# Great Optically Luminous Dropout Research Using Subaru HSC (GOLDRUSH). I. UV Luminosity Functions at $z \sim 4-7$ Derived with the Half-Million Dropouts on the 100 deg$^2$ Sky

## TL;DR

This study uses extensive Subaru HSC data to derive UV luminosity functions at redshifts 4 to 7, revealing the need for modified models at the bright end due to gravitational lensing effects.

## Contribution

It provides the largest sample of dropout candidates across 100 deg² and refines UV luminosity functions with unprecedented statistical accuracy for high-redshift galaxies.

## Key findings

- UV LFs span a wide luminosity range from 0.002 to 100 L_UV*
- The faint-end slope and normalization decrease from z~4 to 7
- Bright-end galaxy LFs require modified models beyond Schechter functions

## Abstract

We study the UV luminosity functions (LFs) at $z\sim 4$, $5$, $6,$ and $7$ based on the deep large-area optical images taken by the Hyper Suprime-Cam (HSC) Subaru strategic program (SSP). On the 100 deg$^2$ sky of the HSC SSP data available to date, we make enormous samples consisting of a total of 579,565 dropout candidates at $z\sim 4-7$ by the standard color selection technique, 358 out of which are spectroscopically confirmed by our follow-up spectroscopy and other studies. We obtain UV LFs at $z \sim 4-7$ that span a very wide UV luminosity range of $\sim 0.002 - 100 \, L_{\rm UV}^\ast$ ($-26 < M_{\rm UV} < -14$ mag) by combining LFs from our program and the ultra-deep Hubble Space Telescope legacy surveys. We derive three parameters of the best-fit Schechter function, $\phi^\ast$, $M_{\rm UV}^\ast$, and $\alpha$, of the UV LFs in the magnitude range where the AGN contribution is negligible, and find that $\alpha$ and $\phi^\ast$ decrease from $z\sim 4$ to $7$ with no significant evolution of $M_{\rm UV}^\ast$. Because our HSC SSP data bridge the LFs of galaxies and AGNs with great statistical accuracy, we carefully investigate the bright end of the galaxy UV LFs that are estimated by the subtraction of the AGN contribution either aided with spectroscopy or the best-fit AGN UV LFs. We find that the bright end of the galaxy UV LFs cannot be explained by the Schechter function fits at $> 2 \sigma$ significance, and require either double power-law functions or modified Schechter functions that consider a magnification bias due to gravitational lensing.