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The VST ATLAS Survey -- IV: Galaxy, LRG and QSO bias and HODs via ACT CMB Lensing

This paper analyzes VST ATLAS galaxy, LRG, and QSO clustering cross-correlated with ACT DR6 CMB lensing to derive bias and HOD parameters, finding that while LRGs align with $\Lambda$ CDM predictions, QSOs exhibit unexpectedly high bias and mass, and low-redshift galaxies require an anti-bias hypothesis, collectively suggesting that standard halo models may fail to describe intermediate-scale clustering for these populations.

Original authors: Harshnoor Kaur (CEA, Physics Dept., Durham University, UK), T. Shanks (CEA, Physics Dept., Durham University, UK), S. Bose (ICC, Physics Dept., Durham University, UK), A. C. Edge (CEA, Physics Dept.

Published 2026-07-17

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Original authors: Harshnoor Kaur (CEA, Physics Dept., Durham University, UK), T. Shanks (CEA, Physics Dept., Durham University, UK), S. Bose (ICC, Physics Dept., Durham University, UK), A. C. Edge (CEA, Physics Dept., Durham University, UK)

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 or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible ocean made of dark matter. We can't see this ocean directly, but we know it's there because it has gravity. Just like a boat creates ripples in water, massive objects like galaxies and quasars (super-bright, ancient black holes) create "ripples" in the fabric of space-time. When light from the very edge of the universe travels through these ripples on its way to us, it gets bent and distorted. Astronomers call this "gravitational lensing." By measuring how much the light bends, we can map the invisible ocean of dark matter, even though we can't see it.

To understand how this ocean works, scientists study how galaxies and quasars are clustered together. Do they hang out in tight groups, or are they spread out? This clustering tells us about the "bias" of these objects—basically, how much more likely they are to be found in heavy, dark-matter-rich areas compared to the average spot in the universe. If we know how they cluster, we can test our biggest theory about the universe's history, called the "Lambda Cold Dark Matter" (ΛCDM) model. This model is like the rulebook for how the universe grew from a tiny dot into the vast cosmos we see today. If the rulebook predicts one thing but our observations show another, it means we might need to rewrite the rules.

The Cosmic Detective Story: Mapping the Invisible with a Sharper Lens

In this paper, a team of astronomers from Durham University acts like cosmic detectives, trying to solve a mystery about how galaxies and quasars are arranged in the universe. They used two powerful tools: the VST ATLAS survey, which took pictures of millions of galaxies and quasars, and the Atacama Cosmology Telescope (ACT), which provided a brand-new, high-resolution map of the invisible dark matter ocean. Think of the ACT map as a new pair of glasses that is three times sharper than the old ones (which came from the Planck satellite). With this super-sharp vision, the team could see the details of the dark matter ripples much more clearly than ever before.

The team looked at three different groups of cosmic objects:

Normal Galaxies: A huge crowd of about 6.2 million galaxies, mostly young and active, sitting relatively close to us (about 150 million years ago in light-travel time).
LRGs (Luminous Red Galaxies): A smaller, more exclusive club of about 38,000 massive, red, and old galaxies.
QSOs (Quasars): A group of about 126,000 super-bright, ancient black holes sitting very far away, from about 1.7 billion years ago.

The Big Surprise: The "Anti-Bias" Mystery

The scientists wanted to see if the standard rulebook (ΛCDM) could explain how these objects clustered. They expected the galaxies and quasars to act like magnets, sticking together in the heaviest parts of the dark matter ocean.

For the LRGs and the QSOs, the rulebook worked pretty well. The LRGs were found to be very "biased," meaning they lived in the heaviest, most crowded dark matter neighborhoods, just as the theory predicted. The QSOs were even more extreme, living in the most massive dark matter "cities" imaginable, with a bias of about 4.44. This suggests they are the kings of the dark matter world.

However, the normal galaxies (the 17 < r < 21 group) threw a massive curveball. When the team tried to fit the standard "halo model" (a theory that says galaxies live inside specific bubbles of dark matter called halos) to the data, it failed miserably. The model predicted that these galaxies should be clustered a certain way, but the ACT map showed they were clustered differently.

In fact, to make the math work, the team had to assume these normal galaxies had an "anti-bias." Imagine if, instead of clustering together in a crowd, these galaxies actively avoided the heavy dark matter spots, or perhaps they were spread out so evenly that they looked like they were "anti-clustering." The data suggested a bias value of about 0.55, which is much lower than the expected 1.0. This means the standard "halo" model, which works great for the LRGs and QSOs, doesn't seem to describe how these normal galaxies live.

