Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6

We present, for the first time, dark matter halo (DMH) mass measurement of quasars at z ∼ 6 based on a clustering analysis of 107 quasars. Spectroscopically identified quasars are homogeneously extracted from the Hyper Suprime-Cam Strategic Survey Program wide layer over 891 deg ^2 . We evaluate the clustering strength by three different autocorrelation functions: projected correlation function, angular correlation function, and redshift–space correlation function. The DMH mass of quasars at z ∼ 6 is evaluated as ${5.0}_{-4.0}^{+7.4}\times {10}^{12}\,{h}^{-1}{M}_{\odot }$ with the bias parameter b = 20.8 ± 8.7 by the projected correlation function. The other two estimators agree with these values; though, each uncertainty is large. The DMH mass of quasars is found to be nearly constant ∼10 ^12.5 h ^−1 M _⊙ throughout cosmic time, suggesting that there is a characteristic DMH mass where quasars are always activated. As a result, quasars appear in the most massive halos at z ∼ 6, but in less extreme halos thereafter. The DMH mass does not appear to exceed the upper limit of 10 ^13 h ^−1 M _⊙ , which suggests that most quasars reside in DMHs with ${M}_{\mathrm{halo}}\lt {10}^{13}{h}^{-1}{M}_{\odot }$ across most of the cosmic time. Our results supporting a significant increasing bias with redshift are consistent with the bias evolution model with inefficient active galactic nucleus feedback at z ∼ 6. The duty cycle ( f _duty ) is estimated as 0.019 ± 0.008 by assuming that DMHs in some mass interval can host a quasar. The average stellar mass is evaluated from stellar-to-halo mass ratio as ${M}_{* }={6.5}_{-5.2}^{+9.6}\times {10}^{10}\,{h}^{-1}{M}_{\odot }$ , which is found to be consistent with [C ii ] observational results.