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The FLAMINGO project: cosmological hydrodynamical simulations for large-scale structure and galaxy cluster surveys

Joop Schaye, Roi Kugel, Matthieu Schaller, John C. Helly, Joey Braspenning, Willem Elbers, Ian G. McCarthy, Marcel P. van Daalen, Bert Vandenbroucke, Carlos S. Frenk, Juliana Kwan, Jaime Salcido, Yannick M. Bahé, Josh Borrow, Evgenii Chaikin, Oliver Hahn, Filip Huško, Adrian Jenkins, Cedric G. Lacey, Folkert S. J. Nobels

arXiv:2306.04024v3astro-ph.COastro-ph.GA

TL;DR

Large-scale-structure surveys require accurate predictions where baryons alter matter clustering, but feedback and its observational effects remain uncertain. FLAMINGO presents large-volume hydrodynamical simulations calibrated across resolutions; comparisons with dark-matter-only runs show substantial baryonic suppression of structure statistics.

  • Problem

    Baryonic effects on the matter power spectrum are larger and more uncertain on smaller scales, complicating precision measurements relevant to observational surveys.

    Source: §8 · p. 33

  • Method

    FLAMINGO introduces large-volume hydrodynamical simulations with three resolutions calibrated to common observational data and includes astrophysical and cosmological variations.

    Source: §1 · p. 3

  • Results

    At M200m ∼10^13 M⊙, the halo mass function is reduced by ≈20 per cent in hydrodynamical runs relative to corresponding dark-matter-only runs.

    Source: §9 · p. 37

  • Takeaways & Limitations

    The fiducial simulations reproduce their calibration data within the mass ranges where predictions converge with resolution and box size.

    Source: §9 · p. 37

    Observed stellar-mass fractions depend on whether extended low-surface-brightness emission is included; total and 50 kpc aperture-limited fractions bracket observed values.

    Source: §5.3 · p. 21

Abstract

from arXiv · show

We introduce the Virgo Consortium's FLAMINGO suite of hydrodynamical simulations for cosmology and galaxy cluster physics. To ensure the simulations are sufficiently realistic for studies of large-scale structure, the subgrid prescriptions for stellar and AGN feedback are calibrated to the observed low-redshift galaxy stellar mass function and cluster gas fractions. The calibration is performed using machine learning, separately for three resolutions. This approach enables specification of the model by the observables to which they are calibrated. The calibration accounts for a number of potential observational biases and for random errors in the observed stellar masses. The two most demanding simulations have box sizes of 1.0 and 2.8 Gpc and baryonic particle masses of $1\times10^8$ and $1\times10^9 \text{M}_\odot$, respectively. For the latter resolution the suite includes 12 model variations in a 1 Gpc box. There are 8 variations at fixed cosmology, including shifts in the stellar mass function and/or the cluster gas fractions to which we calibrate, and two alternative implementations of AGN feedback (thermal or jets). The remaining 4 variations use the unmodified calibration data but different cosmologies, including different neutrino masses. The 2.8 Gpc simulation follows $3\times10^{11}$ particles, making it the largest ever hydrodynamical simulation run to $z=0$. Lightcone output is produced on-the-fly for up to 8 different observers. We investigate numerical convergence, show that the simulations reproduce the calibration data, and compare with a number of galaxy, cluster, and large-scale structure observations, finding very good agreement with the data for converged predictions. Finally, by comparing hydrodynamical and `dark-matter-only' simulations, we confirm that baryonic effects can suppress the halo mass function and the matter power spectrum by up to $\approx20$ per cent.

1 INTRODUCTION

Upcoming large-scale-structure surveys need accurate predictions on scales where baryons do not trace cold dark matter, but baryonic effects and feedback are uncertain. FLAMINGO addresses this with large-volume hydrodynamical simulations calibrated to observations across resolutions, with variations in astrophysics and cosmology.