The "Mass Tracer" Alternative

Since the standard "halo" model failed for the normal galaxies, the team tested an older, different idea. This idea suggests that instead of living inside specific dark matter bubbles, these galaxies simply "trace" the mass of the universe directly. It's like saying the galaxies aren't tenants in specific apartments (halos); they are just the dust motes floating in the air, showing you exactly where the air is thickest.

When they used this "mass tracer" model (specifically a model proposed by Williams & Irwin in 1998), the fit was perfect. The data showed that for these normal galaxies, the way they cluster looks exactly like the way the dark matter itself is distributed, just scaled down. This suggests that at the scales they were looking at (between 1 and 8 times the distance from Earth to the Sun, measured in "h⁻¹ Mpc"), these galaxies follow a different set of rules than the LRGs and QSOs. They seem to follow a "hierarchical clustering" model, where they are more tightly woven into the fabric of the universe than the standard halo model allows.

The QSO Mass Mystery

There was another twist with the quasars. When the team used the new, sharper ACT data to estimate the mass of the dark matter "cities" hosting the quasars, they found something shocking. The quasars seemed to be living in halos that were about 10 times more massive than anyone expected. The estimated effective mass was around 5 × 10¹⁴ solar masses. This is a huge number, suggesting these ancient black holes are sitting in the most massive structures in the universe, far heavier than previous studies suggested. However, the authors are careful to note that because the data is still a bit fuzzy at the very smallest scales, this result is a strong hint rather than a final, proven fact.

The Growth Rate Puzzle

Finally, the team looked at how fast the universe's structures are growing. By comparing the clustering at different distances (and therefore different times in the past), they calculated a value called σ₈, which measures how "clumpy" the universe is. For the distant quasars, they found a value of 0.49, which is significantly lower than the standard prediction of 0.8. This implies that the universe's structures are growing faster than our current rulebook predicts. It's as if the universe is building skyscrapers much quicker than the blueprints say it should.

What This Means

The paper doesn't claim to have solved the mystery of the universe, but it has definitely shaken up the rulebook. It suggests that:

Standard models work for the heavyweights: LRGs and QSOs fit the standard "halo" model well.
Standard models fail for the common folk: Normal, low-redshift galaxies seem to ignore the standard "halo" model and instead follow a simpler rule where they just trace the dark matter directly.
The universe might be growing too fast: The data hints that the universe is clumping together faster than the standard ΛCDM model predicts, especially at high redshifts.

The authors conclude that while the "halo" model is great for describing the massive LRGs and QSOs, the dominant population of normal galaxies at lower redshifts might need a different explanation, perhaps one where galaxies are more intimately tied to the dark matter than we thought. They also suggest that if the "anti-bias" idea sounds too weird, maybe the amount of matter in the universe (Ωₘ) is actually higher than we think, which would change the growth rate calculations. But for now, the data points to a universe that is a bit more complex and dynamic than our current textbooks admit.

Technical Summary: The VST ATLAS Survey - IV: Galaxy, LRG and QSO bias and HODs via ACT CMB Lensing

Problem and Motivation
This study addresses discrepancies in the measurement of galaxy and quasar (QSO) clustering biases and halo occupation distributions (HODs) when compared to $\Lambda$ CDM predictions. Previous analyses using Planck CMB lensing maps (resolution $\approx 6'$ ) were limited in their ability to resolve mass profiles and HODs at small scales. Furthermore, historical tensions exist between QSO lensing analyses (e.g., Boyle et al. 1988; Myers et al. 2003, 2005), which found higher lensing signals than predicted by $\Lambda$ CDM, and SDSS-based analyses (Scranton et al. 2005) that found consistency with $\Lambda$ CDM using HOD models. The authors aim to resolve these issues by utilizing the Atacama Cosmology Telescope (ACT) DR6 CMB lensing map, which offers approximately $3\times$ higher resolution than Planck, to re-examine the clustering of VST ATLAS galaxies, Luminous Red Galaxies (LRGs), and QSOs.

Methodology
The authors employ a "2 $\times$ 2 point" analysis combining angular auto-correlation functions ( $w_{gg}$ , $w_{qq}$ ) and cross-correlation functions between the tracers and the CMB lensing convergence map ( $w_{g\kappa}$ , $w_{q\kappa}$ ).

