A Wide and Deep Exploration of Radio Galaxies with Subaru HSC (WERGS).
  VI. Distant Filamentary Structures Pointed by High-z Radio Galaxies at z~4
  We present the environmental properties around high-$z$ radio galaxies
(HzRGs) at $z\sim4$, which have been poorly investigated because of their
rarity. We use the largest samples of HzRGs and $g$-dropout galaxy overdense
regions at $z\sim4$, which were constructed from Hyper Suprime-Cam Subaru
Strategic Program, to characterize the HzRG environments statistically. We
measure the $g$-dropout galaxy overdensities around 21 HzRGs whose rest-frame
1.4 GHz radio luminosities ($L_{1.4\mathrm{GHz}}$) are $10^{26-27}$ W
Hz$^{-1}$. We find that the overdensities around the faint HzRGs with
$L_{1.4\mathrm{GHz}}\sim10^{26.0-26.5}$ W Hz$^{-1}$ tend to be higher than that
of the $g$-dropout galaxies. On the other hand, no significant difference of
density environments is found between the luminous HzRGs with $
L_{1.4\mathrm{GHz}}\sim10^{26.5-27.0} $ W Hz$^{-1}$ and the $g$-dropout
galaxies. The HzRGs are found to occupy more massive halos than $g$-dropout
galaxies through a cross-correlation between the HzRGs and $g$-dropout
galaxies. This trend is more pronounced in the faint HzRGs. These results are
consistent with a scenario where HzRGs get older and more massive as the
radio-luminosity decreases. The HzRGs are expected to trace the progenitors of
local cluster halos from their calculated halo mass. In addition, we find that
surrounding galaxies tend to distribute along the radio-jet major axis of the
HzRGs at angular distances less than $\lesssim500$ physical kpc. Our findings
imply the onset of the filamentary structures around the HzRGs at $z\sim4$.
