We investigate the mean star formation rates (SFRs) in the host galaxies of ~3000 optically selected QSOs from the SDSS survey within the Herschel-ATLAS fields, and a radio-luminous sub-sample, covering the redshift range of z = 0.2-2.5. Using WISE & Herschel photometry (12 - 500{mu}m) we construct composite SEDs in bins of redshift and AGN luminosity. We perform SED fitting to measure the mean infrared luminosity due to star formation, removing the contamination from AGN emission. We find that the mean SFRs show a weak positive trend with increasing AGN luminosity. However, we demonstrate that the observed trend could be due to an increase in black hole (BH) mass (and a consequent increase of inferred stellar mass) with increasing AGN luminosity. We compare to a sample of X-ray selected AGN and find that the two populations have consistent mean SFRs when matched in AGN luminosity and redshift. On the basis of the available virial BH masses, and the evolving BH mass to stellar mass relationship, we find that the mean SFRs of our QSO sample are consistent with those of main sequence star-forming galaxies. Similarly, the radio-luminous QSOs have mean SFRs that are consistent with both the overall QSO sample and with star-forming galaxies on the main sequence. In conclusion, on average QSOs reside on the main sequence of star-forming galaxies, and the observed positive trend between the mean SFRs and AGN luminosity can be attributed to BH mass and redshift dependencies.
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