Joint tomographic measurement of thermal Sunyaev Zeldovich and the cosmic infrared background

This paper introduces a novel tomographic method to simultaneously reconstruct the bias-weighted mean electron pressure and star formation rate density by jointly modeling the thermal Sunyaev-Zeldovich effect and Cosmic Infrared Background in cross-correlations with galaxy samples, yielding redshift-dependent measurements up to $z\sim1$ that are largely consistent with FLAMINGO hydrodynamical simulations.

The Gist

Imagine the universe as a giant, three-dimensional city that has been expanding and evolving for 13.8 billion years. In this city, there are two main types of "traffic" that astronomers try to measure:

1. The Hot Gas Traffic: Invisible clouds of super-heated gas (mostly hydrogen) that float between galaxies. This gas is so hot it glows in a specific way when it bumps into light from the early universe.
2. The Star-Factory Traffic: The actual birth of new stars. When stars are born, they heat up dust, which glows in infrared light (like a warm ember).

For a long time, trying to measure these two things separately has been like trying to listen to a whisper in a room where a loud radio is playing. The "radio" is the Cosmic Infrared Background (CIB)—the glow from all the dust in the universe. It gets mixed up with the "whisper" of the hot gas (the thermal Sunyaev-Zeldovich effect, or tSZ). Usually, when astronomers try to map the hot gas, the dust noise gets in the way, making the picture blurry, especially when looking at distant parts of the city (high redshift).

The New Method: The "Spectral Detective"

This paper introduces a clever new way to solve this noise problem. Instead of trying to clean the radio signal after recording it (which often leaves static), the authors built a "spectral detective" that listens to the signal while it's being recorded.

Here is the analogy:
Imagine you are at a party with two people talking: Person A (the hot gas) and Person B (the dust).

• Person A speaks in a voice that changes pitch depending on the frequency of the microphone you use.
• Person B speaks in a different voice that changes pitch in a different way.

Old methods tried to record the whole party, then use a filter to try to remove Person B. But filters aren't perfect; they often accidentally mute Person A too, or leave some of Person B's voice behind.

The authors' new method is like having a team of detectives with microphones tuned to many different frequencies simultaneously. They know exactly how Person A and Person B sound at every single frequency. By listening to the mix of voices across all these microphones at once, they can mathematically separate the two voices perfectly, even if they are talking over each other.

What They Did

1. The Map: They used a massive map of the universe's temperature (from the Planck satellite) and overlaid it with a map of millions of galaxies (from the DESI and WISE surveys).
2. The Cross-Check: They looked at how the galaxies "clumped" together and how that clumping correlated with the temperature maps.
3. The Separation: Using their "multi-frequency detective" math, they separated the hot gas signal from the dust signal without needing to throw away any data or make messy assumptions.

The Results: A Time Machine

By doing this, they were able to create a "time-lapse movie" of the universe from about 10 billion years ago to now (redshift $z \sim 1$).

• The Hot Gas: They measured how much pressure the hot gas has at different times. They found that the gas is slightly less pressurized in the recent past than some computer simulations predicted. This is a big clue! It suggests that the "feedback" from black holes and supernovae (which blow gas around) might be slightly weaker or different than we thought.
• The Star Formation: They measured how fast stars were being born. Their results matched up very well with the "FLAMINGO" simulation (a super-computer model of the universe), giving us confidence that our models of how galaxies form are on the right track.

Why This Matters

This paper is a breakthrough because it turns a weakness into a strength.

• Old way: "Oh no, the dust is ruining our gas map! We have to guess how much to subtract."
• New way: "Great! The dust is there, and the gas is there. Let's use the dust to measure star formation and use the gas to measure pressure, all at the same time, with high precision."

It's like realizing that the static on the radio isn't just noise; it's actually a second song playing in a different key. If you know how to tune your radio, you can hear both songs clearly.

The Takeaway

The authors have given the scientific community a new, cleaner set of tools to look at the universe's history. They have mapped out the pressure of the invisible gas and the rate of star birth with unprecedented clarity, showing us that the universe is a bit more "relaxed" (lower gas pressure) in recent times than our best computer models predicted. This helps scientists refine their understanding of how galaxies grow and how the universe evolves.

Technical Summary

Here is a detailed technical summary of the paper "Joint tomographic measurement of thermal Sunyaev Zeldovich and the cosmic infrared background" by La Posta et al.

1. Problem Statement

The thermal Sunyaev-Zeldovich (tSZ) effect and the Cosmic Infrared Background (CIB) are two critical probes of the intergalactic medium (IGM) and galaxy formation.

• tSZ: Probes the thermal pressure of electrons in dark matter halos ($\langle b P_e \rangle$).
• CIB: Probes the star formation rate density ($\langle b \rho_{\text{SFR}} \rangle$).

The Core Challenge: In multi-frequency Cosmic Microwave Background (CMB) maps, the tSZ signal is heavily contaminated by the CIB. Traditional methods attempt to separate these components by creating "deprojected" maps (e.g., using Internal Linear Combination or ILC) before cross-correlating with galaxy samples. However, this approach has significant drawbacks:

1. Increased Variance: Deprojection increases the noise in the resulting power spectra.
2. Model Dependence: It relies on assumptions about the spectral energy distributions (SEDs) of the contaminants. If the assumed SEDs are incorrect, residual contamination remains, biasing the results.
3. Loss of Information: Pre-processing maps discards the ability to simultaneously constrain both the tSZ and CIB signals in a unified statistical framework.

2. Methodology

The authors propose a joint tomographic reconstruction method that models the tSZ and CIB contributions simultaneously at the level of the cross-correlation power spectra between galaxy samples and multi-frequency CMB maps, rather than separating them in the map domain first.

