The Most Massive Active Black-Holes at z~1.5-3.5 Have High Spins and
  Radiative Efficiencies
  The radiative efficiencies ($\eta$) 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 ${\rm H}\beta$ 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 $\eta>0.2$ - 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 $L_{\rm bol}$ (i.e., $L_{\rm
bol}=3\times \lambda L_{\lambda}$[5100$\AA$]), 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.
