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Clustering properties of the CatWISE2020 quasar catalogue and their impact on the cosmic dipole anomaly

By analyzing the clustering properties of the CatWISE2020 quasar catalogue and confirming the absence of significant large-scale power beyond the dipole, this study validates the existence of an anomalously high cosmic dipole that challenges the standard Cosmological Principle.

Original authors: Sebastian von Hausegger, Nathan Secrest, Harry Desmond, Mohamed Rameez, Roya Mohayaee, Subir Sarkar

Published 2026-02-25

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CC BY 4.0

Original authors: Sebastian von Hausegger, Nathan Secrest, Harry Desmond, Mohamed Rameez, Roya Mohayaee, Subir Sarkar

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

The Big Mystery: The Universe's "Tilt"

Imagine the Universe as a giant, perfectly smooth ocean. According to the standard rules of cosmology (the Cosmological Principle), if you zoom out far enough, this ocean should look the same in every direction. It should be isotropic (no preferred direction) and homogeneous (evenly spread out).

However, there is a strange "tilt" in the data.

The CMB Dipole: We know our Solar System is moving through space at about 370 km/s. This motion creates a "Doppler effect" in the Cosmic Microwave Background (CMB)—the afterglow of the Big Bang. It looks slightly hotter in the direction we are moving and cooler behind us. This is the "kinematic dipole," and it's expected.
The Quasar Dipole: Now, look at distant quasars (super-bright black holes at the centers of galaxies). If the Universe is truly smooth and isotropic, the distribution of these quasars should show the exact same tilt as the CMB.
The Problem: When astronomers looked at 1.6 million quasars from the CatWISE2020 catalogue, they found a tilt that was twice as strong as the one predicted by our motion. It's like driving a car and seeing the road ahead stretch out twice as much as the speedometer says it should. This is the "Cosmic Dipole Anomaly."

The Skeptics' Theory: "It's Just a Trick of the Light"

Some scientists argued that this huge tilt wasn't real. They suggested it might be an illusion caused by clumping.

Imagine you are looking at a crowd of people in a stadium. If you are standing near a VIP section where people are packed tightly together, it might look like the whole stadium is crowded in that direction, even if the rest of the stadium is empty.

The skeptics (specifically a group led by Abghari et al.) proposed that the quasars might be clumping in a specific pattern (an octupole, or an 8-lobed shape) that, when mixed with the missing parts of the sky (because the Milky Way blocks our view), creates a fake "tilt" that looks stronger than it really is. They thought the astronomers had missed this hidden pattern, leading to a false alarm.

What This Paper Did: The "Cosmic Detective" Work

The authors of this paper decided to play detective. They didn't just look at the tilt; they looked at the entire picture to see if there were any hidden patterns messing up the results.

Here is how they did it, using some analogies:

1. Checking the "Noise" (The Static on the Radio)

When you listen to a radio, you hear static. In astronomy, "shot noise" is the randomness of counting stars. If you have a million stars, the randomness is small. If you have ten, it's huge.

The Discovery: The authors found that the quasars in this catalogue aren't just randomly scattered like raindrops; they are "clumpy" in a way that creates more noise than a simple random scatter. They used a special mathematical tool (a Generalized Poisson likelihood) to account for this extra "clumpiness," ensuring they weren't misinterpreting noise as a signal.

2. The "Ecliptic Latitude" Glitch

The telescope that took these pictures (WISE) scans the sky in a specific pattern. It turns out the telescope was slightly biased: it counted fewer quasars near the "poles" of its scanning path (the ecliptic poles) and more near the "equator."

The Fix: The team treated this like a bad microphone that gets quieter in one corner of the room. They mathematically corrected for this bias, ensuring the "tilt" they measured wasn't just the telescope being picky about where it looked.

3. Hunting for the "Octupole" (The Hidden Pattern)

This was the main event. They asked: "Is there a hidden 8-lobed pattern (octupole) hiding in the data that is faking the tilt?"

The Result: They built a model that allowed for a dipole (tilt), a quadrupole (football shape), and an octupole (8-lobed shape) all at once.
The Verdict: Nope. They found no evidence for a significant octupole. The data is consistent with random noise on those large scales. The "tilt" is real, and it's not being faked by a hidden pattern.

