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The host halo masses of AGNs and quasars at $z \sim 3-7$ with TNG-Cluster, FLAMINGO and other cosmological galaxy simulations

Using large-scale cosmological simulations, this study reveals that while AGN luminosity generally increases with host halo mass up to a threshold, the relationship is highly non-linear with significant scatter, indicating that the most luminous quasars at $z \sim 3-7$ typically inhabit intermediate-mass haloes ( $10^{12-12.5}$ M $_{\odot}$ ) rather than the most massive ones, a finding that aligns well with observational estimates.

Original authors: Akanksha Kapahtia, Annalisa Pillepich, Joey Braspenning, Dylan Nelson, Joop Schaye, Eduardo Bañados, Silvia Belladitta, Frederick Davies

Published 2026-06-15✓ Author reviewed ⓘ

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CC BY 4.0

Original authors: Akanksha Kapahtia, Annalisa Pillepich, Joey Braspenning, Dylan Nelson, Joop Schaye, Eduardo Bañados, Silvia Belladitta, Frederick Davies

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Finding the "Sweet Spot" for Cosmic Superstars

Imagine the universe as a giant, growing city. In this city, the "dark matter halos" are the neighborhoods, and the "Active Galactic Nuclei" (AGNs) or "Quasars" are the massive, blindingly bright lighthouses at the center of the most important buildings. These lighthouses are powered by supermassive black holes eating gas.

For a long time, astronomers have been trying to answer a simple question: How big does a neighborhood (halo) need to be to host the brightest lighthouse (quasar)?

Most observations suggest that these super-bright quasars live in neighborhoods that are roughly the same size, no matter how far back in time (or how far away) you look. They seem to prefer a "Goldilocks" zone: not too small, not too big.

This paper uses massive computer simulations to test that idea. The researchers built digital universes (using models like TNG-Cluster and FLAMINGO) to see if their virtual quasars behave like the real ones.

The Main Discovery: It's Not a Straight Line

The researchers found that the relationship between the size of the neighborhood and the brightness of the lighthouse is not a straight line. It's more like a hill with a peak.

The Climb: As the neighborhood gets bigger (more massive), the lighthouse generally gets brighter. This makes sense; bigger neighborhoods have more gas to feed the black hole.
The Peak: This trend only goes up to a certain point (about $10^{12}$ times the mass of our Sun).
The Drop-off: Once the neighborhood gets too massive, the lighthouse actually gets dimmer or stays the same.

The Analogy: Think of it like a party.

In a small house (small halo), you have a few people, and the music is quiet.
In a medium-sized house (the sweet spot), you have the perfect crowd, and the party is loud and energetic.
In a massive stadium (a huge halo), the party actually gets quieter. Why? Because the "host" (the black hole) gets so greedy and powerful that it starts blowing the guests out of the room (this is called AGN feedback). It pushes the gas away, starving itself and stopping the party from getting louder.

The "Chaos" Factor: Huge Scatter

One of the most surprising findings is how messy the data is. The paper compares two ways of looking at the data:

Scenario A: If you pick a specific neighborhood size, how bright is the lighthouse?
- Result: Wildly unpredictable. The brightness can vary by a factor of 1,000 to 10,000 (3 to 4 "decades" of difference). One house of the same size could have a tiny nightlight, while another has a blinding spotlight.
Scenario B: If you pick a specific brightness (e.g., a super-bright quasar), how big is the neighborhood?
- Result: Much more predictable. If you see a super-bright lighthouse, it is almost certainly in a neighborhood of a specific size range.

The Analogy: Imagine trying to guess how much a person weighs just by looking at their height.

If you pick a specific height (e.g., 6 feet), people can weigh anywhere from 140 lbs to 300 lbs. That's a huge scatter.
But if you pick a specific weight (e.g., 250 lbs), the person is almost certainly around 6 feet tall. The weight predicts the height much better than the height predicts the weight.

The paper concludes that the size of the neighborhood is a poor predictor of how bright the black hole is right now. The black hole's brightness is chaotic and depends on many other things (like how much gas is currently available), not just the size of the neighborhood.

The "Sweet Spot" Confirmed

Despite the chaos, the simulations confirmed the observational idea: Quasars prefer a specific neighborhood size.

Whether the universe is 3 billion years old or 7 billion years old, the brightest quasars tend to live in halos with a mass of about $10^{12}$ to $10^{12.5}$ solar masses.
They rarely live in the most massive haloes (the super-cities).
They rarely live in the smallest haloes (the tiny villages).

This suggests that there is a "sweet spot" for black hole growth. If the neighborhood is too small, the black hole can't get enough food. If it's too big, the black hole's own feedback (blowing gas away) stops it from growing.

Why This Matters

The paper argues that we can't just look at the size of a galaxy's neighborhood to guess how bright its black hole is. The connection is too loose and too chaotic. However, if we see a super-bright quasar, we can be fairly confident about the size of its home.

The simulations also show that this "sweet spot" stays roughly the same size throughout cosmic history, even though the universe is expanding and changing. This implies that the rules governing how black holes feed and how they shut themselves off are consistent across billions of years.

Summary in One Sentence

The paper finds that while supermassive black holes live in a specific "Goldilocks" size of cosmic neighborhood, the brightness of the black hole is so chaotic that knowing the neighborhood size tells you very little about how bright the black hole is at any given moment.

