Probing The Dark Matter Halo of High-redshift Quasar from Wide-Field Clustering Analysis

TL;DR

This work tackles how the most luminous quasars at $5 \le z < 6.3$ occupy dark matter halos and what that implies for SMBH growth. It uses a wide-field, machine-learning–selected sample of $N \approx 2.17\times10^5$ high-$z$ quasar candidates from LS DR9 and WISE, and performs a probability-weighted projected two-point correlation analysis to extract the bias $b$ and typical halo mass $M_h$, aided by halo-model connections. The resulting halo masses are $\log(M_h/M_\odot)=12.2^{+0.2}_{-0.7}$ for $5.0\le z<5.7$ and $11.9^{+0.3}_{-0.7}$ for $5.7\le z<6.3$ with biases $b \approx 12.3$ and $11.5$, respectively, suggesting a possibly non-monotonic evolution of quasar-host halos. Duty cycles, inferred with multiple quasar luminosity functions, span $\log(f_{\rm duty}) \approx -3.8$ to $-4.2$ under standard QLFs, but can rise to $f_{\rm duty} \sim 0.008$–$0.003$ when using the TRINITY model, illustrating sensitivity to QLF prescriptions. The results demonstrate the power of wide-area clustering to mitigate cosmic variance and provide a robust framework for connecting high-$z$ quasar activity to the assembly history of early large-scale structure.

Abstract

High-redshift quasars have been an excellent tracer to study the astrophysics and cosmology at early Universe. Using 216,949 high-redshift quasar candidates ($5.0 \leq z < 6.3$) selected via machine learning from the Legacy Survey Data Release 9 and the Wide-field Infrared Survey Explorer, we perform wide-field clustering analysis to investigate the large-scale environment of those high-redshift quasars. 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 $\log(M_h/M_{\odot})=12.2 ^{+0.2}_{-0.7}$ ($11.9^{+0.3}_{-0.7}$), with the bias parameter $b$ of $12.34 ^{+4.26}_{-4.37}$ ($11.52^{+4.02}_{-4.14}$) for the redshift interval of $5.0 \leq z <5.7$ ($5.7 \leq z <6.3$). Our results, combined with other measurements of dark matter halo masses for quasars or active galactic nucleus which obtain a lower dark matter halo mass of $\sim 10^{11.5}$ M$_\odot$ at similar redshift, suggest a more complex, and possibly non-monotonic evolution of quasar hosting dark matter halo. Moreover, we estimate the duty cycle of those quasars, which is $0.008^{+0.135}_{-0.007}$ ($0.003+^{+0.047}_{-0.003}$) for the redshift interval of $5.0 \leq z <5.7$ ($5.7 \leq z <6.3$).

Figures (5)

• Figure 1: The distribution of $\rm M_{1450}$ versus photometric redshift for the 216,949 high-redshift quasar candidates, which are color-code by its corresponding predicted probability. The red stars denote the true high-redshift quasars.
• Figure 2: The sky distribution of quasar candidates for $5.0 \leq z <5.7$ (left) and $5.7 \leq z <6.3$ (right). The color coding denotes the predicted probability of being a high-$z$ quasar obtained in Ye_2024ApJS. Red stars represent the spectra-verified quasars within the same redshift range. Megenta solid line represent the Galactic plane. Orange solid lines in the color bar stand for the three probability thresholds of $p_{\rm thre}=0.41,~0.6,~0.8$.
• Figure 3: Projected auto correlation function for quasar at $5.0 \leq z <5.7$ (left) and $5.7 \leq z <6.3$ (right) with a probability threshold of $p_{\rm thre} = 0.8$. The red dots represent the measurements of the projected auto correlation and the solid line stands for the best-fit model to the observational correlation.
• Figure 4: Projected quasar auto correlation function for $5.0 \leq z <5.7$ (left) and $5.7 \leq z <6.3$ (right) for $p_{\rm thre}=0.41, ~0.6$, respectively.
• Figure 5: The cosmic evolution of the bias parameters (a), the typical DMH mass (b), the minimum DMH mass (c), the duty cycle (d) based on clustering analysis from $z = 0$ to $z\sim 7.3$. The typical DMH mass estimations are from DMHM_Croom_2005DMHM_Shen_2007Bias_Ross_2009DMHM_Krumpe_2010DMHM_White_2012DMHM_Timlin_2018DMHM_Herrero_Alonso_2021DMHM_Arita_2023DMHM_Arita_2025DMHM_Ikeda_2025DMHM_John_William_2025DMHM_Lin_2025 and this work, while the minimum DMH masses are from DMHM_Eftekharzadeh+2015DMHM_He_2018DMHM_Eilers_2024DMHM_Giner_Mascarell_2025DMHM_Schindler_2025JT2025 and this work. Grey shaded area in (b) panel represents the typical DMH mass range of type-I quasars.