FLAMINGO Cosmological Hydrodynamical Simulations

• FLAMINGO is a suite of large cosmological hydrodynamical simulations that model cosmic structure formation by integrating dark matter and baryonic physics.
• It employs machine learning–calibrated subgrid techniques to accurately simulate star formation, feedback processes, and gas cooling across vast cosmic volumes.
• Its high-resolution, multi-scale framework delivers precise predictions for galaxy clustering, weak lensing, and cluster scaling relations to support next-generation surveys.

The FLAMINGO Simulation refers to a suite of large cosmological hydrodynamical simulations developed primarily by the Virgo Consortium to model the formation and evolution of cosmic structure, galaxy clusters, and galaxies across cosmic time. Its design enables self-consistent modeling of both dark matter and baryonic physics—including star formation, feedback processes, and gas cooling—at volumes and resolutions suitable for interpreting data from next-generation large-scale structure (LSS) surveys. The FLAMINGO project systematically incorporates machine learning–calibrated subgrid physics, a range of feedback implementations, lightcone outputs, and extensive model and cosmology variations to deliver precise, observationally anchored predictions for a range of key cosmological observables.

1. Simulation Objectives and Scientific Scope

The primary aim of FLAMINGO is to simulate the evolution of large-scale cosmic structure, with a particular focus on the interplay of baryonic physics and dark matter, and their imprint on observables such as galaxy clustering, cluster scaling relations, and weak lensing signals (Schaye et al., 2023, Braspenning et al., 2023). This is motivated by the need to:

• Accurately reproduce galaxy formation and feedback processes on scales relevant to both galaxies and massive clusters,
• Enable unbiased interpretation and systematic-error mitigation in current and future LSS and galaxy surveys (e.g., Euclid, LSST, DESI),
• Supply reference hydrodynamic predictions for calibration and validation of fast theoretical and empirical models (e.g., HOD, SHAM).

FLAMINGO distinguishes itself by targeting both large simulation volumes (up to (2.8 Gpc)$^3$ with $3\times10^{11}$ particles) and high baryonic mass resolution (down to $1\times10^8\,M_\odot$ per baryonic particle), enabling robust statistical sampling across cosmic environments and mass scales.

2. Methodology and Simulation Suite

2.1 Hydrodynamics and Physical Models

FLAMINGO employs the SWIFT code, using the “SPHENIX” Smoothed Particle Hydrodynamics (SPH) scheme, which evolves baryons (gas, stars, metals) and dark matter, and incorporates the δf method for massive neutrinos (Braspenning et al., 2023, Schaye et al., 2023). The incorporated subgrid physics modules are:

• Radiative cooling and heating: Metal-dependent, tabulated with CLOUDY.
• Star formation: Calibrated to observed SF laws.
• Stellar evolution and feedback: Kinetic implementation for SN feedback.
• Black hole seeding, growth, and AGN feedback: Includes both isotropic thermal and collimated jet feedback; parameters such as temperature jump ($\Delta T_{\mathrm{AGN}}$) and accretion scaling are varied.
• Metal enrichment: Element-by-element tracking.

2.2 Calibration Strategy

A defining methodological feature is machine learning–driven calibration of subgrid models. A Gaussian process emulator is trained on simulation grids constructed via Latin hypercube sampling in the subgrid parameter space (Schaye et al., 2023, Kugel et al., 2023). Key calibration datasets include:

• Galaxy stellar mass function (SMF) from surveys such as GAMA,
• Cluster gas mass fractions ($f_{\mathrm{gas}}$) from X-ray and weak lensing observations (with hydrostatic mass bias correction),
• Black hole mass–stellar mass relation and scaling relations.

Priors on subgrid parameters and uncertainty quantification for observational biases (stellar mass, cosmic variance, hydrostatic equilibrium) are integrated into an MCMC calibration workflow.

2.3 Box Hierarchy, Resolution, and Model Variations

• Box sizes: Flagship runs at (1 Gpc)$^3$ and (2.8 Gpc)$^3$ for m8/m9/m10 resolutions (higher particle mass in larger boxes).
• Mass resolutions: Baryonic particle mass ranging from $1.07 \times 10^8 M_\odot$ (m8, high-res) to $8 \times 10^9 M_\odot$ (m10, low-res).
• Cosmology variations: Flat $\Lambda$CDM (e.g., DES Year 3) and alternatives (Planck, LS8, various neutrino masses).
• Feedback variations: Systematic shifts of $f_{\mathrm{gas}}$ and SMF calibration targets, and AGN feedback channel (thermal/jets).
• Lightcone outputs: On-the-fly, multi-observer outputs for lensing, SZ, and clustering analyses.

3. Selected Results and Comparisons with Observations

3.1 Galaxy and Cluster Statistics

FLAMINGO simulations recover the calibration targets (SMF, $f_{\mathrm{gas}}$, BH scaling laws) down to near resolution limits (Schaye et al., 2023, Braspenning et al., 2023). Detailed comparisons to observations yield:

• Cluster scaling relations (X-ray $L_X$–$M$, $T$–$M$, $Y_\mathrm{SZ}$–$M$): Excellent agreement in slope, normalization, and minimal evolution after self-similar scaling, except notably high core metallicities (Braspenning et al., 2023).
• Radial thermodynamic profiles: Self-similar evolution in temperature, entropy, pressure, and density with metallicity decreasing at higher $z$.
• Feedback effects: Stronger AGN/stellar feedback (as calibrated to lower $f_{\mathrm{gas}}$) increases the baryonic suppression in the power spectrum, yields hotter cores, and reduces cool-core prevalence in clusters.
• Matter power spectrum: Baryonic suppression up to $\sim 20\%$ at $k\sim 1-10\,h\,\mathrm{Mpc}^{-1}$. Variations in stellar and gas fractions or AGN feedback channel are reflected in the scale and amplitude of suppression (Schaller et al., 22 Oct 2024).

