Black versus Dark: Rapid Growth of Supermassive Black Holes in Dark
  Matter Halos at z ~ 6
  We report on the relation between the mass of supermassive black holes
(SMBHs; M_BH) and that of hosting dark matter halos (M_h) for 49 z ~ 6
quasi-stellar objects (QSOs) with [CII]158um velocity-width measurements. Here,
we estimate M_h assuming that the rotation velocity from FWHM_CII is equal to
the circular velocity of the halo; we have tested this procedure using z ~ 3
QSOs that also have clustering-based M_h estimates. We find that a vast
majority of the z ~ 6 SMBHs are more massive than expected from the local M_BH
- M_h relation, with one-third of the sample by factors >~ 10^2. The median
mass ratio of the sample, M_BH/M_h = 6 x 10^{-4}, means that 0.4% of the
baryons in halos are locked up in SMBHs. The mass growth rates of our SMBHs
amount to ~ 10% of the SFRs, or ~ 1% of the mean baryon accretion rates, of the
hosting galaxies. A large fraction of the hosting galaxies are consistent with
average galaxies in terms of SFR and perhaps of stellar mass and size. Our
study indicates that the growth of SMBHs (M_BH ~ 10^{8-10} Msun) in luminous z
~ 6 QSOs greatly precedes that of hosting halos owing to efficient gas
accretion even under normal star formation activities, although we cannot rule
out the possibility that undetected SMBHs have local M_BH/M_h ratios. This
preceding growth is in contrast to much milder evolution of the stellar-to-halo
mass ratio.
