Locating the missing baryons in the warm-hot intergalactic medium with fast radio bursts and the Sunyaev-Zel'dovich effect

This paper reports the first detection of spatial cross-correlations between the dispersion measures (DMs) of fast radio bursts (FRBs) from the second CHIME/FRB catalog and the thermal Sunyaev-Zel'dovich (tSZ) Compton-y map from the Planck satellite, providing direct observational evidence for the location of missing baryons in the warm-hot intergalactic medium (WHIM).

Background and Motivation: Traditional astronomical censuses in the late-time Universe can only account for a fraction of the baryonic matter budget. Hydrodynamical simulations predict that the missing baryons reside in the vast filamentary structures of the cosmic web as a highly diffuse, warm-hot intergalactic medium, shock-heated to temperatures between 10 5 K and 10 7 K. The WHIM is extremely difficult to observe directly—while the low-temperature portion (T ≤ 3 × 10 5 K) has been detected in ultraviolet absorption, the hotter portion is too faint for X-ray detection.

Methodology: The authors cross-correlate the DMs of 2656 extragalactic FRBs from CHIME/FRB Catalog 2 with the all-sky Compton-y parameter map derived from Planck PR4 frequency maps via the Needlet Internal Linear Combination (NILC) method. The key innovation is that FRB DMs trace the total column density of free electrons regardless of thermodynamic state, while the tSZ effect is sensitive to the thermal energy (electron pressure) of the gas. Their cross-correlation naturally excises the dominant noise sources of each observable: the FRB host DM scatter and the tSZ Cosmic Infrared Background emission are physically uncorrelated.

To isolate the diffuse WHIM signal, the authors apply strict masking strategies: they mask virialized galaxy clusters using the PSZ2 and MCXC-II catalogs, excluding regions within multiples of θ500 (baseline 1θ500, with 3θ500 for robustness tests). They also apply Galactic and point-source masks, yielding a final sky fraction of fsky ≈ 56%. The angular cross-power spectrum is measured using the pseudo-Cl estimator in NaMaster, with a catalog-based field formalism for FRBs to avoid pixelization artifacts. Uncertainties are estimated via spatial jackknife resampling with 53 valid patches.

Key Results:

1. The measured cross-power spectrum shows a broadly positive correlation across the multipole range 109 ≤ l ≤ 6144.

2. The detection significance is 3.05σ (p-value 0.0023, >99.77% confidence level) against the null hypothesis of no correlation.

3. Joint Bayesian parameter inference constrains the WHIM baryon fraction to fWHIM = 0.48 with a 68% confidence interval of 0.27 < fWHIM < 0.61, anchored at a mean WHIM temperature of 2.4 × 10 6 K.

4. The effective FRB localization scale is constrained to lloc = 477 (68% CI: 338 < lloc < 1321), consistent with theoretical expectations (lloc ≈ 315–1396) based on CHIME's instrumental properties.

Robustness Tests:

• Expanding the cluster mask from 1θ500 to 3θ500 reduces detection significance to 2.06σ (expected due to reduced sky fraction) but yields nearly identical parameters (fWHIM ≈ 0.494, lloc ≈ 418), confirming the signal originates from the diffuse WHIM rather than residual intracluster medium.

• A null test with 512 RA-randomized catalogs (preserving declination and DM distributions) produces mean spectra consistent with zero, ruling out false correlations from non-uniform CHIME sky coverage.

• Using a CIB-deprojected y-map yields fWHIM ≈ 0.423, confirming physical robustness, though with reduced significance (2.4σ) due to variance penalties from the deprojection technique.

Cosmic Baryon Budget: Combining their result with existing measurements—stars and ISM (7%), cold neutral gas (1.7%), CGM (5%), ICM (4%), and diffuse photoionized Lyα forest (28% ± 11%)—the authors construct a comprehensive census showing that the WHIM constitutes approximately 48% of all ordinary matter. Cumulatively, these components account for roughly 94% of the total cosmological baryonic mass, with the nominal 6.4% residual fully covered by 1σ statistical uncertainties. The paper concludes that the missing baryons are mainly hiding in the diffuse, warm-hot plasma permeating the vast filaments of the cosmic web, closing the cosmic baryon budget in the local Universe.

Improvements to AI Systems:

1. Uncertainty-Aware Multi-Tracer Cross-Correlation Pipeline

• Implement a generalized framework that combines two observables with complementary noise properties (e.g., DM from FRBs and tSZ from CMB) to automatically suppress uncorrelated systematics.

• The improved AI can jointly estimate signal significance and physical parameters (e.g., baryon fraction, localization scale) with full posterior distributions, using jackknife resampling and null-test validation as built-in safeguards.

