# Clustering of quasars in a wide luminosity range at redshift 4 with Subaru Hyper Suprime-Cam wide field imaging

## TL;DR

This study investigates the clustering of quasars across a wide luminosity range at redshift 4, revealing no significant luminosity dependence and estimating host dark matter halo masses and duty cycles.

## Contribution

It provides the first measurement of quasar clustering over a broad luminosity range at z~4 using cross-correlation with Lyman Break Galaxies, highlighting luminosity-independent clustering.

## Key findings

- Quasar bias factors are similar across luminosities at z~4.
- Luminous quasars have smaller bias factors when estimated by CCF compared to ACF.
- Host dark matter halos of less luminous quasars are estimated to be 0.3-2×10^12 h^{-1} M_sun.

## Abstract

We examine the clustering of quasars over a wide luminosity range, by utilizing 901 quasars at $\overline{z}_{\rm phot}\sim3.8$ with $-24.73<M_{\rm 1450}<-22.23$ photometrically selected from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) S16A Wide2 date release and 342 more luminous quasars at $3.4<z_{\rm spec}<4.6$ having $-28.0<M_{\rm 1450}<-23.95$ from the Sloan Digital Sky Survey (SDSS) that fall in the HSC survey fields. We measure the bias factors of two quasar samples by evaluating the cross-correlation functions (CCFs) between the quasar samples and 25790 bright $z\sim4$ Lyman Break Galaxies (LBGs) in $M_{\rm 1450}<-21.25$ photometrically selected from the HSC dataset. Over an angular scale of \timeform{10.0"} to \timeform{1000.0"}, the bias factors are $5.93^{+1.34}_{-1.43}$ and $2.73^{+2.44}_{-2.55}$ for the low and high luminosity quasars, respectively, indicating no luminosity dependence of quasar clustering at $z\sim4$. It is noted that the bias factor of the luminous quasars estimated by the CCF is smaller than that estimated by the auto-correlation function (ACF) over a similar redshift range, especially on scales below \timeform{40.0"}. Moreover, the bias factor of the less-luminous quasars implies the minimal mass of their host dark matter halos (DMHs) is $0.3$-$2\times10^{12}h^{-1}M_{\odot}$, corresponding to a quasar duty cycle of $0.001$-$0.06$.