FLAMINGO Hydrodynamical Simulations in Cosmology

• FLAMINGO hydrodynamical simulations are advanced, large-volume cosmological models that combine gravity, hydrodynamics, and subgrid galaxy formation to capture cluster-scale astrophysics.
• They employ state-of-the-art machine learning calibration and vary AGN feedback implementations to precisely map observables from galaxy clusters to large-scale structure.
• The simulations generate detailed outputs like lightcone maps and synthetic survey products, bridging theory with observations and addressing baryonic effects on structure formation.

The FLAMINGO hydrodynamical simulations are an advanced suite of large-volume cosmological simulations developed by the Virgo Consortium to enable precision modeling of both large-scale structure (LSS) and cluster-scale astrophysics in a self-consistent physical framework. By coupling gravity, hydrodynamics, subgrid models of galaxy formation, and massive neutrino physics, FLAMINGO is designed for robust predictions of key cosmological observables relevant to ongoing and next-generation galaxy and cluster surveys. The suite’s unique workflow—combining machine learning calibration, hundreds of billions of particles, state-of-the-art baryonic modeling, and detailed model variations—has established new standards for large-volume, baryon-rich cosmological simulation.

1. Simulation Architecture and Scale

FLAMINGO comprises simulations with box sizes of (1 Gpc)$^3$ (L1) and (2.8 Gpc)$^3$ (L2p8), spanning three mass resolutions:

• m8: $m_{\mathrm{baryon}} \approx 1 \times 10^8\,M_\odot$
• m9: $m_{\mathrm{baryon}} \approx 1 \times 10^9\,M_\odot$
• m10: $$m_{\mathrm{baryon}} \approx 8.6 \times 10^9\,M_\odot$$

The largest simulation (L2p8_m9) evolves $\sim$3×10$^{11}$ particles, distributing computational effort between baryons, cold dark matter, and neutrinos. This volume and resolution enable FLAMINGO to resolve halos over a wide dynamic mass range and to produce unprecedentedly large samples of galaxy clusters (e.g., 4.6×10$^3$ halos with $M_{200m} > 10^{15}~M_\odot$ at $z=0$). The codebase is built on Swift, adopting the SPHENIX smoothed particle hydrodynamics scheme, and employs an advanced treatment of massive neutrinos via the δf-method to reduce shot noise.

2. Subgrid Physics and Calibration

FLAMINGO employs calibrated subgrid models for star formation, stellar feedback, black hole physics, and active galactic nucleus (AGN) feedback. Calibration is central to the realism of the suite, performed independently at each resolution using a machine learning workflow:

• Latin hypercube sampling of subgrid parameter space is run in small-box simulations.
• Gaussian Process (GP) emulators are constructed to interpolate key observables—specifically, the galaxy stellar mass function (GSMF) and cluster gas fractions—as functions of both mass and subgrid parameters,
• Emulator predictions are coupled to Markov Chain Monte Carlo (MCMC) samplers to maximize likelihood with respect to observational constraints (e.g., GAMA GSMF, X-ray and weak lensing gas fractions).
• Observational systematics, including Eddington bias (via lognormal stellar mass scatter), cosmic variance, and hydrostatic mass bias, are included directly in the likelihood model.

Calibration is performed separately for each resolution, enabling a "weak convergence" test, and all model variations (including cosmological and feedback parameter shifts) are defined by direct manipulation of the observables, not arbitrary subgrid parameter adjustments.

3. Model Variations and Cosmological Sampling

The suite comprises a wide sweep of physical and cosmological variations:

• At fixed cosmology, eight runs impose $\pm2\sigma$, $-4\sigma$, or $-8\sigma$ shifts in cluster gas fractions or $-1\sigma$ shift in the GSMF prior to calibration, allowing systematic exploration of gas content and feedback efficacy.
• AGN feedback is implemented in both standard “thermal” (isotropic energy injection) and “kinetic jet” modes. Models are separately recalibrated so that differences in resulting cosmic structures reflect only the feedback physical mechanism.
• Cosmological parameter variations span the fiducial DES Y3 cosmology (with minimal neutrino mass $M_\nu=0.06$ eV), Planck 2020 constraints, high-neutrino variants ($M_\nu=0.24$ eV), and a “lensing cosmology” (lower $S_8$), allowing direct exploration of the impact of cosmological biases on large-scale observables.

