The mechanisms responsible for the production of relativistic jets from supermassive black holes (SMBHs) accreting at near-Eddington rates are not well understood. Simple theoretical expectations indicate that SMBHs in quasars accrete via thin discs which should produce at most very weak jets. This is contradicted by observations of powerful jets in flat-spectrum radio quasars (FSRQs). We use gamma-ray luminosities observed with the Fermi Large Area Telescope as a proxy of the jet power for a population of 154 FSRQs. Assuming typical quasar accretion rates and using black hole (BH) mass measurements from a variety of methods, we find a mean jet production efficiency of about 10 per cent for FSRQs, with values as high as 222 per cent. We find that this is consistent with FSRQs hosting moderately thin, magnetically arrested accretion discs around rapidly spinning BHs. Modelling our observations using general relativistic magnetohydrodynamic (GRMHD) simulations of jets from thin discs, we find an average lower limit of a_*=0.59 for the SMBH spins of FSRQs, with tendency for the spins to decrease as the BH mass increases. Our results are consistent with the merger-driven evolution of SMBHs. 3 per cent of the sample cannot be explained by current GRMHD models of jet production from Kerr BHs due to the high efficiencies. Along the way, we find a correlation between BH masses and L{gamma}_ which may be an useful mass estimator in blazar gamma-ray studies.

Cone search capability for table J/MNRAS/495/981/tablea1 (Data on the objects used in this work)