4. The "Small Scale" Check

They also checked the small-scale clustering (how quasars group together locally). They compared this to the standard model of the Universe (Lambda-CDM).

The Result: On small scales, everything looks perfect. The quasars are clumping exactly as the standard model predicts. This proves the data is high-quality and the telescope isn't broken. The problem is only on the very largest scales (the dipole).

The Final Conclusion: The Anomaly is Real

After stripping away all the possible excuses (noise, telescope bias, hidden patterns, local clumping), the "tilt" remains.

The Clustering Dipole: Even if you assume the standard model is perfect, the amount of "tilt" caused by quasars naturally clumping together (the clustering dipole) is tiny—about 140 times smaller than the weird tilt they are actually seeing.
The Verdict: The anomaly is not a mistake. It is a robust feature of the data. The quasars are pointing in a direction with a strength that is twice what our motion through the Universe should produce.

Why Does This Matter?

This is a big deal. The standard model of cosmology (Lambda-CDM) relies on the idea that the Universe is the same everywhere. If the matter in the Universe (quasars) is pointing in a different direction and with a different strength than the light from the Big Bang (CMB), it suggests one of two things:

Our Physics is Wrong: The Cosmological Principle might be broken. The Universe might not be as uniform as we thought.
New Physics: There might be something massive and unknown pulling on our local universe, or the laws of gravity/expansion work differently on the largest scales.

In short: The authors looked for every possible reason why the "tilt" might be a fake. They found none. The tilt is real, it's huge, and it challenges our current understanding of how the Universe works. It's like finding a compass that points North, but the stars are arranged in a way that suggests the Earth is actually spinning on a different axis entirely.

1. Problem Statement

The Cosmological Principle, a foundational assumption of the standard $\Lambda$ CDM model, posits that the Universe is statistically isotropic and homogeneous on large scales. A significant challenge to this principle is the cosmic dipole anomaly: the observed dipole anisotropy in the distribution of cosmologically distant sources (quasars) is significantly larger (amplitude $\sim 2\times$ ) and slightly misaligned compared to the dipole expected from the Solar System's motion relative to the Cosmic Microwave Background (CMB).

While previous studies using the CatWISE2020 catalogue (Secrest et al. 2021, 2022) confirmed this anomaly with high statistical significance ( $>5\sigma$ ), a lingering concern remained: could unaccounted systematics or higher-order multipoles (specifically an octupole, $\ell=3$ ) be biasing the dipole measurement?

The Hypothesis: Critics (e.g., Abghari et al. 2024) argued that the masking of the Galactic plane and the ecliptic latitude trend could couple the dipole with an octupole, artificially inflating the measured dipole amplitude.
The Goal: This paper aims to rigorously test the clustering properties of the CatWISE2020 quasar sample to determine if higher multipoles or local clustering effects can explain the anomalous dipole, or if the anomaly remains a robust feature of the data.

2. Methodology

The authors employed a comprehensive Bayesian inference framework combined with angular power spectrum analysis to re-examine the CatWISE2020 quasar catalogue (1.6 million mid-infrared quasars).

A. Real-Space Multipole Inference

Template Fitting: The authors decomposed the sky distribution into low-order multipoles (monopole, dipole, quadrupole, octupole) using a generalized parameterization based on multipole vectors. This allowed for flexible fitting of arbitrary orientations, not just aligned with coordinate axes.
Likelihood Modeling: Recognizing that the source counts exhibit super-Poissonian overdispersion (variance exceeding the mean), the authors rejected the standard Poisson likelihood used in previous works. Instead, they utilized:
- Generalised Poisson Distribution: To model the variance scaling.
- Gamma-Poisson (Negative Binomial) Distribution: An alternative super-Poissonian model.
- These were compared against the standard Poisson likelihood using Bayesian evidence.
Systematic Corrections: The analysis explicitly modeled the linear trend of source density with ecliptic latitude (an artifact of the WISE satellite scanning pattern) as a modulation term, preventing it from contaminating the dipole signal.
Model Comparison: Various models were tested (e.g., Dipole only, Dipole + Ecliptic trend, Dipole + Quadrupole + Octupole) to compute Bayesian evidences ( $\Delta \log_{10} Z$ ) and determine the most probable physical description of the data.

