Star Formation in Luminous Quasars at 2<z<3

We investigate the relation between star formation rates ($\dot{M}_{s}$) and AGN properties in optically selected type 1 quasars at $2<z<3$ using data from Herschel and the SDSS. We find that $\dot{\rm{M}}_s$ remains approximately constant with redshift, at $300\pm100~\rm{M}_{\odot}$yr$^{-1}$. Conversely, $\dot{\rm{M}}_s$ increases with AGN luminosity, up to a maximum of $\sim600~\rm{M}_{\odot}$yr$^{-1}$, and with CIV FWHM. In context with previous results, this is consistent with a relation between $\dot{\rm{M}}_s$ and black hole accretion rate ($\dot{\rm{M}}_{bh}$) existing in only parts of the $z-\dot{\rm{M}}_{s}-\dot{\rm{M}}_{bh}$ plane, dependent on the free gas fraction, the trigger for activity, and the processes that may quench star formation. The relations between $\dot{\rm{M}}_s$ and both AGN luminosity and CIV FWHM are consistent with star formation rates in quasars scaling with black hole mass, though we cannot rule out a separate relation with black hole accretion rate. Star formation rates are observed to decline with increasing CIV equivalent width. This decline can be partially explained via the Baldwin effect, but may have an additional contribution from one or more of three factors; $M_i$ is not a linear tracer of L$_{2500}$, the Baldwin effect changes form at high AGN luminosities, and high CIV EW values signpost a change in the relation between $\dot{\rm{M}}_s$ and $\dot{\rm{M}}_{bh}$. Finally, there is no strong relation between $\dot{\rm{M}}_s$ and Eddington ratio, or the asymmetry of the CIV line. The former suggests that star formation rates do not scale with how efficiently the black hole is accreting, while the latter is consistent with CIV asymmetries arising from orientation effects.