Probing Dark Matter Halos of High-redshift Quasars via Wide-Field Clustering

High-redshift quasars have been an excellent tracer to study the astrophysics and cosmology at early Universe. Using 577 spectroscopically confirmed high-redshift quasars and 1,796 highly reliable photometric quasar candidates (all with $5.0 \leq z < 6.2$, median $M_{1450} \sim -25.9$) selected via machine learning, we perform wide-field clustering analyses to investigate the large-scale environment of these objects. We construct the projected auto correlation function of those high-redshift quasars that is weighted by its predicted probability of being a true high-redshift quasar, from which we derive the bias parameter and the typical dark matter halo mass of those quasars. The dark matter halo mass of quasars estimated from the projected auto correlation function is $\log(M_h/M_{\odot})=12.13 \pm 0.07$ ($12.45 \pm 0.14$), with the bias parameter $b$ of $14.80 \pm 0.84 $ ($24.18 \pm 3.11$) for the redshift interval of $5.0 \leq z <5.6$ ($5.6 \leq z <6.2$). Moreover, we estimate the duty cycle of those quasars, which is $0.0002 \pm 0.0001$ ($0.0021^{+0.0049}_{-0.0014}$) for the redshift interval of $5.0 \leq z <5.6$ ($5.6 \leq z <6.2$), well aligning with the $f_{\rm duty} - M_{\rm halo}$ scaling relation. These comparably small duty cycle estimates might indicate that a significant fraction of supermassive black hole growth occurs in an obscured phase.