Where Do Quasars Live? DESI DR1 Constraints from PAC Measurements
Source: arXiv:2607.21749 · Published 2026-07-23 · By Shanquan Gui, Kun Xu, Donghai Zhao
TL;DR
This paper addresses the question of the dark matter halo environments hosting quasars at intermediate redshift (0.8 < z < 1.0), crucial for understanding supermassive black hole growth and galaxy co-evolution. It introduces precise small-scale quasar environment measurements using the Photometric Objects Around Cosmic Webs (PAC) method, applied to the DESI Data Release 1 quasar and photometric galaxy samples. This approach circumvents shot noise and fiber collision limitations in spectroscopic surveys by leveraging abundant photometric galaxies to measure excess projected surface density around quasars down to stellar masses of 10^{10.8} solar masses over separations 0.1 to 15 h^{-1} Mpc. The authors jointly model these PAC measurements with quasar and luminous red galaxy (LRG) autocorrelations and quasar-LRG cross-correlations using N-body simulations and a stellar-to-halo mass relation (SHMR). They assume a Gaussian quasar occupation function in halo accretion mass and allow a free parameter B to measure the relative quasar-halo occupation probability for satellite subhalos versus central halos at fixed mass. The key quantitative result is that the quasar occupation peaks at log10(M_acc/h^{-1} M_sun) = 12.88 ± 0.02 with width σ_q = 0.51 ± 0.02, and satellite-hosting relative probability B = 1.01 ± 0.03, consistent with equal quasar likelihood in satellite and central halos. They carefully quantify and mitigate magnitude-lensing magnification contamination effects from foreground galaxies, which biased B upwards if uncorrected. Overall, PAC offers a powerful means to deliver precise constraints on the quasar-halo connection and satellite occupation on sub-Mpc scales complimentary to traditional clustering methods. This work refines the picture that halo mass, rather than satellite vs central status, governs quasar triggering at z ~ 0.9.
Key findings
- Gaussian quasar occupation function peaks at log10(Macc/h^-1 M_sun) = 12.88^{+0.02}_{-0.02} with width σ_q = 0.51^{+0.02}_{-0.01}.
- Relative satellite-hosting parameter B = 1.01^{+0.03}_{-0.03} after mitigating magnification bias, indicating equal quasar occupation probability in satellites and centrals at fixed halo mass.
- Ignoring foreground magnification increases B to 1.19^{+0.07}_{-0.06}, showing magnification systematics bias satellite occupation inference.
- Stellar-to-halo mass relation parameters constrained jointly with quasar occupation: M0 ~ 10^{11.95} h^{-1} M_sun, slopes α=0.46, β=2.70, scatter σ=0.23 after magnification correction.
- Combined PAC measurements cover projected separations 0.1 < r_p < 15 h^{-1} Mpc and probe both one-halo and two-halo regimes.
- Photometric galaxy sample completeness established down to stellar mass 10^{10.8} M_sun over DECaLS footprint.
- Joint MCMC modeling incorporates quasar/LRG autocorrelation and quasar-LRG cross-correlation functions to break degeneracies.
- Use of CosmicGrowth N-body simulation snapshot at z=0.92 with SHMR and subhalo abundance matching enables physical interpretation of PAC measurements.
Methodology — deep read
The authors target quasar environments at 0.8 < z < 1.0 using the PAC method, which cross-correlates spectroscopic quasars with a dense photometric galaxy sample to measure the excess projected surface density ¯n_2 w_p(r_p). This allows measurement down to small scales (<1 Mpc) avoiding spectroscopic fiber collisions and shot noise from quasar rarity.
Spectroscopic samples come from DESI DR1: 72,855 quasars and luminous red galaxies (LRGs) in the target redshift interval. The photometric galaxy sample comes from the DECaLS Legacy Imaging Surveys DR9 covering ~9000 deg² with grz photometry reaching a 10σ z-band magnitude depth of 22.33 capturing galaxies complete to stellar mass 10^{10.8} M_sun. Photometric stellar masses are estimated via SED fitting with CIGALE including multiple metallicities and star formation history models.
Measurements involve a Landy–Szalay type estimator for ¯n_2 w_p in four redshift bins combined with inverse variance weighting. Covariances are estimated via jackknife resampling. They also measure spectroscopic autocorrelation of quasars and LRGs and cross-correlations, restricting to scales >1 h^{-1} Mpc to avoid fiber collision systematics.
To interpret the measurements, they use the CosmicGrowth N-body simulation (600 h^{-1} Mpc box, particle mass 5.54e8 h^{-1} M_sun) at z ≈ 0.92. Dark matter halos and subhalos are identified with FoF and HBT+ merger trees. Galaxies are assigned to halos/subhalos using subhalo abundance matching (SHAM) with a 5-parameter double power-law stellar-to-halo mass relation and constant log-normal scatter.
Quasar occupation is modeled as a Gaussian in log halo accretion mass with peak µ and width σ_q, identically for centrals and satellites except satellites have a relative quasar probability B. The parameter B tests environmental dependence of quasar activity on central vs satellite status.
Foreground magnification by lensing of background quasars by lower-z large-scale structure is carefully modeled and mitigated by excluding photometric galaxies with z_p < 0.6, as magnification biases quasar-galaxy correlations upward.
Model parameters (SHMR, incompleteness corrections, quasar occupation parameters) are jointly fit using MCMC with emcee to the combined observables (PAC ¯n_2 w_p, spectroscopic clustering, cross-correlations). Model predictions use Corrfunc to compute projected correlation functions from mock catalogs.
