Measurement of angular cross-correlation between the cosmological dispersion measure and the thermal Sunyaev--Zeldovich effect

This paper reports the first detection of a positive angular cross-correlation between fast radio burst dispersion measures and the thermal Sunyaev-Zeldovich effect, a finding that constrains the average electron temperature of the intergalactic medium and offers a new pathway to break degeneracies in cosmological parameters.

The Gist

The Big Picture: Listening to the Universe's "Static"

Imagine the universe is filled with a giant, invisible fog made of hot, ionized gas (mostly electrons). This fog exists everywhere, even in the empty spaces between galaxies. Scientists have been trying to map this fog to understand how the universe is built, but it's very hard to see directly.

This paper reports a new way to "see" this fog by combining two different cosmic tools:

1. Fast Radio Bursts (FRBs): Think of these as cosmic lighthouses. They are incredibly bright, short flashes of radio waves coming from deep space. As these flashes travel through the universe, the invisible fog slows them down slightly. By measuring how much they are slowed, scientists can calculate how much fog they passed through. This measurement is called the Dispersion Measure (DM).
2. The Sunyaev–Zeldovich (tSZ) Effect: Imagine the Cosmic Microwave Background (CMB) as the "afterglow" of the Big Bang, a uniform glow filling the sky. When this glow passes through hot gas, the gas gives the light a tiny energy boost (like a pinball hitting a moving paddle). This creates a specific "shadow" or distortion in the glow. This is measured by the Compton y parameter.

The Goal: The authors wanted to see if these two measurements are connected. If you look at a spot in the sky with a lot of "fog" (high DM), do you also see a strong "energy boost" (high y)? If they match, it proves they are both tracing the same invisible gas, and it helps scientists figure out how hot that gas is.

The Analogy: The Rain and the Puddle

To understand what the scientists did, imagine a rainy day:

• The FRB (DM) is like a runner sprinting through the rain. By measuring how wet the runner gets, you can estimate how much rain fell along their path.
• The tSZ (y) is like looking at the puddles on the ground. The bigger the puddle, the more water is there.

The scientists asked: "If I see a runner who is very wet (high DM), is there a big puddle nearby (high y)?"

In the past, scientists tried to measure the "wetness" of the runners (DM) and see if the runners were clustered together. But that was like trying to find a pattern in a few drops of rain—it was too hard to detect.

Instead, this paper says: "Let's look at the runners (FRBs) and compare their wetness to the puddles (tSZ) in the same area of the sky." Because we have very detailed maps of the puddles (from satellites like Planck and ACT), this method is much easier to detect.

What They Did

1. Gathered the Runners: They collected data on 133 Fast Radio Bursts whose locations and distances are known.
2. Cleaned the Data: They subtracted the "rain" that fell right here in our own Milky Way galaxy to focus only on the "rain" from deep space.
3. The Comparison: They looked at the sky maps of the "puddles" (the tSZ effect from Planck and ACT satellites) and checked if the "wetness" of the runners correlated with the size of the puddles at different angles.

The Results

• They Found a Match: They successfully detected a positive connection. Where there was more gas (higher DM), there was also more thermal pressure (higher y).
• The Strength: The connection was very strong when using data from the Planck satellite (a 4-sigma detection, which is a very confident "yes"). The data from the ACT telescope also showed a match, though with less certainty due to the smaller area it covers.
• Temperature: Based on how strong this connection was, they calculated that the average temperature of this invisible cosmic gas is about 20 million degrees Celsius. That is incredibly hot!

Why This Matters (According to the Paper)

The paper claims this is the first time this specific connection has been measured.

• Breaking the Code: Usually, if you only measure the "wetness" (DM), you can't tell if the gas is dense but cool, or sparse but hot. It's a "degeneracy" (a confusing mix of possibilities).
• The Solution: By combining the "wetness" (DM) with the "puddle size" (tSZ), they can separate the density from the temperature. It's like knowing both the volume of water and the size of the container tells you exactly how deep the water is.
• Cosmology: The strength of this signal is very sensitive to how matter clumps together in the universe (a parameter called $\sigma_8$) and how galaxies push gas around (baryon feedback). This suggests that in the future, using both methods together will help scientists pin down the exact rules of how the universe expands and evolves.

Summary in One Sentence

The authors successfully detected a link between the amount of invisible gas in the universe (measured by radio bursts) and the heat of that gas (measured by cosmic background distortions), proving that these two methods work together to reveal the temperature and distribution of the universe's hidden matter.

