🔭 astrophysics

FLAMINGO: The thermal history of the Universe from tSZ effect cross-correlations and its dependencies on cosmology and baryon physics

Using the FLAMINGO suite of cosmological hydrodynamical simulations, this study demonstrates that cross-correlating large-scale structure tracers with the thermal Sunyaev-Zel'dovich effect provides a powerful probe of the Universe's thermal history, revealing a steep dependence on the cosmological parameter $S_8$ and showing that baryonic feedback enhances the bias-weighted mean electron pressure, thereby enabling joint constraints on cosmology and galaxy formation physics.

Original authors: Jaime Salcido, Tianyi Yang, Ian G. McCarthy, Emily E. Costello, Jonah T. Conley, Willem Elbers, Carlos S. Frenk, Matthieu Schaller, Joop Schaye, Amol Upadhye, Marcel P. van Daalen, Bert Vandenbroucke

Published 2026-05-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jaime Salcido, Tianyi Yang, Ian G. McCarthy, Emily E. Costello, Jonah T. Conley, Willem Elbers, Carlos S. Frenk, Matthieu Schaller, Joop Schaye, Amol Upadhye, Marcel P. van Daalen, Bert Vandenbroucke

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

Imagine the Universe as a giant, invisible ocean of hot gas. This isn't water, but a superheated plasma that fills the space between galaxies. For decades, astronomers have tried to measure the "temperature" and "pressure" of this cosmic ocean to understand how the Universe grew from a smooth soup into the clumpy web of galaxies we see today.

This paper, written by a team of cosmologists using a massive set of computer simulations called FLAMINGO, acts like a high-tech weather report for this cosmic ocean. Here is what they found, explained in simple terms.

1. The Cosmic "Thermal Fingerprint"

The researchers focused on a specific signal called the thermal Sunyaev-Zel'dovich (tSZ) effect.

The Analogy: Imagine shining a flashlight through a foggy window. The light hits the water droplets (electrons) in the fog and gets slightly scrambled, changing its color. In the Universe, ancient light from the Big Bang (the Cosmic Microwave Background) travels through the hot gas of the Universe. As it passes, the hot electrons "kick" the light, leaving a specific fingerprint.
The Goal: By measuring this fingerprint, astronomers can calculate the average pressure of the gas in the Universe at different times in history.

2. The Two Main Ingredients: Cosmology and Feedback

The team wanted to know: What shapes this cosmic ocean? They identified two main forces:

Cosmology (The Recipe): The fundamental rules of the Universe, specifically how much matter there is and how "clumpy" it is. They focused on a number called $S_8$ , which measures how much the Universe likes to clump together.
Baryonic Feedback (The Stirring): This refers to the violent actions of galaxies, like supermassive black holes shooting out jets or stars exploding as supernovae.
- The Analogy: Think of the Universe as a pot of soup. Cosmology is the recipe (how much water and how many vegetables). Feedback is the chef stirring the pot. Usually, we think stirring makes things settle down. But in this cosmic soup, the "stirring" (feedback) actually pushes the hot gas out of the dense centers of galaxy clusters and spreads it into the wider, empty space between them.

3. The Big Surprise: Stronger Stirring Makes the Signal Louder

In many other areas of astronomy, strong "stirring" (feedback) makes things harder to see because it smears out the signal.

The Paper's Finding: The authors discovered that for this specific measurement of cosmic pressure, stronger feedback actually makes the signal stronger.
Why? Because the feedback pushes the hot gas out of the dense centers and spreads it over huge distances. Since the measurement they are using looks at the "big picture" (large scales), this spreading gas actually makes the signal brighter and easier to detect. It's like if a chef took a concentrated spice paste and spread it evenly across the whole table; the whole table would smell stronger, even though the center of the bowl is less spicy.

4. Solving the Mystery: The "Low-Clump" Universe

The team compared their computer simulations against real data collected from telescopes (like Planck, SDSS, and DES).

The Problem: When they used the standard "recipe" for the Universe (based on the Planck satellite data), their simulations predicted a signal that was too strong compared to what telescopes actually saw.
The Solution: The simulations that matched the real data best were the ones using a "Low-Clump" recipe (a lower value for $S_8$ ) combined with very strong stirring (strong feedback).
The Result: They found that the Universe is likely less "clumpy" than previously thought, and the black holes and stars have been very effective at pushing gas around.

5. A New Way to Measure the Universe

The paper introduces a new method to untangle these two effects (the recipe vs. the stirring).

The Analogy: Imagine trying to figure out how much sugar is in a cake (cosmology) while also figuring out how much the baker mixed it (feedback). Usually, these are hard to separate.
The Trick: The team found that at low redshift (recent times), the "stirring" doesn't change the taste much, so you can measure the "sugar" (cosmology) very accurately. At high redshift (ancient times), the "stirring" becomes very important. By looking at the data in two different time periods, they can separate the two effects and get a clearer picture of both the Universe's rules and how galaxies form.

Summary of Conclusions

The Signal: The pressure of the hot gas in the Universe is a powerful tool to measure how the Universe grows.
The Physics: Stronger feedback from black holes and stars pushes gas out, increasing the large-scale pressure signal (the opposite of what happens in other measurements).
The Numbers: The data suggests the Universe has a lower "clumpiness" parameter ( $S_8 \approx 0.72$ ) than the standard model predicts, and that galaxy groups retain very little of their gas (only about 10% of the expected amount).
The Future: This method allows scientists to test the rules of the Universe and the physics of galaxy formation simultaneously, using the thermal history of the cosmos as a guide.

In short, the paper shows that by listening to the "heat signature" of the Universe, we can learn that the cosmic soup is less clumpy than we thought, and the "chefs" (black holes and stars) have been stirring it much more vigorously than we expected.

