The radiative efficiencies ( \eta ) of 72 luminous unobscured active galactic nuclei at z \sim 1.5 - 3.5 , powered by some of the most massive black holes ( BHs ) , are constrained .
The analysis is based on accretion disk ( AD ) models , which link the continuum luminosity at rest-frame optical wavelengths and the BH mass ( M _ { BH } ) to the accretion rate through the AD , \dot { M } _ { AD } .
The data are gathered from several literature samples with detailed measurements of the H \beta emission line complex , observed at near-infrared bands .
When coupled with standard estimates of bolometric luminosities ( L _ { bol } ) , the analysis suggests high radiative efficiencies , with most of the sources showing \eta > 0.2 - that is , higher than the commonly assumed value of 0.1 , and the expected value for non-spinning BHs ( \eta = 0.057 ) .
Even under more conservative assumptions regarding L _ { bol } ( i.e. , L _ { bol } = 3 \times L _ { 5100 } ) , most of the extremely massive BHs in the sample ( i.e. , M _ { BH } \gtrsim 3 \times 10 ^ { 9 } M _ { \odot } ) show radiative efficiencies which correspond to very high BH spins ( a _ { * } ) , with typical values well above a _ { * } \simeq 0.7 .
These results stand in contrast to the predictions of a “ spin-down ” scenario , in which a series of randomly oriented accretion episodes lead to a _ { * } \sim 0 .
Instead , the analysis presented here strongly supports a “ spin-up ” scenario , which is driven by either prolonged accretion or a series of anisotropically oriented accretion episodes .
Considering the fact that these extreme BHs require long-duration or continuous accretion to account for their high masses , it is argued that the most probable scenario for the super-massive BHs holes under study is that of an almost continuous sequence of randomly yet not isotropically oriented accretion episodes .