Exploring the $S_8$ Tension: Insights from the CatNorth 1.5-Million Quasar Candidates

Using a machine-learning-enhanced CatNorth quasar catalog and Planck CMB lensing data, this study derives low-redshift $S_8$ measurements that are generally consistent with the standard $\Lambda$CDM model, thereby showing reduced evidence for the persistent $S_8$ tension compared to previous weak lensing results.

The Gist

The Great Cosmic Tug-of-War: A Quasar Detective Story

Imagine the universe as a giant, invisible fabric stretching out in all directions. For decades, scientists have been trying to figure out exactly how "thick" or "clumpy" this fabric is. They use a special number called $S_8$ to measure this. Think of $S_8$ as a "clumpiness score" for the universe. A higher score means matter is packed tightly into big clusters (like galaxies); a lower score means it's spread out more evenly.

Here's the problem: The universe seems to be telling two different stories.

1. The Baby Picture (CMB): When we look at the Cosmic Microwave Background (the "baby photo" of the universe from 13 billion years ago), the math predicts a clumpiness score of about 0.83.
2. The Teenage Photo (Weak Lensing): When we look at the universe today by watching how gravity bends light from distant galaxies, the score often comes out lower, around 0.76.

This gap is the "$S_8$ Tension." It's like if you measured your height as a baby and predicted you'd be 6 feet tall, but when you grew up, you were only 5'6". Either our measuring tape is broken, or we are missing a piece of the puzzle about how the universe grows.

The New Detectives: 1.5 Million Quasars

In this new paper, a team of astronomers (led by Jin Qin and colleagues) decided to bring in a new set of detectives to solve the mystery: Quasars.

Quasars are the brightest lighthouses in the universe. They are super-massive black holes eating gas, shining so brightly they can be seen from billions of light-years away. Because they are so bright and exist at so many different distances (redshifts), they are perfect for mapping the universe's structure.

The team used a massive new catalog called CatNorth, which contains 1.5 million of these quasar candidates. It's like having a map with 1.5 million stars, whereas previous maps only had about 1 million.

The Challenge: The "Fog" of Observation

There's a catch. When we look at the sky, it's not a perfect window.

• Dust clouds in our own galaxy block the view.
• Bright stars confuse the cameras.
• Telescope scanning patterns mean some parts of the sky are looked at more carefully than others.

If you just count the quasars, you might think there are fewer of them in dusty areas, not because they aren't there, but because your telescope couldn't see them. This creates a "fog" that distorts the clumpiness score.

The Solution: The AI Filter
To clear the fog, the team built a Machine Learning "Selection Function."

• Analogy: Imagine you are trying to count apples in a basket, but some are hidden under leaves, and some are in the dark corners. Instead of just counting what you see, you train a smart robot to learn exactly how the leaves and shadows hide the apples. The robot then calculates, "Okay, in this dark corner, I probably missed 3 apples."
• The team trained a neural network on 10 different "systematic templates" (maps of dust, star density, and telescope depth) to figure out exactly where the data is incomplete. They then used this AI to "fill in the blanks" and correct the map.

The Results: A Tale of Two Ages

After cleaning up the data, they split the quasars into two groups: Young Quasars (closer to us, lower redshift) and Old Quasars (very far away, higher redshift).

1. The Young Group (Closer to us):

   • Result: They measured a clumpiness score of 0.844.
   • Meaning: This matches the "Baby Picture" (Planck CMB) almost perfectly! It suggests that for the nearby universe, the standard model of cosmology is working great. The tension might not be real for this part of the universe.

2. The Old Group (Very far away):

   • Result: They measured a lower score of 0.724.
   • Meaning: This is puzzling. The authors suspect this isn't because the universe is actually less clumpy, but because the data is "fuzzy."
   • Analogy: It's like trying to read a book from 100 miles away. The letters look blurry. The team thinks the "blur" comes from two things:
     • Missing Pages: The faintest, oldest quasars are hard to find, so the map is incomplete.
     • Background Noise: There might be a faint glow (Cosmic Infrared Background) from other galaxies that confuses the gravity measurements at these extreme distances.