1 INTRODUCTION

  • Baryonic effects alter matter clustering on scales relevant to upcoming surveys, while feedback makes accurate predictions uncertain and unaccounted effects can cause systematic errors in cosmic-shear surveys.Baryons are predicted to be smoother than CDM on scales of 1–10 Mpc and more clustered on smaller scales.Source: §1 · p. 2
  • FLAMINGO uses three resolutions calibrated to the same data, including flagship boxes of 2.8 and 1 Gpc with baryonic particle masses of 1×10^9 and 1×10^8 M⊙, respectively.The 2.8 Gpc volume is more than two orders of magnitude larger than BAHAMAS at the same resolution.Source: §1 · p. 3
  • The 2.8 Gpc simulation follows 3×10^11 particles, and FLAMINGO produces full-sky lightcone outputs on the fly for up to eight observers.The suite also models massive neutrinos with particles using the δf method and uses three-fluid initial conditions.Source: §1 · p. 3
  • Subgrid calibration uses machine-learning emulators and accounts for observational errors and biases, with the model variations expressed through shifts in calibration observables rather than only subgrid parameters.The calibration targets include the stellar mass function and cluster gas fractions, which are relevant to galaxy–halo connections and matter-power suppression.Source: §1 · p. 3
  • The suite includes eight astrophysics variations and four cosmology variations at intermediate resolution in 1 Gpc boxes, including alternative AGN feedback implementations and different neutrino masses.Astrophysics variants shift calibration data within allowed errors; the cosmology variants use the fiducial calibration data.Source: §1 · p. 3
  • The paper documents the simulations and calibration, compares predictions with observations, and reports baryonic effects on structure formation.Hydrodynamical simulations also model baryonic back-reaction and provide gas and galaxy properties for comparison with observations.Source: §1 · pp. 2–3

2 SIMULATION METHODS

The simulation methods combine the Swift gravity and hydrodynamics solver with low-noise treatment of massive neutrinos and subgrid models for unresolved gas and galaxy physics. They prescribe black-hole growth, mergers, and a single AGN feedback mode per run, and note that a black-hole repositioning implementation issue materially affects quenched fractions in massive galaxies.

2.1 The gravity and hydrodynamics solver Swift

  • Swift uses a fourth-order fast multipole method for short-range gravity, particle-mesh gravity for long-range forces, and SPHENIX hydrodynamics with viscosity and conduction limiters.The subgrid models build on OWLS, cosmo-OWLS, BAHAMAS, and EAGLE prescriptions ported from gadget to Swift.Source: §2.1 · pp. 4–5, §2.3 · p. 6

2.2 Treatment of neutrinos

  • The δf method captures nonlinear massive-neutrino evolution while reducing shot noise and particle requirements; weighting is applied only to long-range mesh gravity, while short-range interactions use ordinary massive particles.The reduced early-time shot noise prevents spurious back-reaction on cold dark matter and baryons; neutrino particles use relativistic velocities.Source: §2.2 · p. 5

2.3.1 Radiative cooling and heating

  • Element-by-element radiative cooling uses Ploeckinger & Schaye rates with an evolving UV/X-ray background, self-shielding, dust, and interstellar radiation; reionization heating yields an IGM thermal history agreeing with Lyα-forest observations.When expected internal energy changes by more than one third during a timestep, it is set immediately to the estimated end-of-step value.Source: §2.3.1 · p. 6, Figure 3 · p. 6

2.3.2 Star formation and the pressure of the interstellar medium

  • Because FLAMINGO cannot resolve a multiphase ISM, it imposes a density-dependent pressure floor and forms stars stochastically above density, overdensity, and temperature thresholds, with lower thresholds in low-resolution runs.The pressure relation corresponds to a constant Jeans mass of approximately 10^7 M⊙, which is unresolved in these simulations.Source: §2.3.2 · pp. 6–7

2.3.3 Stellar mass loss

  • Stellar populations use a Chabrier IMF and time-dependent mass loss from winds and supernovae; returned mass and metals are transferred to gas neighbours, and baryonic particles exceeding 4 times the initial gas particle mass are split.The simulations track H, He, C, N, O, Ne, Mg, Si, and Fe abundances for element-by-element cooling.Source: §2.3.3 · p. 7

2.3.4 Stellar energy feedback

  • Stellar energy feedback kinetically kicks gas neighbours of young stars, using paired kicks that conserve linear and angular momentum and energy and an energy-selection method designed for statistically isotropic injection.The stellar feedback energy fraction and target wind velocity are calibrated parameters; wind particles remain coupled to hydrodynamics.Source: §2.3.4 · pp. 7–8

