Massive molecular gas as a fuel tank for AGN feedback in central cluster galaxies

Massive molecular gas has been discovered in giant elliptical galaxies at the centers of galaxy clusters. To reveal its role in AGN feedback in those galaxies, we construct a semi-analytic model of gas circulation. This model especially focuses on the massive molecular gas (interstellar cold gas on a scale of ~10 kpc) and the circumnuclear disk (~ 0.5 Gyr. We also confirm that the small entropy of the hot gas (~< 30 keV cm^2) or the short cooling time (~< 1 Gyr) is a critical condition for the existence of the massive molecular gas in the galaxy. The dissipation time of the interstellar cold gas may be related to the critical cooling time.