We analyzed Chandra X-ray observations of five galaxy clusters whose atmospheric cooling times, entropy parameters, and cooling time to free-fall time ratios within the central galaxies lie below 1 Gyr, below 30 keV cm^2, and between 20 < tcool/tff < 50, respectively. These thermodynamic properties are commonly associated with molecular clouds, bright H-alpha emission, and star formation in central galaxies. However, none of these clusters have detectable H-alpha indicated in the ACCEPT database, nor do they have significant star formation rates or detectable molecular gas. Among these, only RBS0533 has a detectable radio/X-ray bubble which are commonly observed in cooling atmospheres. Signatures of uplifted, high metallicity atmospheric gas are absent. Despite its prominent X-ray bubble, RBS0533 lacks significant levels of molecular gas. Cold gas is absent at appreciable levels in these systems perhaps because their radio sources have failed to lift low entropy atmospheric gas to an altitude where the ratio of the cooling time to the free-fall time falls below unity.
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