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 similar to 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 similar to 6 is evaluated as 5.0(-4.0)(+7.4) x 10(12) h(-1)M(circle dot) 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 similar to 10(12.5) h(-1)M(circle dot) 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 similar to 6, but in less extreme halos thereafter. The DMH mass does not appear to exceed the upper limit of 10(13) h(-1)M(circle dot), which suggests that most quasars reside in DMHs with M-halo < 10(13) h(-1)M(circle dot) 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 similar to 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) x 10(10) h(-1)M(circle dot), which is found to be consistent with [C II] observational results.