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The UV Luminosity Function of Protocluster Galaxies at $z\sim4$: the Bright-end Excess and the Enhanced Star Formation Rate Density

We report the rest-frame ultraviolet luminosity function of $g$-dropout galaxies in 177 protocluster candidates (PC UVLF) at $z\sim4$ selected in the Hyper Suprime-Cam Subaru Strategic Program. Comparing with the UVLF of field galaxies at the same redshift, we find that the PC UVLF shows a significant excess towards the bright-end. This excess can not be explained by the contribution of only active galactic nuclei, and we also find that this is more significant in higher dense regions. Assuming that all protocluster members are located on the star formation main sequence, the PC UVLF can be converted into a stellar mass function. Consequently, our protocluster members are inferred to have a 2.8 times more massive characteristic stellar mass than that of the field Lyman break galaxies at the same redshift. This study, for the first time, clearly shows that the enhancement in star formation or stellar mass in overdense regions can generally be seen as early as at $z\sim4$. We also estimate the star formation rate density (SFRD) in protocluster regions as $\simeq 6-20\%$ of the cosmic SFRD, based on the measured PC UVLF after correcting for the selection incompleteness in our protocluster sample. This high value suggests that protoclusters make a non-negligible contribution to the cosmic SFRD at $z\sim4$, as previously suggested by simulations. Our results suggest that protoclusters are essential components for the galaxy evolution at $z\sim4$.