  Quasi-stellar objects (QSOs) occur in galaxies in which supermassive black
holes (SMBHs) are growing substantially through rapid accretion of gas. Many
popular models of the co-evolutionary growth of galaxies and SMBHs predict that
QSOs are also sites of substantial recent star formation, mediated by important
processes, such as major mergers, which rapidly transform the nature of
galaxies. A detailed study of the star-forming properties of QSOs is a critical
test of such models. We present a far-infrared Herschel/PACS study of the mean
star formation rate (SFR) of a sample of spectroscopically observed QSOs to z~2
from the COSMOS extragalactic survey. This is the largest sample to date of
moderately luminous AGNs studied using uniform, deep far-infrared photometry.
We study trends of the mean SFR with redshift, black hole mass, nuclear
bolometric luminosity and specific accretion rate (Eddington ratio). To
minimize systematics, we have undertaken a uniform determination of SMBH
properties, as well as an analysis of important selection effects within
spectroscopic QSO samples that influence the interpretation of SFR trends. We
find that the mean SFRs of these QSOs are consistent with those of normal
massive star-forming galaxies with a fixed scaling between SMBH and galaxy mass
at all redshifts. No strong enhancement in SFR is found even among the most
rapidly accreting systems, at odds with several co-evolutionary models.
Finally, we consider the qualitative effects on mean SFR trends from different
assumptions about the star-forming properties of QSO hosts and redshift
evolution of the SMBH-galaxy relationship. While limited currently by
uncertainties, valuable constraints on AGN-galaxy co-evolution can emerge from
our approach.