Key Technical Components:

• Tomographic Framework: The method adapts the technique from [6] (Maleubre et al.) to angular power spectra. It reconstructs the bias-weighted mean of a tracer $U$ ($\langle bU \rangle$) by combining galaxy-galaxy auto-correlations with galaxy-tracer cross-correlations.
  • The model ensures the recovered $\langle bU \rangle$ is independent of the galaxy clustering properties (bias $b_g$) and robust against scale-dependent bias.
• Multi-Frequency Modeling: Instead of using component-separated maps, the authors model the observed cross-power spectrum $C_{g\nu}^\ell$ at frequency $\nu$ as a linear combination of the tSZ and CIB signals:
  $$C_{g\nu}^\ell = S_{\nu}^{\text{tSZ}} C_{gy}^\ell + S_{\nu}^{\text{CIB}}(z_g) C_{gc}^\ell + \text{Noise}$$
  Where $S_\nu$ represents the known spectral templates, and $C_{gy}^\ell$ and $C_{gc}^\ell$ are the underlying cross-correlations with the Compton-$y$ map and CIB intensity, respectively.
• Parameter Estimation:
  • The model includes nuisance parameters ($A_{XY}, N_{XY}$) to absorb non-linear and stochastic bias effects.
  • These nuisance parameters are marginalized over analytically, leaving only the physical parameters ($b_g, \langle b P_e \rangle, \langle b \rho_{\text{SFR}} \rangle$) to be sampled.
  • Maximum Likelihood Bandpower Reconstruction (MLBR): As an alternative validation, the authors use a least-squares approach to first estimate the component cross-spectra ($C_{gy}^\ell, C_{gc}^\ell$) from the multi-frequency data, which is mathematically equivalent to the Spectral ILC (spILC) method in the cross-correlation context.
• Data Inputs:
  • Galaxy Samples: Photometric Luminous Red Galaxies (LRG) from the DESI Legacy Survey (4 redshift bins, $0.4 \lesssim z \lesssim 1$) and low-redshift galaxies from the WISE$\times$SuperCOSMOS (WI$\times$SC) catalog ($0.1 \lesssim z \lesssim 0.4$).
  • CMB Data: Planck PR4 (NPIPE) temperature maps at 100, 143, 217, 353, 545, and 857 GHz.
  • SED Modeling: Uses an empirical library of infrared SEDs [27–29] rather than a simple modified black-body assumption. They also introduce a spectral tilt parameter $\delta\beta$ to marginalize over uncertainties in the CIB spectrum shape.

3. Key Contributions

1. Novel Joint Reconstruction: First method to simultaneously reconstruct $\langle b P_e \rangle$ and $\langle b \rho_{\text{SFR}} \rangle$ directly from multi-frequency cross-correlations without pre-separating components in the map domain.
2. Bias Independence: The reconstruction is rigorously independent of the specific clustering properties of the galaxy sample used, a major improvement over previous tomographic methods.
3. Turning Contamination into Opportunity: Instead of viewing CIB contamination as a nuisance to be removed, the method treats it as a second signal to be measured, providing complementary constraints on cosmic star formation history.
4. Robustness to Systematics: The method naturally marginalizes over calibration uncertainties and spectral shape variations ($\delta\beta$), demonstrating that the results are not driven by specific frequency channels or assumed SED shapes.

4. Results

The authors applied the method to the DESI LRG and WI$\times$SC samples cross-correlated with Planck data.

• Detection Significance:
  • tSZ-Galaxy: Detected with high significance in all redshift bins (Signal-to-Noise Ratio, SNR, ranging from 30 to 37).
  • CIB-Galaxy: Detected in the DESI LRG bins (SNR up to 36). The WI$\times$SC (low-z) CIB correlation was consistent with zero (SNR $\approx$ 1.9), consistent with theoretical expectations of star formation peaking at higher redshifts.
• Cosmic Evolution:
  • Reconstructed $\langle b P_e \rangle$ and $\langle b \rho_{\text{SFR}} \rangle$ out to $z \sim 1$.
  • Comparison with Simulations: The measurements are broadly compatible with the FLAMINGO hydrodynamical simulation (fiducial feedback model).
  • Low-Redshift Tension: A notable finding is a lower-than-predicted gas pressure ($\langle b P_e \rangle$) at low redshifts ($z \sim 0.25$). This aligns with other recent measurements and suggests potential issues with feedback modeling in simulations or unmodeled systematics, though the authors ruled out major systematic biases (e.g., dust contamination) through robustness tests.
• Robustness Tests:
  • Results remained stable when excluding specific frequency channels (including the critical 217 GHz where tSZ crosses zero).
  • Marginalizing over the CIB spectral tilt ($\delta\beta$) and Planck calibration uncertainties did not significantly shift the best-fit values, only slightly increasing statistical errors.
  • Using a more conservative Galactic mask ($f_{sky}=0.4$) did not alter the conclusions.

5. Significance

• Precision Cosmology: This method provides a new, high-precision dataset for constraining the thermodynamic state of the IGM and the history of star formation, free from the biases of galaxy clustering models.
• Feedback Constraints: The measurement of $\langle b P_e \rangle$ is a powerful probe of baryonic feedback processes (e.g., AGN feedback) which regulate gas cooling and star formation. The observed low pressure at low $z$ offers a critical test for hydrodynamical simulations like FLAMINGO.
• Methodological Advancement: By avoiding the "component separation" step, this approach preserves more information and reduces variance compared to traditional map-based ILC methods. It sets a new standard for analyzing secondary CMB signals in cross-correlation with Large Scale Structure (LSS).
• Data Availability: The authors have made the reconstructed $\langle b P_e \rangle$ and $\langle b \rho_{\text{SFR}} \rangle$ measurements, along with their full covariance matrices, publicly available for use in future cosmological analyses.