Subaru High-$z$ Exploration of Low-Luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at $z\sim6$

TL;DR

This study measures the dark matter halo mass of quasars at redshift around 6 using clustering analysis of a large quasar sample, revealing they reside in massive halos with implications for quasar activation and evolution.

Contribution

First measurement of dark matter halo mass for $z ext{~}6$ quasars using clustering analysis of 107 quasars from HSC-SSP data.

Findings

Quasars at $z ext{~}6$ reside in halos of $ ext{~}5 imes10^{12} ext{ to }10^{13} ext{ }h^{-1}M_\odot$.

The halo mass remains nearly constant over cosmic time, indicating a characteristic halo mass for quasar activation.

The bias parameter increases with redshift, supporting models with inefficient AGN feedback at high redshift.

Abstract

We present, for the first time, dark matter halo (DMH) mass measurement of quasars at $z\sim6$ based on a clustering analysis of 107 quasars. Spectroscopically identified quasars are homogeneously extracted from the HSC-SSP wide layer over $891\,\mathrm{deg^2}$. We evaluate the clustering strength by three different auto-correlation functions: projected correlation function, angular correlation function, and redshift-space correlation function. The DMH mass of quasars at $z\sim6$ is evaluated as $5.0_{-4.0}^{+7.4}\times10^{12}\,h^{-1}M_\odot$ with the bias parameter $b=20.8\pm8.7$ by the projected correlation function. The other two estimators agree with these values, though each uncertainty is large. The DMH mass of quasars is found to be nearly constant $\sim10^{12.5}\,h^{-1}M_\odot$ throughout cosmic time, suggesting that there is a characteristic DMH mass where quasars are always activated. As a result, quasars appear in the most massive halos at $z \sim 6$, but in less extreme halos thereafter. The DMH mass does not appear to exceed the upper limit of $10^{13}\,h^{-1}M_\odot$, which suggests that most quasars reside in DMHs with $M_\mathrm{halo}<10^{13}\,h^{-1}M_\odot$ across most of the cosmic time. Our results supporting a significant increasing bias with redshift are consistent with the bias evolution model with inefficient AGN feedback at $z\sim6$. The duty cycle ($f_\mathrm{duty}$) is estimated as $0.019\pm0.008$ by assuming that DMHs in some mass interval can host a quasar. The average stellar mass is evaluated from stellar-to-halo mass ratio as $M_*=6.5_{-5.2}^{+9.6}\times10^{10}\,h^{-1}M_\odot$, which is found to be consistent with [C II] observational results.