Problem Statement
The thermal energy content of the Universe encodes critical information regarding the formation and evolution of cosmic structure, reflecting the interplay between cosmological structure growth and baryonic feedback mechanisms (e.g., AGN and supernovae). While the thermal Sunyaev-Zel'dovich (tSZ) effect provides a probe of this thermal reservoir, extracting the thermal history ( $d y/d z$ ) from observations requires a model for the bias-weighted mean electron pressure ( $\langle b_h P_e \rangle$ ). Previous studies have relied on the halo model formalism to correct for bias, but uncertainties regarding how bias depends on cosmology and baryonic physics have not been fully elucidated. Furthermore, there is a need to understand the degeneracies between cosmological parameters (such as $S_8$ ) and baryonic feedback when interpreting tSZ cross-correlation measurements with large-scale structure tracers.

Methodology
The authors utilize the FLAMINGO suite of cosmological hydrodynamical simulations, which spans volumes up to $(2.8 \text{ Gpc})^3$ and includes 18 variants covering different cosmological parameters (specifically $S_8$ , neutrino mass, and $\Omega_m$ ) and baryonic feedback implementations. The simulations employ the SPH method (SPHENIX) and are calibrated against observed galaxy stellar mass functions and cluster gas fractions using machine-learning emulators.

The study employs two complementary approaches to analyze thermal pressure signatures:

3D Power Spectra: The bias-weighted mean electron pressure $\langle b_h P_e \rangle$ is measured from the ratio of the matter–electron pressure cross-spectrum to the matter auto-power spectrum in the large-scale limit ( $k < 0.03 \, h/\text{Mpc}$ ).
Lightcone Maps: Full-sky Compton- $y$ maps are constructed from particle lightcones to directly quantify the integrated tSZ signal and derive the thermal history $d y/d z$ without relying on bias models.

The authors compare these simulation results with existing observational cross-correlation measurements from SDSS, BOSS, eBOSS, DES, and DESI against Planck tSZ maps. They also evaluate the accuracy of the standard self-similar halo model in predicting the $y$ -weighted halo bias ( $b_y$ ).

Key Contributions

Parameterisation of $\langle b_h P_e \rangle$ : The authors derive a compact phenomenological parameterisation for $\langle b_h P_e \rangle$ as a function of redshift, cosmology (specifically $S_8$ ), and the baryon fraction of group-mass haloes ( $f_b$ ).
Bias Characterisation: They compute the $y$ -weighted halo bias directly from simulations and compare it to halo model predictions, identifying where the self-similar assumption breaks down.
Thermal History Reconstruction: The study reconstructs the thermal history $d y/d z$ and the sky-averaged Compton- $y$ monopole using both bias-corrected pressure measurements and direct map integration.
Feedback vs. Cosmology: The work disentangles the effects of cosmology and baryonic feedback, demonstrating that their impacts on $\langle b_h P_e \rangle$ are separable at low redshift but degenerate at higher redshifts.

Results

Cosmological Dependence: $\langle b_h P_e \rangle$ scales steeply with $S_8$ , following an effective relation $\langle b_h P_e \rangle \propto S_8^{\epsilon(z)}$ where $\epsilon(z) \approx 3$ over $0.1 \le z \le 1$ . Models with higher $S_8$ (e.g., Planck cosmology) systematically overpredict observational data, while lower $S_8$ models (e.g., LS8 cosmology, $S_8=0.766$ ) provide a better fit.
Baryonic Feedback Dependence: Contrary to weak lensing analyses where strong feedback suppresses small-scale power, stronger AGN feedback boosts the large-scale $\langle b_h P_e \rangle$ signal. This occurs because feedback redistributes thermal energy from halo cores to larger scales (the two-halo regime), enhancing the pressure signal on the scales probed by cross-correlations.
Joint Inference: A joint fit to observational data using the derived parameterisation yields $S_8 = 0.72^{+0.03}_{-0.03}$ and a normalised group-mass halo baryon fraction at $z=0.1$ of $f_b(10^{13} M_\odot, z=0.1)/(\Omega_b/\Omega_m) = 0.10^{+0.09}_{-0.05}$ . The model with the lowest $S_8$ and strongest feedback ( $LS8-f_{gas}-8\sigma$ ) provides the best match to observations.
Bias and Thermal History: The $y$ -weighted halo bias increases with redshift but deviates from self-similar halo model predictions at $z \gtrsim 2.5$ , attributed to deviations in the $Y-M$ scaling relation from self-similarity. The thermal history peaks at $z \approx 0.5-1$ . Approximately 45% of the $d y/d z$ signal originates from within $r_{200c}$ of haloes, with the remainder arising from the diffuse intergalactic medium and halo outskirts; this fraction is controlled primarily by feedback strength rather than cosmology.
Monopole Constraints: The inferred sky-averaged $y$ -monopole from the LS8 models agrees well with recent observational estimates (Chiang et al. 2020), whereas Planck cosmology models predict higher values.

Significance
The paper demonstrates that the thermal history of the Universe, probed via tSZ cross-correlations, offers a powerful route for simultaneously constraining cosmological parameters (specifically $S_8$ ) and testing models of galaxy formation. The study highlights that the thermal pressure signal is sensitive to feedback in a manner distinct from cosmic shear, providing a novel test for baryonic feedback models. The developed parameterisation allows for the efficient inclusion of tSZ cross-correlation data in cosmological inference pipelines, potentially breaking degeneracies between cosmology and baryonic physics when combined with low-redshift data that is less sensitive to feedback. The results suggest a preference for low- $S_8$ cosmologies and strong feedback models, consistent with recent tSZ power spectrum and cross-spectrum analyses, though they remain in tension with primary CMB constraints.