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We investigate the mean star formation rates (SFRs) in the host galaxies of~3000 optically selected QSOs from the SDSS survey within the Herschel-ATLASfields, 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 constructcomposite SEDs in bins of redshift and AGN luminosity. We perform SED fittingto measure the mean infrared luminosity due to star formation, removing thecontamination from AGN emission. We find that the mean SFRs show a weakpositive trend with increasing AGN luminosity. However, we demonstrate that theobserved trend could be due to an increase in black hole (BH) mass (and aconsequent increase of inferred stellar mass) with increasing AGN luminosity.We compare to a sample of X-ray selected AGN and find that the two populationshave consistent mean SFRs when matched in AGN luminosity and redshift. On thebasis of the available virial BH masses, and the evolving BH mass to stellarmass relationship, we find that the mean SFRs of our QSO sample are consistentwith those of main sequence star-forming galaxies. Similarly, theradio-luminous QSOs have mean SFRs that are consistent with both the overallQSO 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 theobserved positive trend between the mean SFRs and AGN luminosity can beattributed to BH mass and redshift dependencies.

The mean star formation rates of unobscured QSOs: searching for evidence of suppressed or enhanced star formation