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Quasar clustering and duty cycle measurements at $0\leq z\leq 4$ with the Gaia-unWISE Catalog

Mariona Giner Mascarell, Anna-Christina Eilers, Kate Storey-Fisher

TL;DR

This study uses a homogeneous all-sky Gaia-unWISE Quaia quasar catalog to measure the projected two-point correlation function $w_p(r_p)$ in four redshift bins spanning $0 o4$, enabling robust inferences about quasar host halos. By modeling $\xi(r)$ as a power law and mapping the measured $r_0$ to a minimum halo mass $M_{ m min}$ with halomod (Tinker mass function and bias) under a simple step-function HOD, the authors find a nearly constant characteristic host mass around $ obreak imes10^{12.8} ext{--}10^{12.9}\,M_\odot$ across all redshifts. Combining the quasar number density with the halo abundance yields duty cycles that rise from roughly $2 ext{--}3 ext%$ to $ obreak 7 ext%$ with increasing redshift, corresponding to integrated quasar lifetimes of $ frac{t_{ m QSO}}{t_H(z)} o obreak 10^{8}$ years. These results point to a self-regulated growth scenario in which both the typical host halo mass and the duration of luminous quasar phases remain remarkably stable over more than 12 Gyr of cosmic time, with implications for the connection between quasar triggering, feedback, and galaxy quenching.

Abstract

We measure the two-point correlation function of a uniformly selected, all-sky sample of $\sim$1.3 million quasars with magnitudes $G\leq20.5$ from the Gaia--unWISE Quasar Catalog (Quaia) over the redshift range $0 \leq z \leq 4$ to trace the evolution of the quasar clustering strength across cosmic time. We find a steady increase in the correlation length $r_0$ with redshift, i.e. $r_0 = 6.8 \pm 0.2\,h^{-1}\mathrm{Mpc}$ at $0 \leq z < 1$, $r_0=8.0 \pm 0.2\,h^{-1}\mathrm{Mpc}$ at $1 \leq z < 2$, $r_0=10.8 \pm 0.2\,h^{-1}\mathrm{Mpc}$ at $2 \leq z < 3$, and $r_0=13.9 \pm 1.2\,h^{-1}\mathrm{Mpc}$ at $3 \leq z < 4$, and slopes consistent with $γ\approx 2$. Our measurements suggest a slightly weaker clustering signal at $z>3$ than previous studies, and thus we find a smooth, monotonic rise in clustering strength. Using a bias-halo mass relation and a step-function for the halo occupation distribution, we infer characteristic minimum halo masses of quasar hosts of $\log_{10}(M_{\mathrm{min}}/M_\odot) \approx 12.8$ across all redshifts. Combining these with the observed quasar number densities yields duty cycles that rise from $f_{\mathrm{duty}} \approx 2\%$ to $\approx 7\%$ with increasing redshift, corresponding to integrated quasar lifetimes of $t_{\rm QSO}\sim10^8$~years. These results suggest that both the characteristic halo mass of active quasars and their typical lifetimes have remained remarkably stable over more than $12 \sim$ Gyr of cosmic time, implying a self-regulated growth process largely independent of epoch.

Quasar clustering and duty cycle measurements at $0\leq z\leq 4$ with the Gaia-unWISE Catalog

TL;DR

This study uses a homogeneous all-sky Gaia-unWISE Quaia quasar catalog to measure the projected two-point correlation function in four redshift bins spanning , enabling robust inferences about quasar host halos. By modeling as a power law and mapping the measured to a minimum halo mass with halomod (Tinker mass function and bias) under a simple step-function HOD, the authors find a nearly constant characteristic host mass around across all redshifts. Combining the quasar number density with the halo abundance yields duty cycles that rise from roughly to with increasing redshift, corresponding to integrated quasar lifetimes of years. These results point to a self-regulated growth scenario in which both the typical host halo mass and the duration of luminous quasar phases remain remarkably stable over more than 12 Gyr of cosmic time, with implications for the connection between quasar triggering, feedback, and galaxy quenching.

Abstract

We measure the two-point correlation function of a uniformly selected, all-sky sample of 1.3 million quasars with magnitudes from the Gaia--unWISE Quasar Catalog (Quaia) over the redshift range to trace the evolution of the quasar clustering strength across cosmic time. We find a steady increase in the correlation length with redshift, i.e. at , at , at , and at , and slopes consistent with . Our measurements suggest a slightly weaker clustering signal at than previous studies, and thus we find a smooth, monotonic rise in clustering strength. Using a bias-halo mass relation and a step-function for the halo occupation distribution, we infer characteristic minimum halo masses of quasar hosts of across all redshifts. Combining these with the observed quasar number densities yields duty cycles that rise from to with increasing redshift, corresponding to integrated quasar lifetimes of ~years. These results suggest that both the characteristic halo mass of active quasars and their typical lifetimes have remained remarkably stable over more than Gyr of cosmic time, implying a self-regulated growth process largely independent of epoch.

Paper Structure

This paper contains 11 sections, 12 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Data
  3. Quaia: Gaia's quasar sample
  4. Selection functions and random catalogs
  5. Quasar correlation function
  6. Auto-correlation function and scale length measurements
  7. Comparison to previous work
  8. Host Dark Matter Halo Masses and Quasar Duty Cycle
  9. Estimating the minimum host dark matter halo mass
  10. Quasar Number Density and Duty Cycle
  11. Summary and Discussion

Figures (5)

  • Figure 1: Two-dimensional histogram of the Quaia quasar sample as a function of redshift and absolute magnitude $M_{1450}$.
  • Figure 2: The projected auto-correlation function for the four redshift bins is shown with jackknifing errors for the four redshift bins, with errors estimated using jackknife resampling. The dashed lines and shaded areas show the best power-law fits with $2 \sigma$ uncertainties. The legend shows the best-fit parameter values of the power-law model fit to the data.
  • Figure 3: Comparison of the projected auto-correlation function of Quaia sources with SDSS sources analyzed by Shen2007 for $0.8 \leq z \leq 2.1$, $2.9 \leq z \leq 3.5$, and $z \geq 3.5$ (their good fields). Black measurements indicate results by Shen2007, while red data points show the results from this study.
  • Figure 4: Minimum dark matter halo mass vs $r_0$ comparison. Horizontal dashed lines represent measured values through auto-correlation fits; vertical lines are the predicted mass for each measurement.
  • Figure 5: Redshift evolution of the quasars’ auto-correlation scale length (left) and the quasars’ duty cycle (right). Our measurements are shown in red, while results from previous studies are shown in different colors Shen2007Ross2009White2012Eftekharzadeh2015Laurent2017Arita2023Eilers2024Pizzati2024Schindler2025. Dashed lines in the left panel show the clustering strength for a constant dark matter halo mass, making the same assumption as in our study, i.e. a step-function HOD with the Tinker2010 relation modeled with halomod. The dashed lines in the right panel indicate the duty cycle corresponding to a constant integrated quasar lifetime $t_{\rm QSO}$.