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Self-consistent secondary cosmic microwave background anisotropies and extragalactic foregrounds in the FLAMINGO simulations

This paper presents a new set of self-consistent mock CMB maps derived from the FLAMINGO hydrodynamical simulations that accurately reproduce observational constraints and offer improved predictions for secondary anisotropies and their cross-correlations compared to previous dark matter-only models.

Original authors: Tianyi Yang, Ian G. McCarthy, Fiona McCarthy, Boris Bolliet, Jens Chluba, William Coulton, John C. Helly, Matthieu Schaller, Joop Schaye

Published 2026-03-31

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CC BY 4.0

Original authors: Tianyi Yang, Ian G. McCarthy, Fiona McCarthy, Boris Bolliet, Jens Chluba, William Coulton, John C. Helly, Matthieu Schaller, Joop Schaye

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, ancient movie screen. The Cosmic Microwave Background (CMB) is the oldest "static" or "snow" on that screen, a faint glow left over from the Big Bang. For decades, astronomers have studied this static to understand the beginning of time.

But here's the catch: as that ancient light travels across the universe to reach our telescopes, it doesn't travel through empty space. It passes through a crowded, messy neighborhood filled with galaxies, hot gas, black holes, and dust. These cosmic obstacles leave "fingerprints" on the light, distorting it and adding new layers of noise. These are called secondary anisotropies.

This paper is like a cosmic "flight simulator" built by a team of scientists using the FLAMINGO supercomputer simulation. Instead of just looking at the real sky and trying to guess what's causing the noise, they built a perfect, self-consistent virtual universe to see exactly how these fingerprints are made.

Here is a breakdown of their work using simple analogies:

1. The "Self-Consistent" Kitchen

Previous attempts to model this cosmic noise were a bit like a chef trying to make a stew by adding ingredients one by one without a recipe. They might guess how much salt (gas) to add, then guess how much pepper (dust) to add, assuming the two don't really interact.

The FLAMINGO team did something different. They built a self-consistent kitchen. In their simulation, the gas, stars, black holes, and dark matter all interact naturally. If the black holes blow out gas (feedback), the stars stop forming. If the stars form, they heat the gas. Everything is connected. This means when they generate the "noise" on their CMB map, it's not a guess; it's the natural result of the physics playing out in their virtual universe.

2. The Five Types of Cosmic "Graffiti"

The team mapped out five specific ways the universe messes with the CMB signal. Think of these as different types of graffiti on the ancient screen:

CMB Lensing (The Funhouse Mirror): As light passes through massive clumps of dark matter, gravity bends the light, slightly distorting the image of the background static. It's like looking at a poster through a warped glass window.
The Sunyaev-Zel'dovich (SZ) Effects (The Hot Air Balloon):
- Thermal SZ (tSZ): Imagine hot gas in galaxy clusters acting like a giant, hot air balloon. When the cold CMB light hits this hot gas, the gas kicks the light particles, giving them a boost of energy. This changes the "color" of the static in specific spots.
- Kinetic SZ (kSZ): This is like a wind blowing past a microphone. If a cloud of gas is moving toward or away from us, it shifts the pitch of the light (Doppler effect), even if the gas isn't hot.
Patchy Screening (The Dirty Window): Some areas have so many free electrons that they act like a semi-transparent screen, slightly dimming the background static. It's like looking at a light through a dusty, uneven window.
Cosmic Infrared Background (CIB) (The Dusty City Lights): This isn't the ancient static at all; it's the glow from billions of dusty, star-forming galaxies. It's like the collective glow of all the city lights in the universe, which looks like a fuzzy haze on the screen.
Radio Point Sources (The Bright Streetlamps): These are individual, bright radio signals from active black holes. They are like bright streetlamps that can blind your telescope if you aren't careful.

3. Why This Simulation is a Big Deal

The authors compared their "perfect kitchen" simulation to previous models that were more like "paint-by-numbers."

The Old Way: "Let's put a hot spot here and a dusty spot there based on a rule of thumb."
The New Way (FLAMINGO): "Let's simulate the physics of the universe, and let the hot spots and dusty spots appear naturally where the physics says they should."

They found that their simulation matches real-world observations (from telescopes like Planck) just as well as the old models, but with a huge advantage: it keeps the connections intact. Because everything is linked, they can study how the "dusty city lights" (CIB) correlate with the "hot air balloons" (tSZ) in a way that previous models couldn't do accurately.

