The luminosity function and clustering of bright quasars in the FLAMINGO cosmological simulations

TL;DR

The paper assesses how well the FLAMINGO large-volume cosmological hydrodynamical simulations reproduce the bright quasar population, focusing on the quasar luminosity function (QLF) and quasar clustering. It finds good agreement with observations at low redshift and for faint quasars, but a significant underprediction of bright quasars around cosmic noon; introducing a log-normal luminosity scatter of $0.75$ dex boosts the bright end via upscattering from lower-mass BHs, partially restoring consistency while revealing tensions related to SMBH growth and Eddington ratios. Decomposing the QLF by black hole mass shows that, with scatter, lower-mass BHs dominate the bright end, whereas the most massive BHs remain relatively quiescent due to feedback, suggesting that the simulated high-redshift massive BHs are either too rare or underfed. Quasar clustering in FLAMINGO generally agrees with measurements up to $z\lesssim3$, and the scatter-induced reduction in luminosity dependence brings the predictions in line with observations, though high-$z$ ($z\approx4$) clustering remains weaker than some data, consistent with other models and observational uncertainties. The work highlights the importance of resolution and SMBH fueling physics for modeling the bright quasar population and provides a framework for interpreting quasar-halo connections in future large-volume simulations and surveys.

Abstract

Cosmological hydrodynamical simulations are essential tools for studying the formation and evolution of galaxies and their central supermassive black holes. While they reproduce many key observed properties of galaxies, their limited volumes have hindered comprehensive studies of the AGN and quasar populations. In this work, we leverage the FLAMINGO simulation suite, focusing on its large $(2.8$ $\mathrm{Gpc})^3$ volume, to investigate two key observables of quasar activity: the quasar luminosity function (QLF) and quasar clustering. FLAMINGO reproduces the observed QLF at low redshift ($z \lesssim 1$) and for faint quasars ($L_\mathrm{bol} \lesssim 10^{45}$ $\mathrm{erg s^{-1}}$), but significantly underpredicts the abundance of bright quasars at $z \approx 1$-$3$. Introducing a 0.75 dex log-normal luminosity scatter to represent unresolved small-scale variability boosts the number of bright quasars by upscattering lower-luminosity systems, thereby improving agreement with observations at the bright end. A decomposition of the QLF by black hole mass reveals that this boost is primarily driven by low-mass black holes radiating above the Eddington limit. Nevertheless, limitations remain in fully reproducing the rise and decline of the bright quasar population over cosmic time and in matching the black hole masses inferred from quasar spectra. Thanks to FLAMINGO's large volume, we can robustly sample rare, luminous quasars and measure their spatial clustering for $\log_{10} L_\mathrm{bol}/\mathrm{erg s^{-1}} \gtrsim 45.5$. The simulation reproduces the observed clustering across $0 \lesssim z \lesssim 3$, and the reduced luminosity dependence introduced by scatter aligns with observational trends. However, it underpredicts the clustering strength at $z \approx 4$, consistent with other models and possibly reflecting high-redshift observational uncertainties.

Figures (13)

• Figure 1: Comparison of the bolometric quasar luminosity function (QLF) computed for the FLAMINGO L2p8_m9 run (red lines) with observational data compiled by shen2020 (blue points) for different redshifts. The red dashed lines represent the QLF obtained directly from the FLAMINGO catalogues (see \ref{['sec:method']}), while the red solid lines represent the effect of adding log-normal scatter (with $\sigma=0.75$ dex) to the bolometric luminosity of quasars.
• Figure 2: Cumulative Quasar Luminosity Function (cQLF) in different bolometric luminosity bins. The colored lines represent the predictions from the FLAMINGO L2p8_m9 simulation with (solid) and without (dashed) 0.75 dex of additional scatter in bolometric luminosity. The shaded region represents the range between the maximum and minimum values obtained by reproducing the constraints from "Global Fit A" and "Global Fit B" taken from the shen2020 model of observational data at different redshifts.
• Figure 3: The projected auto-correlation functions of quasars at different redshifts. Solid lines represent the results for the FLAMINGO L2p8_m9 run with the inclusion of 0.75 dex of scatter in quasar luminosity, while dashed lines show the clustering when scatter is not included. When computing the auto-correlation functions, we only include quasars that are brighter than a luminosity threshold $L_\mathrm{bol,thr}$, that -- whenever possible -- is set close to that used by observations (see main text for details). For $z=1.0$ and $z=4.0$, we employ a lower luminosity threshold, but show the results obtained using the same luminosity $L_\mathrm{bol,thr}$ as in the observations -- which becomes possible only in the case with scatter -- with solid orange lines. Blue points show the measured auto-correlation functions of quasars at the same redshifts from SDSS Ross2009Shen_2006 and BOSS Eftekharzadeh_2015. The shaded blue region highlights the 1-sigma confidence interval for the power-law fit performed on the observational data, and serves as a useful reference in our data-model comparison.
• Figure 4: Correlation length, $r_0$, as a function of redshift. Colored lines show the predictions from the FLAMINGO L2p8_m9 simulation for different luminosity thresholds, while data points correspond to observational data for sources with $L_{\rm bol} \gtrsim 10^{45}\, {\rm erg}\,{\rm s}^{-1}$ (green) and $L_{\rm bol} \gtrsim 10^{45.5}\, {\rm erg}\,{\rm s}^{-1}$ or higher (yellow). The solid (dashed) lines correspond to the case with (without) the addition of 0.75 dex of scatter in quasar luminosity. Correlation length measurements are taken from the $-2$ power-law fits performed by Eftekharzadeh_2015, Shen_2009Shen_2006, Ross2009, and Porciani2006.
• Figure 5: Eddington ratio distribution functions (ERDFs) split in bins of black hole mass, with different colors representing different black hole mass ranges. Dashed lines show results from the original FLAMINGO L2p8_m9 run, while solid lines show the effect of including 0.75 dex of scatter to the quasar luminosities. Adding scatter produces a broader ERDF that allows for super-Eddington ratios, and brings low-mass black holes to quasar-like bolometric luminosities.