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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 (AGNs) at $z\sim1.5-3.5$, 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 black hole mass ($M_{\rm BH}$) to the accretion rate through the AD, $\dot{M}_{\rm AD}$. The data are gathered from several literature samples with detailed measurements of the ${\rm H}β$ emission line complex, observed at near-IR bands. When coupled with standard estimates of bolometric luminosities ($L_{\rm bol}$), 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 $L_{\rm bol}$ (i.e., $L_{\rm bol}=3\times λL_λ$[5100$Å$]), most of the extremely massive BHs in the sample (i.e., $M_{\rm BH} > 3\times10^9\,M_{\rm \odot}$) show radiative efficiencies which correspond to very high BH spins ($a_{\rm *}$), with typical values well above $a_{\rm *}\simeq0.7$. These results stand in contrast to the predictions of a "spin-down"scenario, in which a series of randomly-oriented accretion episodes lead to $a_{\rm *}\simeq0$. 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 continuous accretion to account for their high masses, it is argued that the most probable scenario for the SMBHs under study is that of an almost continuous sequence of randomly- yet not isotropically-oriented accretion episodes.