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New millimeter-wave CO and HCN observations of the host galaxies ofinfrared-excess Palomar Green quasi-stellar objects (PG QSOs) previouslydetected in CO are presented. These observations are designed to assess thevalidity of using the infrared luminosity to estimate star formation rates ofluminous AGN by determining the relative significance of dust-heating by young,massive stars and active galactic nuclei (AGN) in QSO hosts and IRAS galaxieswith warm, AGN-like infrared colors. The HCN data show the PG QSO host IZw1 andmost of the warm IRAS galaxies to have high L_IR / L'_HCN (>1600) relative tothe cool IRAS galaxy population for which the median L_IR / L'_HCN ~890(+440,-470). If the assumption is made that the infrared emission from coolIRAS galaxies is reprocessed light from embedded star-forming regions, thenhigh values of L_IR / L'_HCN are likely the result of dust heating by the AGN.Further, if the median ratio of L'_HCN / L'_CO ~ 0.06 observed for Seyfertgalaxies and IZw1 is applied to the PG QSOs not detected in HCN, then thederived L_IR / L'_HCN correspond to a stellar contribution to the production ofL_IR of ~ 7-39%, and star formation rates ~ 2-37 M_sun/yr are derived for theQSO hosts. Alternatively, if the far-infrared is adopted as the star formationcomponent of the total infrared in cool galaxies, the stellar contributions inQSO hosts to their L_FIR are up to 35% higher than the percentages derived forL_IR. This raises the possibility that the L_FIR in several of the PG QSOhosts, including IZw1, could be due entirely to dust heated by young, massivestars. Finally, there is no evidence that the global HCN emission is enhancedrelative to CO in galaxies hosting luminous AGN.Comment: LaTex, 31 pages, including 9 postscript figures, AJ, in press  (December 2006

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