4. The "Knob-Twisting" Experiment

One of the coolest parts of the paper is that the FLAMINGO team didn't just run one simulation; they ran many with different "knobs" turned.

Cosmology Knobs: They changed the amount of dark matter or the expansion rate of the universe.
Feedback Knobs: They changed how violently black holes blow gas out of galaxies.

The Discovery: They found that these "knobs" change the patterns of the noise in very specific ways.

If you turn up the "black hole wind" (feedback), the hot gas gets pushed out, and the "hot air balloon" signal gets weaker.
If you change the cosmology (the amount of matter), the "funhouse mirror" effect changes.

This is crucial because it means future telescopes (like the Simons Observatory) can look at these specific patterns of noise and figure out exactly how black holes behave and what the universe is made of.

5. The Bottom Line

This paper provides a high-definition, self-consistent map of the cosmic "noise."

Think of it as providing astronomers with a perfectly calibrated reference manual. When they look at the real sky and see a weird pattern, they can now compare it to this simulation to ask: "Is this pattern caused by a specific type of galaxy, a specific black hole behavior, or a specific type of dark matter?"

By creating these realistic "mock" maps, the team is giving the next generation of telescopes the tools they need to decode the universe's secrets, separating the signal from the noise with unprecedented precision.

1. Problem Statement

Secondary anisotropies in the Cosmic Microwave Background (CMB) and extragalactic foregrounds (such as the Cosmic Infrared Background and radio point sources) contain crucial information about cosmology, galaxy formation, and the thermodynamic state of the intergalactic medium. However, extracting these signals from observational data is challenging due to:

Component Degeneracy: Different physical processes (e.g., thermal Sunyaev-Zel'dovich effect vs. CIB) overlap in frequency and spatial distribution.
Modeling Limitations: Previous simulations used to generate "mock" CMB maps often relied on dark matter-only (DMO) simulations. In these models, baryonic components (gas, stars, black holes) are "painted" onto dark matter halos using semi-analytic prescriptions. This approach lacks self-consistency; the correlations between different components (e.g., how star formation in a halo relates to its gas pressure) are not physically coupled, potentially leading to biases in cross-correlation studies.
Lack of Full-Sky Hydrodynamical Mocks: While individual secondary effects have been studied in hydrodynamical simulations, no previous study had produced a self-consistent, full-sky, multi-component CMB map suite derived directly from large-volume cosmological hydrodynamical simulations.

2. Methodology

The authors utilized the FLAMINGO suite of cosmological hydrodynamical simulations to generate a new set of mock CMB maps.

Simulation Suite:
- Fiducial Run: A large-volume $(2.8 \text{ Gpc})^3$ intermediate-resolution run ( $m_{gas} \approx 1.1 \times 10^9 M_\odot$ ) evolved to $z=0$ .
- Variants: Multiple $(1 \text{ Gpc})^3$ runs with systematically varied subgrid feedback models (stellar feedback strength, AGN feedback strength, jet vs. thermal modes) and cosmological parameters (Planck-like vs. LS8 low- $S_8$ cosmology).
- Physics: Includes radiative cooling, star formation, black hole growth, and feedback from supernovae and AGN.
Map Construction:
- Lightcone Generation: The authors constructed HEALPix lightcone maps by stacking spherical shells ( $\Delta z = 0.05$ at low $z$ , $\Delta z = 0.25$ at high $z$ ) from the simulation snapshots up to $z=4.5$ (or $z=3.0$ for smaller boxes).
- Components Modeled:
  1. CMB Lensing ( $\kappa$ ): Projected convergence field derived from the total matter density.
  2. Sunyaev-Zel'dovich (SZ) Effects:
    - Thermal (tSZ): Compton- $y$ parameter maps derived from gas pressure ( $n_e T_e$ ). Relativistic corrections were applied using the SZpack code based on local electron temperatures.
    - Kinetic (kSZ): Doppler parameter maps derived from the line-of-sight bulk velocity of ionized gas.
  3. Anisotropic Screening: Optical depth ( $\tau$ ) maps from Thomson scattering.
  4. Cosmic Infrared Background (CIB): Derived from the Star Formation Rate (SFR) lightcone. The authors employed a three-parameter SED model (dust temperature $T_0$ , spectral index $\beta_d$ , and redshift evolution $\alpha$ ) calibrated against Planck and Lenz et al. (2019) data.
  5. Radio Point Sources: Black holes were identified as radio AGN based on Eddington ratios ( $\lambda_{Edd}$ ). Radio luminosities were assigned via abundance matching to the LOFAR 150 MHz luminosity function and extrapolated to CMB frequencies.
- Lensing: All secondary maps were lensed using the integrated $\kappa$ -map to account for gravitational deflection.