Why This Matters

This paper is a crucial step in solving the $S_8$ mystery.

• It clears the air: By using a better catalog (CatNorth) and a smarter AI filter, the team showed that the tension might be less severe than we thought, at least for the nearby universe.
• It points the way: The fact that the "far away" data still looks weird tells us where to look next. We need better telescopes to see the faintest, oldest quasars clearly.
• The Future: The authors mention that upcoming telescopes like the Vera C. Rubin Observatory and the Chinese Space Station Telescope (CSST) will act like super-hi-res cameras. They will find millions more quasars, allowing us to see the "old" universe clearly and finally decide if the universe is truly clumpy or if our math needs a rewrite.

In short: The universe's "clumpiness" seems to match our predictions for the nearby world, but the far-away world is still a bit of a mystery. With better tools and AI, we are getting closer to the truth.

Technical Summary

Here is a detailed technical summary of the paper "Exploring the S8 Tension: Insights from the CatNorth 1.5-Million Quasar Candidates."

1. Problem Statement

The paper addresses the $S_8$ tension, a persistent $\sim3\sigma$ discrepancy between measurements of cosmic structure growth derived from high-redshift Cosmic Microwave Background (CMB) anisotropies (Planck 2018: $S_8 = 0.834 \pm 0.016$) and low-redshift weak gravitational lensing (WGL) surveys (e.g., KiDS-1000, DES-Y3, HSC-Y3), which typically yield lower values ($S_8 \approx 0.76-0.78$).

While previous studies using quasar catalogs (specifically the Quaia catalog) attempted to resolve this via cross-correlation with CMB lensing, they faced challenges:

• Systematic Biases: Quasar selection is prone to stellar contamination and spatial depth variations.
• Redshift Errors: Photometric redshift ($z_{ph}$) uncertainties and emission line misidentifications (e.g., C IV vs. Ly$\alpha$) degrade cosmological constraints.
• Incompleteness: Spatial incompleteness in quasar catalogs induces artificial power spectrum excesses on large scales, biasing $S_8$ estimates.

2. Methodology

Data Sources

• Quasar Catalog: The authors utilize the CatNorth catalog, containing 1.5 million quasar candidates over $3\pi$ steradians.
  • Improvements over Quaia: Built using Gaia DR3, Pan-STARRS1 (5 bands), and CatWISE2020 (2 bands). It employs an XGBoost classifier to achieve $\sim90\%$ purity (up from 52% in Gaia DR3) and uses ensemble regression/convolutional neural networks for improved photometric redshifts.
• CMB Lensing: Planck DR4 CMB lensing convergence maps ($\kappa$), processed via the NIPIPE pipeline for optimized signal-to-noise.

Systematics Mitigation: Machine Learning Selection Function

To address spatial incompleteness and selection biases (dust extinction, stellar density, scanning patterns), the authors developed a Machine Learning (ML) based selection function, $S(\hat{n})$.

• Approach: Instead of Gaussian Processes (used in Quaia), they employ a Multilayer Perceptron (MLP) neural network.
• Inputs: 10 systematics templates including dust extinction ($A_V$), stellar density, Gaia scanning patterns ($M_{10}$), and median magnitudes from Pan-STARRS1 (g, r, i, z, y) and CatWISE2020 (W1, W2).
• Efficiency: The MLP approach is significantly more memory-efficient ($\sim2$ GB vs. $>35$ GB for Gaussian Processes) and scalable to higher resolutions ($N_{side}=64$).
• Correction: The observed quasar overdensity $\delta(\hat{n})$ is derived by dividing the observed number density by the selection function: $\delta(\hat{n}) = \frac{n_{obs}(\hat{n})}{S(\hat{n})\bar{n}_u(\hat{n})} - 1$. Pixels with $S(\hat{n}) < 0.5$ are masked to ensure numerical stability.