2.3.5 Black holes

  • Black-hole seeds of 10^5 M⊙ are placed in sufficiently massive haloes, and black holes are repositioned to nearby gas at lower gravitational potential to compensate for unresolved dynamical friction.The seed mass is increased by a factor of 100 in low-resolution simulations; repositioning is critical because without it black-hole growth and AGN feedback are dramatically reduced.Source: §2.3.5 · p. 8
  • The new black-hole merger criterion treats merging as a gravitational process and leads to somewhat faster mergers, particularly in low-density environments.Mergers conserve momentum, subgrid black-hole mass, and particle mass, while removing the particle carrying the lower-mass black hole.Source: §2.3.5 · pp. 8–9
  • Black holes accrete at a boosted, Eddington-limited modified Bondi-Hoyle rate; low-density gas is left unboosted to avoid unrealistic depletion of the ISM and inner CGM.The boost is motivated by unresolved Bondi radii and the absence of a modeled multiphase ISM; at low densities, gas lacks a cold phase or accretion may be resolved.Source: §2.3.5 · p. 9
  • When a black hole’s subgrid mass exceeds its particle mass, it nibbles mass and momentum from SPH neighbours, reducing the relative difference between the two masses.Neighbour contributions are weighted by their contribution to the SPH density at the black-hole location; unlike the BAHAMAS method, this does not stochastically swallow whole gas particles.Source: §2.3.5 · p. 9

2.3.6 AGN feedback

  • The fiducial model uses thermal AGN feedback, while some intermediate-resolution runs use anisotropic kinetic feedback to test sensitivity to implementation.Each run employs only one AGN feedback mode.Source: §2.3.6 · p. 9

Fiducial model: thermal injection

The fiducial thermal AGN model stores feedback energy until it can heat gas particles without numerical overcooling. Its coupling efficiency, heating choices, and temperature increment set aspects of the model, with the temperature increment calibrated to observations.

Fiducial model: thermal injection

  • Feedback energy accumulates in a black-hole reservoir until it can heat n_heat gas particles by ΔT_AGN, avoiding numerical overcooling.A black-hole time-step limiter helps sample feedback while limiting reservoir growth between steps.Source: Fiducial model: thermal injection · p. 9
  • The coupling efficiency ε_f sets the black-hole mass needed for self-regulation, while other galaxy properties are described as insensitive to its value.The model adopts ε_f = 0.15, corresponding to 0.015 of accreted rest-mass energy used for feedback.Source: Fiducial model: thermal injection · p. 9
  • With n_heat = 1, FLAMINGO thermal AGN events are an order of magnitude less energetic than BAHAMAS events at fixed mass resolution and ΔT_AGN.Energy is injected into the gas particle nearest the black hole, minimizing feedback at large distances.Source: Fiducial model: thermal injection · p. 9
  • The model calibrates ΔT_AGN, while its fiducial thermal outflows can be anisotropic and produce buoyantly rising high-entropy bubbles in clusters.The anisotropy arises as outflows take the path of least resistance.Source: Fiducial model: thermal injection · p. 9

Model variation: kinetic, jet-like injection

The Jet variation applies a simplified spin-based jet model at all accretion rates, with calibrated jet velocity and infrequent expected redirection. The simulations also use multi-fluid initial conditions and a two-stage halo and subhalo analysis pipeline.

Model variation: kinetic, jet-like injection

  • The Jet runs use jet-mode physics at all accretion rates and a constant feedback efficiency of 0.015, chosen to maximize contrast with the fiducial thermal model.The efficiency yields black-hole masses consistent with observations; spins determine jet direction only.Source: Model variation: kinetic, jet-like… · p. 10
  • The assumed outer-disc direction follows gas in the black-hole smoothing kernel, while jet redirection is expected on roughly Gyr rather than Myr timescales.The authors identify the direction assumption as strong at the simulations’ low resolution; redirection more frequent than a typical jet episode could make effects direction-sensitive.Source: Model variation: kinetic, jet-like… · p. 10
  • Jets kick two gas particles near the black-hole spin axis, and the calibrated target jet velocity controls the energy threshold for each pair of kicks.Energy conservation can make the actual velocity increase differ from the target velocity.Source: Model variation: kinetic, jet-like… · p. 10

2.4 Initial conditions

  • FLAMINGO uses multi-fluid third-order Lagrangian perturbation theory initial conditions to reproduce relative growth among fluid components, including massive neutrinos.The combined CDM and baryon fluid is initialized first, then split by perturbing particle masses and velocities; mass perturbations suppress discreteness errors.Source: §2.4 · p. 10
  • Initial conditions use partially fixed modes to limit cosmic variance, and generalized back-scaling and neutrino phase-space integration account for massive-neutrino effects.Neutrinos are integrated from z = 109 to z = 31; the back-scaling procedure starts from the desired z = 0 transfer functions.Source: §2.4 · pp. 10–11