3. Key Contributions

First Self-Consistent Hydro Mocks: This is the first time a comprehensive set of full-sky CMB secondary anisotropies and foregrounds has been generated directly from a large-volume hydrodynamical simulation, ensuring physical consistency between components (e.g., the correlation between hot gas pressure and star formation).
Relativistic Corrections: The inclusion of relativistic corrections for the tSZ effect, which are significant in massive clusters, providing a more accurate template for future high-resolution surveys.
Systematic Parameter Exploration: By leveraging FLAMINGO's model variants, the authors quantified how feedback physics (stellar vs. AGN) and cosmology (specifically $\sigma_8$ ) impact the power spectra and cross-correlations of these signals.
Radio Source Modeling: A novel approach to modeling radio point sources using abundance matching to LOFAR data, allowing for the study of correlations between radio AGN and other CMB components.

4. Key Results

Power Spectra Agreement:
- The tSZ and kSZ auto-power spectra from the fiducial FLAMINGO run agree well with observational constraints and other simulations (WebSky, AGORA), though amplitudes vary based on feedback strength.
- The CIB auto-power spectra (353, 545, 857 GHz) fit observational data (Lenz et al. 2019) well using the derived SED parameters ( $T_0 \approx 35$ K, $\beta_d \approx 1.65$ ).
- Radio Point Sources: The simulated radio source counts and auto-power spectra match observations from SPT, ACT, and Planck, particularly after applying flux cuts to mask bright sources.
Cross-Correlations:
- CIB–tSZ: Shows a weak correlation, as expected due to environmental quenching (star formation suppressed in high-density cluster environments).
- CIB–Lensing ( $\kappa$ ): Shows a strong correlation, consistent with the CIB tracing the underlying matter distribution.
- Radio–CMB: The cross-correlation between radio sources and tSZ/CIB depends on the Eddington ratio cut, revealing how different AGN populations trace different environments.
Feedback and Cosmology Dependence:
- Feedback: Strong stellar feedback significantly suppresses the CIB power spectrum (by ~30-40%) by reducing star formation. Strong AGN feedback suppresses small-scale power in the CIB–tSZ cross-correlation by expelling gas from halos.
- Cosmology: The LS8 model (lower $S_8$ ) consistently yields lower amplitudes across all statistics (CIB, tSZ, kSZ) due to reduced structure formation.
- SED Flexibility: When CIB SED parameters are refitted for each model to match the CIB auto-power spectrum, the sensitivity to feedback/cosmology in the auto-spectrum is largely lost. However, the cross-correlations (e.g., CIB–tSZ, CIB– $\kappa$ ) retain significant sensitivity to the underlying physics, offering a way to break degeneracies.
Monopoles: The predicted tSZ monopole ( $\langle y \rangle$ ) for the fiducial model is $(1.52 \pm 0.01) \times 10^{-6}$ , consistent with COBE-FIRAS limits and Planck tomographic estimates.

5. Significance

Resource for Future Surveys: These mock maps serve as a critical resource for forecasting and analyzing upcoming high-resolution CMB experiments like the Simons Observatory and CMB-HD.
Component Separation: The self-consistent nature of the mocks allows for rigorous testing of component separation algorithms (e.g., NILC, SMICA) to disentangle foregrounds from secondary anisotropies without the biases introduced by uncorrelated "painted" components.
Probing Baryonic Physics: The study demonstrates that cross-correlations between CIB and other tracers (like tSZ or lensing) are powerful probes of baryonic feedback and cosmology, even when the CIB auto-spectrum is degenerate with SED parameters.
Validation of Hydrodynamics: The results validate the FLAMINGO simulation suite's ability to reproduce a wide range of observational constraints, reinforcing its utility for studying the interplay between galaxy formation and the large-scale structure of the universe.