Dense Molecular Gas and the Role of Star Formation in the Host Galaxies of Quasi-stellar Objects

New millimeter-wave CO and HCN observations of the host galaxies of infrared-excess Palomar-Green (PG) quasi-stellar objects (QSOs) previously detected in CO are presented. These observations are designed to assess the validity of using the infrared luminosity to estimate star formation rates of luminous active galactic nuclei (AGNs) by determining the relative significance of dust heating by young, massive stars and AGNs in QSO hosts and IRAS galaxies with warm, AGN-like infrared colors. The analysis of these data is based, in part, on evidence that HCN traces high-density (>10⁴ cm^-3) molecular gas, and that the starburst-to-HCN luminosity ratio, L_SB/L, of IRAS-detected galaxies is constant. The new CO data provide a confirmation of prior claims that PG QSO hosts have high infrared-to-CO luminosity ratios, L_IR/L, relative to IRAS galaxies of comparable L_IR. Such high L_IR/L ratios may be due to significant heating of dust by the QSO or to an increased star formation efficiency in QSO hosts relative to the bulk of the luminous IRAS galaxy population. The HCN data show a similar trend, with the PG QSO host I Zw 1 and most of the warm IRAS galaxies having high L_IR/L (>1600) relative to the cool IRAS galaxy population, for which the median ⟨L_IR/L⟩_cool ∼ 890. If the assumption is made that the infrared emission from cool IRAS galaxies is reprocessed light from embedded star-forming regions, then high values of L_IR/L are likely the result of dust heating by the AGNs. Further, if the median ratio of L/L ∼ 0.06 observed for Seyfert galaxies and I Zw 1 is applied to the PG QSOs not detected in HCN, then the derived L_IR/L values correspond to a stellar contribution to the production of L_IR of ∼7%-39%, and star formation rates of ∼2-37 M_⊙ yr^-1 are derived for the QSO hosts. The corresponding values for the warm galaxies are ∼10%-100% and ∼3-220 M_⊙ yr^-1. Alternatively, if the far-infrared is adopted as the star formation component of the total infrared in cool galaxies, i.e., ⟨L_FIR/L⟩_cool ∼ L_SB/L, the stellar contributions in QSO hosts and warm galaxies to their L_FIR are up to 35% and 10% higher, respectively, than the percentages derived for L_IR. This raises the possibility that the L_FIR in several of the PG QSO hosts, including I Zw 1, could be due entirely to dust heated by young, massive stars. Finally, there is no evidence that the global HCN emission is enhanced relative to CO in galaxies hosting luminous AGNs.