2.5 Structure finding

  • VELOCIraptor identifies haloes with 3D friends-of-friends, then finds dynamically distinct substructures using iterative 6D phase-space searches and unbinding.The most prominent substructure is labeled the central; remaining objects are satellites.Source: §2.5 · p. 11
  • SOAP takes VELOCIraptor centers and particle memberships as input to compute halo properties across 3D or projected apertures.Apertures can include or exclude other substructures and unbound particles, and can be specified by physical radius or mean internal overdensity.Source: §2.5 · p. 11

3 CALIBRATION OF SUBGRID PARAMETERS AND OBSERVATIONAL BIASES

FLAMINGO calibrates its subgrid physics to the present-day galaxy stellar mass function and low-redshift cluster gas fractions, using separate emulators for each resolution. The calibration accounts for observational biases and measurement scatter, and the fitted parameters vary with resolution and feedback model.

3 CALIBRATION OF SUBGRID PARAMETERS AND OBSERVATIONAL BIASES

  • The calibration targets are the present-day stellar mass function and cluster gas fractions, which constrain the galaxy–halo relation and baryonic suppression of matter and cluster mass functions.The stellar mass function uses z=0 GAMA results; gas fractions use X-ray data at z≈0.1 and weak-lensing data at z≈0.3.Source: §3 · p. 11, §3.2 · p. 12

3.1 Emulation

  • Gaussian-process emulators trained on 32 simulations per resolution predict the stellar mass function and cluster gas fractions, with parameter values fitted by MCMC to data and emulator uncertainty.The maximum-likelihood parameters are used; the two gas-fraction datasets receive equal weight, as do their combined result and the stellar mass function.Source: §3.1 · p. 12
  • Each resolution is calibrated separately because resolving different gas densities and scales changes unresolved-process behavior; the authors call comparisons of recalibrated resolutions weak convergence tests.The Latin-hypercube simulations use volumes of (100 Mpc)^3, (200 Mpc)^3, and (400 Mpc)^3 at high, intermediate, and low resolution.Source: §3.1 · p. 12

3.2 Calibration data

  • Stellar masses are defined as bound subhalo stellar mass within a 50 kpc aperture, and lognormal scatter is added to mimic observational measurement errors and Eddington bias.The added scatter is σ(log10 M*) = min(0.070 + 0.071z, 0.3) dex; the authors do not make virtual-observation measurements because they lack resolution for realistic mocks of galaxies and low-mass clusters.Source: §3.2 · p. 12

3.3 Observational bias factors

  • Three constant observational bias factors shift the stellar-mass axis, galaxy-number-density axis, and cluster gas-fraction–mass relation; biases are fitted at intermediate resolution and held fixed across other resolutions and models.The hydrostatic mass correction changes the inferred mass axis; its effect on gas fraction within R500c is neglected as small.Source: §3.3 · pp. 12–13
  • The best-fitting stellar-mass and cosmic-variance biases are consistent with no bias, while the hydrostatic mass correction divides observed X-ray total masses by 0.743 and is largely prior-determined.The stellar-mass shift is +0.026 dex and the galaxy number-density factor is 0.995; the hydrostatic mass-bias posterior is 0.74 ± 0.09.Source: §3.3 · p. 13

3.4 Subgrid parameter values

  • At high resolution, stellar feedback requires about twice the energy and half the kick velocity of intermediate resolution, while βBH falls to 0.038; low-resolution parameters are not directly comparable because its model omits stellar feedback.The lower high-resolution βBH implies almost no Bondi–Hoyle accretion boost; the authors attribute parameter shifts to resolution-dependent densities and mass ranges.Source: §3 · p. 12, §3.4 · p. 13
  • Across feedback variations, shifting stellar masses mainly raises fSN, while gas-fraction shifts are driven mostly by ΔTAGN; jet feedback uses a higher jet velocity and lower βBH for the fgas−4σ variant.For each 2σ gas-fraction shift, ΔTAGN changes by 0.13–0.24 dex, with higher ΔTAGN corresponding to lower fgas.Source: §3.4 · pp. 13–14

4 THE SIMULATIONS

The FLAMINGO suite combines hydrodynamical runs across three resolutions and a range of volumes, cosmologies, and feedback models. It includes a 2.8 Gpc run with 2.8 × 10^11 particles, multiple model variants, and on-the-fly lightcone and snapshot outputs.