Technical Summary

Title: Measurement of angular cross-correlation between the cosmological dispersion measure and the thermal Sunyaev–Zeldovich effect

Problem and Motivation
Fast radio bursts (FRBs) provide a unique probe of the intergalactic medium (IGM) through their dispersion measure (DM), which quantifies the column density of free electrons along the line of sight. However, the DM alone cannot disentangle gas density from temperature. Conversely, the thermal Sunyaev–Zeldovich (tSZ) effect, characterized by the Compton $y$ parameter, probes the integrated electron pressure in the IGM and galaxy clusters. While theoretical studies have suggested that cross-correlating DM with other signals (such as weak lensing or foreground galaxies) could yield stronger detections than auto-correlations, a direct measurement of the angular cross-correlation between the cosmological component of DM ($DM_{cos}$) and the tSZ effect ($y$) had not been achieved. This paper addresses this gap by presenting the first detection of the angular cross-correlation between $DM_{cos}$ and the Compton $y$ parameter.

Methodology
The study employs a combination of observational data and theoretical modeling:

1. Observational Data:

   • FRBs: The analysis utilizes 133 localized FRBs (where host galaxies and redshifts are known). The extragalactic DM ($DM_{ext}$) is derived by subtracting the Milky Way contribution (using NE2001 or YMW16 models) from the observed DM. A residual $\Delta DM_{ext}$ is calculated by subtracting the average $DM_{ext}$ predicted by the DM–redshift relation, isolating fluctuations in free-electron density.
   • tSZ Maps: Compton $y$-maps from the Planck satellite (PR2, MILCA method) and the Atacama Cosmology Telescope (ACT, DR6) are used. The analysis covers angular separations from $1'$ to $1000'$.
   • Host Mitigation: To minimize contamination from the host galaxy of the FRB, the authors exclude FRBs associated with massive galaxy clusters (identified via the Planck SZ catalog) and analyze the impact of host contributions using the halo model.

2. Theoretical Modeling:

   • Halo Model (HMx): The primary theoretical prediction is generated using the HMx code, calibrated with hydrodynamic simulations (BAHAMAS). This model accounts for the density and pressure profiles of gas within halos, baryon feedback (via AGN heating temperature $T_{AGN}$), and the distinction between 1-halo (intra-halo) and 2-halo (inter-halo) terms.
   • Alternative Models: A constant gas temperature model and a fitting function based on the IllustrisTNG300 simulation (TNG-fit) are also considered to test sensitivity to baryon feedback assumptions.
   • Cross-Correlation Estimator: An estimator is constructed to measure the cross-correlation function $\hat{w}_{yDM}(\theta)$ between $\Delta DM_{ext}$ and the smoothed $y$-map. The estimator uses inverse-variance weighting to account for uncertainties in the Milky Way DM and host galaxy contributions. Covariance is estimated using jackknife resampling and bootstrap methods.

Key Results

• Detection: The authors detect a positive angular cross-correlation between $DM_{ext}$ residuals and the Compton $y$ parameter.
  • For Planck, the amplitude is $A = 2.01 \pm 0.50$ ($4.0\sigma$ significance), where $A=1$ corresponds to the Planck 2018 $\Lambda$CDM prediction using HMx.
  • For ACT, the amplitude is $A = 1.23 \pm 0.82$ ($1.5\sigma$ significance).
  • The results are consistent across different models for the Milky Way DM and host galaxy evolution.
• Physical Interpretation: Assuming an isothermal gas, the measured amplitude implies an average electron temperature of $\approx 2 \times 10^7$ K.
• Parameter Sensitivity: The cross-correlation amplitude is found to be highly sensitive to the matter clustering parameter $\sigma_8$ and baryon feedback (specifically the AGN heating temperature $T_{AGN}$). Its dependence on the ionized fraction ($f_e$) and Hubble constant ($h$) differs from that of the DM alone.
• Host Contamination: Theoretical estimates indicate that while host galaxy contributions can dominate at very small angular scales ($\theta < 10'$) and low redshifts, the ensemble-averaged host signal remains sub-dominant to the cosmological signal for the majority of the analyzed range, particularly when massive halos are excluded.

Significance and Claims
The paper claims the first measurement of the $y$-$DM_{cos}$ correlation. The authors assert that this detection demonstrates the feasibility of using FRBs as tracers of the large-scale structure of the IGM when combined with CMB data.

The primary significance lies in the potential to break degeneracies among cosmological and astrophysical parameters. Because the cross-correlation depends on parameters like $\sigma_8$, $f_e$, and $h$ differently than the DM auto-correlation or the tSZ auto-correlation alone, future joint analyses of DM and tSZ data could provide tighter constraints on the ionized fraction of the universe, the Hubble constant, and the nature of baryon feedback. The authors note that while the current sample of localized FRBs is limited, ongoing and future surveys (such as CHIME/FRB outriggers, DSA, and CRAFT) will rapidly increase the sample size, enhancing the signal-to-noise ratio and enabling more precise cosmological constraints.