2. Adaptive Masking and Sky-Fraction Optimization

• Develop an AI that dynamically selects optimal masking radii (e.g., 1θ500 vs. 3θ500) based on trade-offs between signal purity and statistical power, using a learned reward function that maximizes detection significance while preserving physical parameter accuracy.

• The system can automatically generate robust masks for any survey footprint, including Galactic, point-source, and cluster masks, and quantify the impact of each mask on the final inference.

3. Catalog-Based Field Construction Without Pixelization Artifacts

• Build an AI that directly operates on sparse, irregularly sampled catalogs (e.g., FRB positions) rather than pixelized maps, using continuous field representations (e.g., spherical harmonic coefficients from point sources).

• This reduces systematic biases from pixelization and allows seamless integration with map-based observables (e.g., Planck y-maps) at arbitrary resolutions.

4. Bayesian Hierarchical Modeling for Multi-Component Baryon Census

• Create an AI that assimilates disparate measurements (FRB DM, tSZ, Lyα forest, CGM, ICM, stars) into a single hierarchical model of the cosmic baryon budget, with explicit priors on temperature, density, and spatial distribution of each phase.

• The improved system can output a full posterior over baryon fractions in each component, automatically propagating uncertainties and identifying which measurements drive the closure of the budget.

5. Robust Null-Test and Randomization Engine

• Implement an AI that generates and evaluates thousands of randomized catalogs (e.g., RA-shuffled FRB positions) to rigorously test for spurious correlations due to survey selection effects.

• The system can flag any non-zero mean null spectrum and automatically adjust the analysis pipeline (e.g., by adding weighting schemes or covariance corrections) to eliminate such biases.

6. Cross-Observable De-Projection and Component Separation

• Develop an AI that can de-project known contaminants (e.g., Cosmic Infrared Background from the tSZ map) using multi-frequency data, while preserving the diffuse WHIM signal.

• The improved system can quantify the variance penalty of deprojection and recommend whether to use deprojected or raw maps based on the scientific goal (e.g., maximizing significance vs. minimizing bias).

7. Predictive Scaling Relations for Future Surveys

• Train an AI to predict the expected detection significance and parameter constraints for upcoming FRB surveys (e.g., CHIME/FRB Catalog 3, DSA-2000, SKA) given their sky coverage, FRB rate, and instrumental localization precision.

• This enables mission design optimization and early identification of whether a survey can close the baryon budget at a desired confidence level.

8. Real-Time Anomaly Detection in Cross-Spectra

• Implement an AI that monitors cross-power spectra for unexpected features (e.g., excess power at specific multipoles) that could indicate new physics (e.g., dark matter decay heating the WHIM) or unmodeled systematics.

• The system can trigger follow-up analysis or alert users to potential contamination, improving the reliability of cosmological inferences.

What the Improved AI System Can Do:

• Automatically produce a complete, validated measurement of the WHIM baryon fraction from any pair of tracers (FRB+CMB, FRB+X-ray, etc.) with minimal human intervention.

• Provide real-time diagnostics on the robustness of the detection, including mask sensitivity, null-test results, and contamination levels.

• Generate a full cosmic baryon budget with correlated uncertainties, enabling direct comparison with hydrodynamical simulations and constraining feedback models.

• Optimize survey strategies for future instruments to maximize the chance of detecting the missing baryons with high significance.

Traditional astronomical censuses in the late-time Universe can only account for a fraction of the baryonic matter budget. Hydrodynamical simulations predict that the missing baryons reside in the vast filamentary structures of the cosmic web as a highly diffuse, warm-hot intergalactic medium (WHIM). Observing the WHIM directly has remained a long-standing challenge due to its typical temperature. In this study, we report the first detection of spatial cross-correlations between the dispersion measures (DMs) of fast radio bursts (FRBs) from the second CHIME/FRB catalog and the thermal Sunyaev-Zel'dovich (tSZ) Compton- y map from the Planck satellite. By masking virialized galaxy clusters to isolate the diffuse signal, we find a positive correlation with a probability >99.77% between FRBs and tSZ maps. Our joint parameter inference constrains the fraction of cosmic baryons in the WHIM to be f WHIM=0.48 with a 68% confidence interval of 0.27<f WHIM<0.61, anchored at a mean WHIM temperature of 2.4 times 10 6 K. More rigorous masking strategies confirm the signal originates from the WHIM instead of galaxy clusters. Our result demonstrates that the missing baryons are residing in the diffuse gas within the cosmic web, closing the cosmic baryon budget in the local Universe.