B. Harmonic Space (Power Spectrum) Analysis

Angular Power Spectrum ( $C_\ell$ ): The authors computed the angular power spectrum using the namaster pseudo- $C_\ell$ method on high-resolution HEALPix maps ( $N_{side}=1024$ ).
Small-Scale Validation: They fitted the power spectrum for multipoles $\ell > 10$ to the theoretical $\Lambda$ CDM prediction (including galaxy bias and shot noise) to validate the clustering properties of the sample.
Large-Scale Extrapolation: By fitting the small-scale clustering, they extrapolated the expected "clustering dipole" (the contribution of large-scale structure to the dipole) to $\ell=1$ to see if it could account for the observed anomaly.
Noise Characterization: They identified an effective noise term ( $\Delta N_\ell$ ) arising from non-Poissonian effects (e.g., source confusion, Eddington bias) that explains the excess power at high $\ell$ .

3. Key Contributions

Robust Likelihood Framework: The paper establishes that the CatWISE2020 data is significantly better described by super-Poissonian likelihoods (Generalised Poisson or Gamma-Poisson) than by a standard Poisson process, providing a more accurate statistical foundation for dipole inference.
Octupole Constraint: The authors provide the first rigorous Bayesian constraints on the octupole ( $\ell=3$ ) amplitude in this specific dataset, directly addressing the "coupling" hypothesis.
Decoupling Systematics: They demonstrate that the ecliptic latitude trend is effectively modeled as a quadrupole-like modulation and does not bias the dipole measurement when properly accounted for.
Clustering Dipole Quantification: They calculate the expected contribution of local large-scale structure (clustering) to the dipole, showing it is negligible compared to the observed anomaly.

4. Key Results

No Evidence for an Octupole: The Bayesian evidence strongly disfavors models including an octupole. The inferred octupole amplitude is consistent with noise ( $\sim 2.3\sigma$ , below the $3\sigma$ detection threshold) and does not significantly alter the dipole measurement.
Dipole Robustness: The measured dipole amplitude remains anomalously high ( $\hat{D} \approx 0.015$ $\hat{D} \approx 0.015$ ) across all model variations (with/without quadrupole, octupole, or different likelihoods).
- Including an octupole actually increases the dipole amplitude slightly (by $\sim 10\%$ ), rather than decreasing it as critics hypothesized.
- The dipole direction remains stable.
Consistency with $\Lambda$ CDM on Small Scales: The angular power spectrum for $\ell \gtrsim 10$ agrees well with $\Lambda$ CDM expectations for a galaxy bias of $b_g \approx 2.27$ .
Negligible Clustering Dipole: The extrapolated "clustering dipole" from the $\Lambda$ CDM fit is $\hat{C}^{clus}_1 \approx 2.21 \times 10^{-6}$ , which is 140 times smaller than the observed dipole power ( $\hat{C}^{obs}_1 \approx 3.10 \times 10^{-4}$ ). The random clustering contribution accounts for less than 5% of the observed anomaly.
Flux Cut Stability: The dipole amplitude remains stable across various flux density cuts, and the ecliptic latitude trend vanishes for brighter (higher signal-to-noise) sources, confirming the trend is likely due to Eddington bias rather than a fundamental cosmological signal.

5. Significance and Conclusion

The study definitively rules out the hypothesis that the cosmic dipole anomaly in the CatWISE2020 catalogue is an artifact of:

Higher-order multipole coupling (specifically an octupole).
Incorrect noise modeling (Poisson vs. super-Poissonian).
Local clustering (the "clustering dipole").

Conclusion: The anomalously large dipole in the distribution of quasars is a robust feature of the data. It persists even after accounting for all known systematics and statistical biases. Since the observed dipole is roughly twice the amplitude expected from the kinematic motion of the Solar System (as derived from the CMB), this result poses a serious challenge to the Cosmological Principle and the standard $\Lambda$ CDM model.

Implications: If future surveys (e.g., LSST, Euclid, SKA) confirm this anomaly, it would imply a breakdown of large-scale isotropy, necessitating new physics beyond the standard cosmological model. The authors suggest that future analyses should employ Bayesian Hierarchical Models (BHM) to simultaneously model cosmological fluctuations and large-scale deviations.