. No significant impacts attributable to these biases are found. Non-cool-core clusters and early spirals produce higher scatter in the M–T relation than cool-core clusters and elliptical galaxies.

Molecular gas flows are analyzed in 14 cluster galaxies (BCGs) centered in cooling hot atmospheres. The BCGs contain $10^{9}-10^{11}~\rm M_\odot$ of molecular gas, much of which is being moved by radio jets and lobes. The molecular flows and radio jet powers are compared to molecular outflows in 45 active galaxies within z < 0.2. We seek to understand the relative efficacy of radio, quasar, and starburst feedback over a range of active galaxy types. Molecular flows powered by radio feedback in BCGs are ∼10–1000 times larger in extent compared to contemporary galaxies hosting quasar nuclei and starbursts. Radio feedback yields lower flow velocities but higher momenta compared to quasar nuclei, as the molecular gas flows in BCGs are usually ∼10–100 times more massive. The product of the molecular gas mass and lifting altitude divided by the AGN or starburst power — a parameter referred to as the lifting factor—exceeds starbursts and quasar nuclei by two to three orders of magnitude, respectively. When active, radio feedback is generally more effective at lifting gas in galaxies compared to quasars and starburst winds. The kinetic energy flux of molecular clouds generally lies below and often substantially below a few percent of the driving power. We find tentatively that star formation is suppressed in BCGs relative to other active galaxies, perhaps because these systems rarely form molecular disks that are more impervious to feedback and are better able to promote star formation.