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.