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CO (J=1-0) Observation of the cD Galaxy of AWM7: Constraints on the Evaporation of Molecular Gas

We have searched for molecular gas in the cD galaxy of a poor cluster of galaxies AWM7 using Nobeyama 45 m telescope. We do not detect CO emission in the galaxy. Our limit of molecular gas in the inner 7.5 kpc is M_H_2< 4 x 10^8 M_sun. We estimate the total mass of molecular gas left in the cD galaxy when the gas deposited by a cooling flow once becomes molecular gas and the molecular gas is continuously evaporated by the ambient hot gas. The observational limit of molecular gas requires f >~ 10^{-3}, where f is the ratio of the heat conduction rate to that of Spitzer. However, this contradicts recent X-ray observations showing f<10^{-5}. Thus, the non-detection of CO cannot be explained by the evaporation, and most of the cooled gas predicted by a cooling flow model may not change into molecular gas in the cD galaxy. Moreover, we estimate the evaporation time of molecular clouds brought to a cD galaxy through the capture of gas-rich galaxies and find that these clouds should not be evaporated if f <~ 10^{-3}-10^{-4}. Therefore, the non-detection of CO in a cD galaxy could constrain the total mass of the molecular clouds brought into it.