Faint Quasars Live in the Same Number Density Environments as Lyman Break Galaxies at z ~ 4

Characterizing high-z quasar environments is key to understanding the co-evolution of quasars and the surrounding galaxies. To restrict their global picture, we statistically examine the g-dropout galaxy overdensity distribution around 570 faint quasar candidates at z ~ 4, based on the Hyper Suprime-Cam Subaru Strategic Program survey. We compare the overdensity significances of g-dropout galaxies around the quasars with those around g-dropout galaxies, and find no significant difference between their distributions. A total of 4 (22) out of the 570 faint quasars, 0.7_{-0.4}^{+0.4} (3.9_{-0.8}^{+0.8}) %, are found to be associated with the > 4 sigma overdense regions within an angular separation of 1.8 (3.0) arcmin, which is the typical size of protoclusters at this epoch. This is similar to the fraction of g-dropout galaxies associated with the > 4 sigma overdense regions. This result is consistent with our previous work that 1.3_{-0.9}^{+0.9} % and 2.0_{-1.1}^{+1.1} % of luminous quasars detected in the Sloan Digital Sky Survey exist in the > 4 sigma overdense regions within 1.8 and 3.0 arcmin separations, respectively. Therefore, we suggest that the galaxy number densities around quasars are independent of their luminosity, and most quasars do not preferentially appear in the richest protocluster regions at z ~ 4. The lack of an apparent positive correlation between the quasars and the protoclusters implies that: i) the gas-rich major merger rate is relatively low in the protocluster regions, ii) most high-z quasars may appear through secular processes, or iii) some dust-obscured quasars exist in the protocluster regions.