For each variant, lightcone outputs are generated on-the-fly for multiple observer positions, and are formatted as all-sky HEALPix maps for downstream emulation of weak lensing, X-ray, and thermal SZ observations.

4. Impact on Large-Scale Structure and Observables

FLAMINGO’s calibrated simulations reproduce the $z=0$ GSMF, observed cluster gas fractions within $R_{500c}$, and the black hole–stellar mass scaling relation. The resulting clusters are used to investigate scaling relations (e.g., $L_X$–$T$, $Y$–$M$), where FLAMINGO predictions match observational data and show minimal deviation from self-similar theory (excepting core metallicities and cool core occurrence, which remain area for model refinement).

A significant output is the quantification of baryonic suppression in the halo mass function and matter power spectrum:

• Baryonic effects suppress the low-mass halo mass function and the $k\simeq1\,h\,\mathrm{Mpc}^{-1}$ matter power spectrum by up to $\approx 20$\%; the effect is nearly negligible for the most massive halos.
• The suppression correlates with the mean baryon fraction in clusters, enabling a direct link between cluster baryonic content and corrections for power spectrum predictions.
• Lightcone maps allow direct computation on-the-fly of the Compton-y parameter:

$y = \int \frac{k_B T_e}{m_e c^2} n_e \sigma_T dl$

for SZE observables, and computation of weak lensing signals for synthetic survey predictions.

5. Technical Innovations and Data Products

Key technical achievements of FLAMINGO include:

• Hierarchical simulation architecture for simultaneous exploration of resolution, feedback, and cosmology parameter space.
• Machine learning–driven calibration using GP emulators and MCMC, allowing direct mapping of observational uncertainties into model prediction uncertainties and supporting “data-centric” model versioning.
• Treatment of massive neutrinos via the δf-method, reducing statistical errors on large scales.
• On-the-fly lightcone generation and mapping to multiple observable formats (full-sky HEALPix, synthetic maps), facilitating direct interface with survey pipelines.
• Quantitative convergence studies across mass resolutions to ensure physical robustness of predictions.

The suite produces outputs essential for survey support: synthetic optical, X-ray, tSZ, and weak lensing sky maps, with baryon-informed corrections for matter power spectra and halo abundances.

6. Scientific Outcomes and Tensions in LSS Interpretation

FLAMINGO findings feed directly into major cosmological debates:

• Comparison of hydrodynamical and dark-matter-only runs demonstrates that baryons, through feedback-driven redistribution, are the dominant source of modeling uncertainty in the small-scale power spectrum and halo masses relevant to weak lensing, cluster cosmology, and CMB lensing.
• Despite increased feedback efficiency, baryonic effects in the simulations are inadequate to fully resolve the observed $S_8$ tension between cosmic shear and CMB-inferred matter clustering amplitudes; the magnitude of baryonic suppression is too constrained by other observables (e.g. gas fractions in massive clusters) to accommodate the $\sim$1–3$\sigma$ deficit in weak lensing and tSZ signal amplitude.
• Models with differing AGN feedback implementations (thermal vs. jet) yield noticeable differences in the thermodynamic properties of cluster cores and the prevalence of cool-core clusters, providing insight for high-resolution X-ray and SZ follow-up.

7. Role within the Cosmological Simulation Landscape

FLAMINGO’s approach—extending hydrodynamical simulation volumes to gigaparsec scales, co-calibrating observables with machine learning, and producing diversified model sets with on-the-fly lightcone outputs—provides a foundation for robust, forward-modeled interpretation of next-generation surveys (Euclid, LSST, DESI, eROSITA, SPT, Planck). It addresses both precision and accuracy requirements by explicitly accounting for baryonic parameter and cosmological uncertainties, and by linking LSS corrections directly to observable cluster and galaxy properties.

Notable outputs include:

• Star formation law: $\dot{m}_* \propto (P/P_0)^n$
• SZE Compton-y integral: $$y = \int \frac{k_B T_e}{m_e c^2}\, n_e\, \sigma_T\, dl$$

Collectively, FLAMINGO represents a state-of-the-art framework bridging cosmological theory and observational data, setting benchmarks for the quantification of baryonic effects, calibration of feedback models, and statistical interpretation of large-scale structure in the era of high-precision cosmology (Schaye et al., 2023, Kugel et al., 2023, McCarthy et al., 2023, Braspenning et al., 2023).