Cosmological Analysis

• Power Spectra: The authors compute auto-correlation ($C^{gg}_\ell$) and cross-correlation ($C^{g\kappa}_\ell$) angular power spectra using the NaMaster library (pymaster).
• Theoretical Framework: Calculations use the Core Cosmology Library (CCL) under the Limber approximation ($\ell \gtrsim 30$).
• Parameters: A flat $\Lambda$CDM model with free parameters $\theta = \{\Omega_m, \sigma_8, h, b_g\}$ (quasar bias).
  • Priors: Uniform priors on $\Omega_m, \sigma_8, h, b_g$, with a BAO prior on $\Omega_m$ and $h$ to break degeneracies.
• Binning: The sample is split into two redshift bins ($z < 1.5$ and $z > 1.5$) based on photometric redshifts, with equal source counts. Volume-limited subsamples are also tested.

3. Key Contributions

1. Novel Selection Function: Introduction of a fast, memory-efficient neural network-based selection function that effectively suppresses large-scale power spectrum excesses induced by systematics without over-suppressing cosmological signals.
2. High-Purity Quasar Sample: Demonstration that the CatNorth catalog, with its improved classification and redshift estimation, provides a more robust dataset for cosmology than previous Gaia-based catalogs.
3. Comprehensive Systematics Testing: Extensive validation including mock simulations (showing no oversuppression), cross-correlation with systematic templates (confirming bias removal), and tests on volume-limited samples and different bias models.

4. Key Results

$S_8$ Constraints

• Low-Redshift ($z < 1.5$):
  • Result: $S_8 = 0.844^{+0.058}_{-0.056}$.
  • Significance: Consistent with Planck 2018 ($S_8 = 0.834 \pm 0.016$) within $1\sigma$. This contrasts with the Quaia low-z result ($S_8 = 0.879$), suggesting Quaia may have overestimated$S_8$ due to selection function issues.
• High-Redshift ($z > 1.5$):
  • Result: $S_8 = 0.724^{+0.058}_{-0.054}$.
  • Significance: Lower than both Planck and the low-z result. The authors attribute this to sample incompleteness in the faint, high-z regime and potential foreground contamination (e.g., Cosmic Infrared Background) in the CMB lensing map.
• Volume-Limited Samples:
  • $z < 2$: $S_8 = 0.835^{+0.053}_{-0.049}$ (consistent with Planck).
  • $0.4 < z < 1.5$:$S_8 = 0.824^{+0.061}_{-0.062}$.
  • $1.5 < z < 2.5$:$S_8 = 0.789^{+0.062}_{-0.062}$.
  • Trend: Confirms the trend of lower $S_8$ at higher redshifts, likely driven by data limitations rather than new physics.

Robustness Checks

• Bias Models: Results are stable across constant, steep, and free bias models, though high-z bins show higher sensitivity to bias assumptions.
• Masking: Varying the selection function threshold ($S(\hat{n}) > 0.4$ vs $0.6$) yields consistent$S_8$ values.
• Photo-z Uncertainties: Incorporating photometric redshift errors does not significantly shift the central $S_8$ values.

5. Significance and Conclusion

• Alleviation of Tension: The study suggests that the $S_8$ tension may be less severe than previously thought when using high-purity quasar samples with rigorous systematics correction. The low-redshift quasar measurements align with CMB constraints, challenging the notion of a universal "low $S_8$" from all low-z probes.
• High-z Challenges: The persistent low $S_8$ in high-redshift bins highlights the difficulty of obtaining unbiased cosmological constraints from faint, distant quasars due to flux limits and foreground contamination.
• Future Outlook: The paper emphasizes that next-generation surveys (Rubin/LSST, Euclid, CSST) with deeper depths and larger volumes will be crucial. These facilities will enable complete quasar samples up to $z \sim 3$, potentially resolving whether the high-z $S_8$ discrepancy is due to residual systematics or new physics.

In summary, this work demonstrates that quasars are a powerful, independent probe for the $S_8$ tension, provided that sophisticated machine learning techniques are used to correct for spatial selection effects. The results currently favor the standard $\Lambda$CDM model, with the tension appearing to be driven by observational limitations in high-redshift samples rather than a fundamental breakdown of the model.