The relationships between AGN power and molecular gas mass within 500 pc of the center of elliptical galaxies

The physical quantity that directly controls the feedback of active galactic nuclei (AGNs) in elliptical galaxies remains to be determined. The discovery of molecular gas around the AGNs suggests that the gas is fueling the AGNs. Therefore, we analyze Atacama Large Millimeter/submillimeter Array (ALMA) data for the CO line (J=1-0, 2-1, 3-2) emission and estimate the mass of molecular gas within 500 pc of the center of 12 non-central elliptical galaxies (NCEGs) and 10 of the brightest cluster galaxies (BCGs). We find that the mass (M_mol   10^5-10^9 M_sun) is correlated with the jet power of their AGNs, which is represented by P_cav   4.1x10^42 (M_mol/10^7 M_sun)^1.3 erg s^-1, although NCEGs alone do not show the correlation. We also find that M_mol is correlated with the AGN continuum luminosities at   1.4 GHz (L_1.4) and   100-300 GHz (L_con). Since P_cav reflects galactic-scale, long-term AGN activity, while the continuum luminosities reflect local ( < 500 pc), short-term AGN activity, our results suggest that AGN activity depends on the amount of gas, regardless of its time scale. On the other hand, we cannot find a clear correlation between the mass of the black holes in the AGNs (M_BH) and P_cav. This suggests that M_mol, rather than M_BH, is the main factor controlling AGN activity. We confirm that the origin of the continuum emission from the AGNs at   1.4-300 GHz is mostly synchrotron radiation.