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.Comment: 5 pages, 1 figure, to be published in PAS
