Constraining Quasar Feedback from Analysis of the Hydrostatic Equilibrium of the Molecular Gas in Their Host Galaxies

We investigate the kinematics and dynamics of the molecular and ionized gas in the host galaxies of three Palomar-Green quasars at low redshifts, benefiting from the archival millimeter-wave interferometric and optical integral field unit data. We study the kinematics of both cold molecular and hot ionized gas by analyzing the CO and H$\alpha$ data cubes, and construct the mass distributions of our sample through gas dynamics, utilizing a priori knowledge regarding the galaxy light distribution. We find no systematic offset between the stellar mass derived from our dynamical method and that from the broad-band photometry and mass-to-light ratio, suggesting the consistency of both methods. We then study the kinetic pressure and the weight of the interstellar medium using our dynamical mass model. By studying the relationship between kinetic pressure and gravitational pressure of the quasar host galaxies, we find an equivalence in the hydrostatic equilibrium states of ISM in the quasar host galaxies, similar to the result of gas equilibrium in normal star-forming galaxies, suggesting minimal quasar feedback. Regarding non-circular motion as indicative of quasar-driven outflows, we observe an exceptionally low coupling efficiency between molecular gas outflow and AGN bolometric luminosities. These results demonstrate the marginal influence of the central engine on the properties of cold molecular gas in quasar host galaxies.