This multi-probe likelihood fitting approach constrains the galaxy and quasar halo connections on small scales with quantified uncertainties and covariances. Detailed posterior distributions and covariances illustrate parameter degeneracies and robustness.
A concrete example end-to-end: measuring ¯n_2 w_p around DESI DR1 quasars in the stellar mass bin 10^{10.8}–10^{10.9} M_sun, combining the four redshift bins, jackknife estimating covariance, then fitting with N-body-based SHMR+quasar occupation model including magnification correction, yielding best-fit B near unity and quasar occupation peaking near 10^{12.88} h^{-1} M_sun halo accretion mass.
Technical innovations
- Application of the PAC method combining spectroscopic tracers and dense photometric galaxies to precisely measure small-scale quasar environments, overcoming spectroscopic fiber collision and shot noise limitations.
- Joint modeling of PAC excess projected density measurements with quasar and LRG autocorrelations and quasar-LRG cross-correlations within a unified MCMC framework to constrain quasar and galaxy halo connections simultaneously.
- Introduction of a relative satellite-hosting parameter B measuring quasar occupation probability in satellites versus centrals at fixed halo accretion mass, enabling direct test of environmental dependence.
- Modeling and mitigation of lensing magnification bias effects in quasar-galaxy projected density measurements via exclusion of low-redshift photometric galaxies and multiband effective number-count slope.
- Use of a state-of-the-art high-resolution N-body simulation (CosmicGrowth) populated via subhalo abundance matching with a flexible double power-law stellar-to-halo mass relation and scatter to interpret small-scale clustering signals.
Datasets
- DESI DR1 Quasars — ~72,855 objects — Public DESI data release
- DESI DR1 Luminous Red Galaxies (LRGs) — subset at 0.8 < z < 1.0 — Public DESI data release
- DESI Legacy Imaging Surveys DR9 photometric galaxies — large-area optical imaging catalog — Public legacy surveys data
- CosmicGrowth N-body simulation snapshot at z=0.92 — 3072³ particles in (600 h⁻¹ Mpc)³ volume — Internal simulation data
Baselines vs proposed
- Full photometric sample fit: B = 1.19^{+0.07}_{-0.06} vs magnification-mitigated fit: B = 1.01^{+0.03}_
- SHMR parameter M0: 11.97^{+0.02}_{-0.02} (full) vs 11.95^{+0.01}_{-0.01} (mitigated)
- Scatter σ in SHMR: 0.26^{+0.01}_{-0.01} (full) vs 0.23^{+0.00}_{-0.00} (mitigated)
- Quasar occupation peak µ: 12.76^{+0.03}_{-0.04} (full) vs 12.88^{+0.02}_{-0.02} (mitigated)
- Quasar occupation width σ_q: 0.48^{+0.04}_{-0.03} (full) vs 0.51^{+0.02}_{-0.01} (mitigated)
Limitations
- The quasar satellite occupation parameter B depends on the assumed Gaussian occupation model; different occupation forms could alter conclusions.
- Foreground lensing magnification is mitigated but residual magnification from z_p=0.6–0.8 foreground galaxies remains unmodeled, possibly biasing results slightly.
- The analysis is at a single effective redshift slice (z ~ 0.9), limiting evolutionary inferences on quasar environments over cosmic time.
- Limited by stellar mass completeness threshold (10^{10.8} M_sun); lower-mass neighbors require model incompleteness corrections which add uncertainty.
- Environmental dependence beyond central-satellite dichotomy, such as halo assembly bias or detailed subhalo properties, is not explored, potentially simplifying quasar triggering physics.
Open questions / follow-ons
- How does quasar satellite probability B and halo occupation evolve with redshift beyond z ~ 0.9?
- What is the impact of alternate quasar occupation models (e.g., non-Gaussian, double-population) on inferred satellite vs central occupation?
- Can PAC measurements combined with multiwavelength AGN data constrain feedback modes and SMBH-galaxy coevolution physics more directly?
- How do environmental properties beyond halo mass, such as recent accretion history or local density, modulate quasar triggering probability within halos?
Why it matters for bot defense
For bot-defense and CAPTCHA practitioners, this work exemplifies how combining sparse spectroscopic objects (quasars) with abundant photometric neighbors can extract high-fidelity small-scale environment measurements despite classic sampling challenges (e.g., fiber collisions). Analogously, CAPTCHA systems could be designed to leverage dense auxiliary signals correlated with scarce primary queries to robustly distinguish legitimate human users from automated bots, exploiting richer context rather than direct pairwise testing. The modeling of environmental dependence through parameter B, and careful treatment of foreground contamination (magnification bias) highlight the importance of explicitly factoring systematic biases when interpreting correlation signals, which is critical in CAPTCHA analytics to avoid false positives or negatives. While astrophysical in domain, the PAC methodology illustrates a sophisticated example of joint modeling across heterogeneous data fidelity levels, a concept transferable to layered bot-defense architectures that combine high-accuracy sparse signals with dense lower-fidelity indicators to enhance detection sensitivity and robustness.
Cite
@article{arxiv2607_21749,
title={ Where Do Quasars Live? DESI DR1 Constraints from PAC Measurements },
author={ Shanquan Gui and Kun Xu and Donghai Zhao },
journal={arXiv preprint arXiv:2607.21749},
year={ 2026 },
url={https://arxiv.org/abs/2607.21749}
}