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; ${M}_{\mathrm{BH}}$) and that of hosting dark matter halos (${M}_{{\rm{h}}}$) for 49 z ∼ 6 quasi-stellar objects (QSOs) with [C ii]158 μm velocity-width measurements. Here, we estimate ${M}_{{\rm{h}}}$ assuming that the rotation velocity from ${\mathrm{FWHM}}_{{\rm{C}}{\rm{II}}}$ is equal to the circular velocity of the halo; we have tested this procedure using z ∼ 3 QSOs that also have clustering-based ${M}_{{\rm{h}}}$ estimates. We find that a vast majority of the z ∼ 6 SMBHs are more massive than expected from the local ${M}_{\mathrm{BH}}$–${M}_{{\rm{h}}}$ relation, with one-third of the sample by factors ≳102. The median mass ratio of the sample, ${M}_{\mathrm{BH}}/{M}_{{\rm{h}}}=6\times {10}^{-4}$, 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 star formation rates (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 (${M}_{\mathrm{BH}}\sim {10}^{8-10}\,{M}_{\odot }$) 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 ${M}_{\mathrm{BH}}/{M}_{{\rm{h}}}$ ratios. This preceding growth is in contrast to much milder evolution of the stellar-to-halo mass ratio.