Faint COSMOS AGN at z~3.3 - I. Black Hole Properties and Constraints on
  Early Black Hole Growth
  We present new Keck/MOSFIRE K-band spectroscopy for a sample of 14 faint,
X-ray-selected active galactic nuclei (AGNs) in the COSMOS field. The data
cover the spectral region surrounding the broad Balmer emission lines, which
enables the estimation of black hole masses (M_BH) and accretion rates (in
terms of L/L_Edd). We focus on 10 AGN at z~3.3, where we observe the Hbeta
spectral region, while for the other four z~2.4 sources we use the Halpha broad
emission line. Compared with previous detailed studies of unobscured AGNs at
these high redshifts, our sources are fainter by an order of magnitude,
corresponding to number densities of order ~10^-6--10^-5 Mpc^-3. The lower AGN
luminosities also allow for a robust identification of the host galaxy
emission, necessary to obtain reliable intrinsic AGN luminosities, BH masses
and accretion rates. We find the AGNs in our sample to be powered by
supermassive black holes (SMBHs) with a typical mass of M_BH~5*10^8 M_Sol --
significantly lower than the higher-luminosity, rarer quasars reported in
previous studies. The accretion rates are in the range L/L_Edd~0.1-0.5, with an
evident lack of sources with lower L/L_Edd (and higher M_BH), as found in
several studies of faint AGNs at intermediate redshifts. Based on the early
growth expected for the SMBHs in our sample, we argue that a significant
population of faint z~6 AGNs, with M_BH~10^6 M_Sol, should be detectable in the
deepest X-ray surveys available, but this is not observed. We discuss several
possible explanations for the apparent absence of such a population, concluding
that the most probable scenario involves an evolution in source obscuration
and/or radiative efficiencies.