Problem Statement
Observational studies and clustering analyses have long suggested that quasars inhabit a narrow range of dark-matter halo masses ( $\sim 10^{12} - 10^{13} \, M_\odot$ ) across cosmic time ( $z \lesssim 7$ ). However, these inferences are often indirect, relying on flux-limited samples and assumptions about the monotonicity of the relationship between Active Galactic Nucleus (AGN) luminosity and host halo mass. A critical gap exists in understanding the intrinsic scatter and the precise nature of this relationship before "Cosmic Noon" ( $z \gtrsim 3$ ), particularly regarding whether the most luminous AGNs reside in the most massive haloes and how feedback mechanisms regulate this connection. Previous simulations were often limited by volume (unable to sample rare, massive haloes) or resolution (unable to resolve small-scale gas dynamics driving AGN luminosities).

Methodology
This work utilizes a suite of cosmological hydrodynamical simulations to directly compare observational pictures with self-consistent galaxy-formation models. The study focuses on AGNs with bolometric luminosities $L_{\text{AGN}}^{\text{bol}} \geq 10^{42} \, \text{erg s}^{-1}$ at redshifts $z = 3 - 7$ .

The primary analysis relies on two large-volume simulation suites:

TNG300 + TNG-Cluster: Part of the IllustrisTNG project, offering high resolution (baryonic target mass $\sim 1.1 \times 10^7 \, M_\odot$ ) across a volume of $300^3 \, \text{cMpc}^3$ and a zoom-in extension targeting massive haloes up to $10^{15} \, M_\odot$ .
FLAMINGO: Encompassing volumes of $1 - 3 \, \text{Gpc}^3$ per side (runs L1_m8 and L2p8_m9), providing superior statistical sampling of the high-mass end of the halo mass function, albeit at lower resolution than TNG.

For benchmarking, the authors include smaller-volume ( $\sim 100 \, \text{cMpc}^3$ ) simulations from previous generations: Illustris, EAGLE, TNG100, and Simba.

AGN bolometric luminosities are not direct simulation outputs but are calculated in post-processing from instantaneous SMBH accretion rates using a bimodal conversion model (Churazov et al. 2005) that distinguishes between radiatively efficient and inefficient accretion regimes. A uniform radiative efficiency of $\epsilon_r = 0.1$ is adopted across all models to isolate differences in underlying accretion physics.

Key Contributions and Results

Non-Linear and Non-Monotonic Relations: Across all models, the median relation between AGN bolometric luminosity and host halo mass is highly non-linear. While more massive haloes tend to host more luminous AGNs on average, this trend persists only up to a characteristic halo mass of $M_{200,\text{crit}} \sim 10^{12} \, M_\odot$ .
- In TNG300+TNG-Cluster, the median relation flattens and even turns over (dips) at $M_{200,\text{crit}} \gtrsim 10^{12} \, M_\odot$ for $z < 5-6$ .
- In FLAMINGO, the relation flattens at the high-mass end but does not show the same pronounced turnover.
- This high-mass quenching is attributed to AGN feedback (kinetic in TNG, thermal in FLAMINGO) which suppresses gas accretion onto SMBHs in massive haloes.
Large Intrinsic Scatter: The paper quantifies a significant object-to-object variation. The scatter in AGN bolometric luminosity at a fixed host halo mass is much larger (up to 3 dex for the 5th–95th percentiles) than the scatter in host halo mass at a fixed AGN luminosity ( $\lesssim 1$ dex). This implies a weak coupling between halo growth and instantaneous SMBH accretion, suggesting that halo mass alone is a poor predictor of instantaneous AGN luminosity.
Quasar Host Halo Masses:
- TNG300+TNG-Cluster: Quasars ( $L_{\text{AGN}}^{\text{bol}} \sim 10^{45} - 10^{47} \, \text{erg s}^{-1}$ ) typically reside in haloes of $10^{12} - 10^{12.5} \, M_\odot$ at $z=3-6$ .
- FLAMINGO: Quasars extend to median masses of $\sim 10^{12.8} \, M_\odot$ at $z \sim 3-4$ .
- Crucially, the most luminous AGNs do not inhabit the most massive haloes available at any given epoch up to $z \approx 7$ . Instead, they reside in progressively rarer haloes at earlier epochs, but typically avoid the very highest mass systems ( $M_{200,\text{crit}} \gtrsim 10^{13} \, M_\odot$ ) due to feedback quenching.
Comparison with Observations: The simulated host halo masses for quasars broadly match observational estimates derived from clustering and cross-correlation measurements, which generally infer characteristic masses of $10^{12} - 10^{13} \, M_\odot$ . The large scatter predicted by the simulations helps reconcile the broad observational constraints.

Significance and Claims
The paper claims that modern cosmological simulations, despite differing in resolution, volume, and sub-grid physics (seeding, accretion, feedback), converge on a consistent picture: the AGN luminosity–halo mass relation is characterized by a "sweet spot" of characteristic halo mass ( $\sim 10^{12} \, M_\odot$ ) where quasars are most prevalent, flanked by quenching in more massive haloes and suppression in less massive ones.

The authors emphasize that the large intrinsic scatter in AGN luminosity at fixed halo mass challenges the assumptions of many semi-empirical halo-occupation models, which often assume a tighter relation. The results suggest that while the typical quasar resides in a specific mass range, individual systems exhibit vast diversity, and the most massive haloes are not necessarily the hosts of the most luminous quasars at any given time. This work provides a quantitative baseline for interpreting high-redshift quasar observations and highlights the role of AGN feedback in shaping the demographics of the most luminous black holes before Cosmic Noon.