Luminous Quasars Do Not Live in the Most Overdense Regions of Galaxies
  at z~4
  We present the cross-correlation between 151 luminous quasars ($M_{
\mathrm{UV}} < -26$) and 179 protocluster candidates at $z \sim 3.8$, extracted
from the Wide imaging survey ($ \sim 121~ $deg$^2$) performed with a part of
the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). We find that only two
out of 151 quasars reside in regions that are more overdense compared to the
average field at $ > 4 \sigma $. The distributions of the distance between
quasars and the nearest protoclusters and the significance of the overdensity
at the position of quasars are statistically identical to those found for
$g$-dropout galaxies, suggesting that quasars tend to reside in almost the same
environment as star-forming galaxies at this redshift. Using stacking analysis,
we find that the average density of $g$-dropout galaxies around quasars is
slightly higher than that around $g$-dropout galaxies on $1.0 - 2.5$ pMpc
scales, while at $ < 0.5$ pMpc that around quasars tends to be lower. We also
find that quasars with higher UV-luminosity or with more massive black holes
tend to avoid the most overdense regions, and that the quasar near zone sizes
are anti-correlated with overdensity. These findings are consistent with a
scenario in which the luminous quasar at $z \sim4 $ resides in structures that
are less massive than those expected for the progenitors of today's rich
clusters of galaxies, and possibly that luminous quasars may be suppressing
star formation in their close vicinity.