3.2 Weak Lensing and Non-Linear Structure

• Lensing statistics: Ray-traced full-sky convergence maps allow direct prediction of WL peak statistics. Realistic baryonic feedback modulates peak counts by $5-30\%$ for $\kappa=0.1-0.4$, compared to $20-60\%$ changes for reasonable cosmological parameter variations (Broxterman et al., 2023, Broxterman et al., 3 Dec 2024).
• Redshift distribution of WL peaks: Shape is nearly insensitive to baryonic physics, but varies with cosmology, enabling joint cosmological and astrophysical inference (Broxterman et al., 3 Dec 2024).
• CMB lensing: Simulations facilitate percent-level testing of fast, hybrid lensing power spectrum calculations; suppression effects from baryons and neutrinos factorize, limiting neutrino mass bias (Upadhye et al., 2023).

3.3 Quenching, Galaxy Formation, and Protoclusters

• Galaxy quenching: Robust correlation of quenching with black hole mass (critical transition at $M_{\mathrm{BH}}\simeq10^7\,M_\odot$), with environment/halo mass playing a secondary role for lower-$M_{\mathrm{BH}}$ galaxies (Lim et al., 2 Apr 2025). Random forest classification demonstrates the primacy of AGN feedback for both centrals and satellites.
• Protoclusters: Correcting for aperture bias is necessary for theoretical/observational matching, with star formation suppression in protocluster cores beginning as early as $z\simeq5$ (Lim et al., 27 Feb 2024).
• Massive high-$z$ quiescent galaxies: FLAMINGO underpredicts their abundance (even considering cosmic variance), with the majority of their stars formed in situ, not via major mergers; AGN feedback assumed instrumental but may require revision at high redshift (Baker et al., 18 Oct 2024).

3.4 Isotropy, Scatter, and Large-Scale Structure

• Cosmic isotropy: FLAMINGO lightcones show the probability of Mimicking observed $H_0$ anisotropy at the $0.12\%$ ($3.2\sigma$) level; much anisotropy arises from intrinsic scatter, not peculiar velocities (He et al., 2 Apr 2025).
• Largest-scale structure: Enhanced clustering analyses (MST, SLHC, CHMS) confirm that Gpc-scale structures like the Giant Arc are not reproduced in FLAMINGO; simulated data are statistically similar to random Poisson distributions in this domain (Lopez et al., 21 Apr 2025).

4. Technical Calibration and Emulator Frameworks

FLAMINGO’s subgrid calibration employs emulators trained on a Latin hypercube and Gaussian processes (Kugel et al., 2023). The approach enables:

• Rapid parameter exploration: Once trained, emulators accelerate parameter inference and systematic uncertainty analysis (e.g., for $f_{\mathrm{gas}}$ shifts, AGN feedback implementations, or stellar mass function shifts).
• Direct data-driven variations: Model variants are defined by perturbing observable calibration data (e.g., $f_{\mathrm{gas}}$ or SMF by $\pm2,4,8\,\sigma$) and mapping to new subgrid parameters. This ties simulation predictions to the uncertainty in the underlying data.
• Uncertainty propagation: Emulator and observation errors are included in the likelihood (see equations for $\mathcal{P}_\mathrm{SMF}$, $\mathcal{P}_\mathrm{gas}$), ensuring the final simulation predictions reflect both numerical and astrophysical uncertainties.

5. Impact, Applications, and Future Directions

FLAMINGO serves as a benchmark for precision cosmology across multiple fronts:

• Reference dataset: High–statistical power for galaxy, cluster, and LSS surveys.
• Calibration of empirical models: Used to validate and refine HOD, SHAM, and other rapid mocks for survey pipelines (Contreras et al., 26 Jul 2024).
• Cosmology/astrophysics disentanglement: Structure and lensing statistics are leveraged to separate baryonic and cosmological signatures, with potential for self-calibration in future LSS analyses.
• Emulator-based theory pipeline: Ongoing development of emulators for matter power spectra and other statistics enables fast exploration of cosmological and astrophysical parameter spaces (Schaller et al., 22 Oct 2024).

The suite’s systematic uncertainties are driven by both subgrid feedback prescriptions and input cosmology, with tensions emerging for extreme baryonic responses (strong feedback models can be at odds with observed $f_{\mathrm{gas}}$). Further work is targeting independent shifts in gas and stellar fractions, broader cosmology coverage, and improved physical models for feedback—especially at high redshift and in the context of massive quenched galaxies.

6. Controversies and Challenges

Current FLAMINGO results confirm that baryonic effects (calibrated to observed constraints) are essential for unbiased cosmological inference, yet also expose persistent discrepancies:

• Quenched high-$z$ galaxies: Underprediction persists even after accounting for cosmic variance, challenging feedback/AGN prescriptions at early times (Baker et al., 18 Oct 2024).
• Largest-scale structure: Observed structures such as the Giant Arc and Big Ring are not reproduced in Gpc-scale ΛCDM volumes, suggesting either a rare statistical fluctuation, unmodeled systematics, or possible new physics (Lopez et al., 21 Apr 2025).
• Hydrostatic mass bias: Simulation-derived X-ray mass biases (e.g., $b_\mathrm{HSE}\sim-0.1$ to $-0.2$) depend sensitively on profile weighting and feedback, with X-ray–weighted measurements tending to overestimate bias (Braspenning et al., 12 Sep 2024).

A plausible implication is that future survey interpretation will require jointly forward-modeling cosmology, subgrid baryonic uncertainties, and observational effects to accurately extract fundamental parameters from LSS and cluster observables. FLAMINGO provides a foundational platform for these endeavors.