Datasets: The study uses VST ATLAS samples: $17 < r < 21$ galaxies ( $z \approx 0.15$ ), $0.16 < z < 0.36$ LRGs, and $17 < g < 22$ QSOs ( $z \approx 1.7$ ). These are cross-correlated with the ACT DR6 lensing convergence map (filtered $40 < l < 3000$ ) and the Planck DR3 map for comparison.
Linear Regime Analysis: At large scales, the authors estimate the linear bias ( $b$ ) and the mass clustering amplitude ( $\sigma_8$ ) by comparing the ratio of the 3-D power spectra derived from auto- and cross-correlations ( $b = P_{gg}/P_{g\kappa}$ ). They utilize the Halofit model (via the Core Cosmology Library, CCL) to model the matter power spectrum.
Non-Linear Regime Analysis: At smaller scales, the authors fit HOD parameters (Zheng et al. 2007 formalism: $M_{min}, M_0, M'_1, \alpha, \sigma_M$ ) to the auto- and cross-correlation functions. They also test the Williams & Irwin (1998) model, which assumes galaxies trace the mass directly (implying $w_{g\kappa} = \kappa/b \times w_{gg}$ ), as an alternative to the standard halo model.

Key Contributions and Results

Bias and $\sigma_8$ Estimates:
- Galaxies ( $z \approx 0.15$ ): The analysis yields a bias $b_G = 1.22 \pm 0.07$ and $\sigma_8(z=0) = 0.71 \pm 0.06$ , consistent with $\Lambda$ CDM.
- LRGs ( $z \approx 0.26$ ): The bias is estimated at $b_{LRG} = 2.76 \pm 0.11$ with $\sigma_8(z=0) = 0.63 \pm 0.15$ , also consistent with $\Lambda$ CDM.
- QSOs ( $z \approx 1.7$ ): A bias of $b_Q = 4.44 \pm 0.24$ is derived, leading to a significantly lower $\sigma_8(z=0) = 0.49 \pm 0.06$ . This implies a gravitational growth rate between $0.15 < z < 1.7$ that is faster than predicted by standard $\Lambda$ CDM, though consistent with an Einstein-de Sitter model ( $\Omega_m=1$ ).
HOD Modeling and Self-Consistency:
- LRGs and QSOs: The HOD models provide self-consistent fits for both auto- and cross-correlation functions for LRGs and QSOs. However, the QSO HOD fit implies an effective halo mass $M_{eff} \approx 5 \times 10^{14} M_\odot$ , roughly $10\times$ higher than previous estimates (Paper III), attributed to the use of CCL instead of the CHOMP code which had issues at high redshifts.
- Galaxies ( $z \approx 0.15$ ): The HOD model fails to provide a self-consistent fit. Parameters that fit the auto-correlation ( $w_{gg}$ ) significantly underestimate the cross-correlation ( $w_{g\kappa}$ ) at intermediate scales ( $1 < r < 8 h^{-1}$ Mpc). To achieve a fit, the authors must assume an "anti-bias" of $b \approx 0.55$ , meaning the galaxies are less clustered than the underlying mass on these scales.
Model Comparison (HOD vs. Mass Tracing):
- For the $z \approx 0.15$ galaxies, the Williams & Irwin (1998) model (where galaxies trace mass) with $b \approx 0.55$ fits the data significantly better than the HOD + NFW halo model. The observed correlation functions follow a power law ( $\propto \theta^{-0.8}$ ) consistent with a hierarchical clustering model (Peebles 1974) where galaxies trace mass, rather than the steeper drop-off expected from NFW halo profiles.
- Conversely, LRGs are well-described by the HOD + NFW model but poorly by the mass-tracing model.
- QSOs are reasonably described by both HOD models and the mass-tracing hierarchical model.

Significance and Claims
The paper claims that the higher resolution of the ACT lensing map reveals a fundamental difference in how different galaxy populations trace mass. While LRGs and QSOs appear to follow standard halo occupation distributions, the dominant population of low-redshift galaxies ( $17 < r < 21$ ) appears to follow a hierarchical clustering model where they trace the mass more closely than predicted by standard halo models, necessitating an "anti-bias" in the context of the HOD framework.

The authors suggest that the discrepancy in the QSO lensing signal (leading to a lower $\sigma_8$ and higher growth rate) may be linked to these intermediate-scale clustering properties. They note that if the anti-bias ( $b \approx 0.55$ ) is unphysical, it could imply a significantly higher matter density parameter ( $\Omega_m \approx 0.6$ ), though this is in tension with other cosmological probes. The authors conclude that while HOD models work well for LRGs, the dominant galaxy population at low redshift may be better described by Peebles' hierarchical clustering model, and that higher-resolution CMB data (e.g., from future surveys like 4MOST, LSST, and Euclid) is required to further test these competing explanations.

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