The most massive active black holes at z ∼ 1.5-3.5 have high spins and radiative efficiencies

The radiative efficiencies (η) of 72 luminous unobscured active galactic nuclei at z ∼ 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, . The data are gathered from several literature samples with detailed measurements of the Hβ 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 η > 0.2, that is, higher than the commonly assumed value of 0.1, and the expected value for non-spinning BHs (η = 0.057). Even under more conservative assumptions regarding L _bol (i.e., L _bol = 3 × L ₅₁₀₀), most of the extremely massive BHs in the sample (i.e., M _BH ≳ 3 × 10⁹ M_⊙) show radiative efficiencies which correspond to very high BH spins (a _*), with typical values well above a _* ≃ 0.7. These results stand in contrast to the predictions of a "spin-down" scenario, in which a series of randomly oriented accretion episodes leads to a _* ∼ 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 black holes under study is that of an almost continuous sequence of randomly yet not isotropically oriented accretion episodes.