4 THE SIMULATIONS

  • The suite includes 16 hydrodynamical and 12 gravity-only simulations, with most hydrodynamical runs using 1 Gpc volumes and intermediate resolution; the largest volume is 2.8 Gpc.The simulations span three resolution levels, with particle mass and spatial resolution changing by factors of 8 and 2 between successive levels.Source: §4 · p. 14
  • Twelve additional 1 Gpc intermediate-resolution hydrodynamical runs vary cosmology or galaxy-formation physics, alongside DMO counterparts and additional gravity-only runs.The cosmology variations include higher neutrino masses and an alternative lower-S8 lensing cosmology; feedback variants include thermal and jet AGN models and shifted calibration data.Source: §4 · p. 14, Table 3 · p. 15
  • The 2.8 Gpc L2p8_m9 run follows approximately 3 × 10^11 particles, making it the largest cosmological hydrodynamical simulation with radiative cooling run to z=0, as far as the authors know.Its particle count exceeds that of similar-resolution BAHAMAS simulations by more than two orders of magnitude.Source: §4 · p. 16
  • In the visual comparisons, neutrinos are smoother than CDM on scales ≲10^2 Mpc, while gas is smoother than CDM on scales ≲1 Mpc around a massive halo.The figures compare a 20 Mpc slice through L2p8_m9 and a 50 × 50 × 20 Mpc slice through L1_m8.Source: §4 · p. 16
  • Across the three resolutions, large-scale images look identical, while higher-resolution insets reveal structure on smaller scales.The comparison shows the same 63 × 63 × 20 Mpc region in L1_m8, L1_m9, and L1_m10.Source: §4 · p. 16
  • Lightcones are produced on the fly for up to eight observers in L2p8 and two in L1 runs, and the simulations save 79 snapshots over redshift.Lightcone maps have Δz = 0.05 shells, with thinner shells available in post-processing from particle lightcone output.Source: §4 · p. 16

5 COMPARISON WITH OBSERVATIONS USED FOR CALIBRATION

This section compares the simulations with calibration observables and related galaxy, cluster, and black-hole measurements. The larger flagship volumes extend predictions to masses beyond the calibration range.

5.1 Galaxy stellar mass function

  • Across the calibrated mass range, FLAMINGO's stellar mass functions generally agree with observations; above it, resolution predictions diverge, though m9 remains consistent within stellar-mass systematics.The m8 agreement is somewhat poorer, and the differences among resolutions become more consequential at the high-mass end.Source: Figure 8 · p. 19, §5.1 · p. 19

5.2 Cluster gas fractions

  • Fiducial cluster gas fractions agree well with observations, and variations calibrated to different gas-fraction targets generally match their respective targets.Above the m9 calibration limit, models converge toward similar gas fractions; jet models have shallower gas-fraction–halo-mass relations.Source: §5.2 · p. 20, Figure 10 · p. 22

5.4 Supermassive black holes

  • FLAMINGO agrees with black-hole–stellar-mass observations for ellipticals above M*=10^11.5 M⊙ and for discs below M*=10^11 M⊙.Rapid black-hole growth begins near M*=10^10.5 M⊙; shifting the target stellar masses shifts this phase by about the same amount, indicating it is determined mostly by halo rather than stellar mass.Source: §5.4 · pp. 22–23

5.3 Cluster star and baryon fractions

  • Stellar fractions decline with halo mass but can be high for massive clusters; total and 50-kpc-aperture fractions bracket observed values.Baryon fractions agree with the data apart from the Zhang et al. (2011) measurements near 10^15 M⊙, and converge slightly below the universal baryon fraction at high mass.Source: §5.3 · p. 21, Figure 11 · p. 23

6 COMPARISON WITH OBSERVATIONS NOT USED FOR CALIBRATION

This section compares FLAMINGO predictions with observations not used for calibration across star-formation, galaxy, cluster, and large-scale-structure probes, assessing agreement and convergence alongside dependencies on resolution, volume, and model variation. It also examines current cross-spectrum data, which cannot distinguish feedback variations but weakly favor low-S8 or high-neutrino-mass cosmologies, with stronger responses to explored cosmological than feedback variations.

6.1 Cosmic star formation history

  • Cosmic SFR densities agree with data below z≈2, but diverge and fall below observations at higher redshifts as resolution limits star formation in dominant haloes.At very high redshift, m10 predicts higher SFRs than m9 because its star-formation threshold density is lower; M*−σ models predict lower SFRs for z<2.Source: §6.1 · pp. 23–24, Figure 13 · p. 25

6.2 Galaxy properties

  • Galaxy properties are nearly box-size converged except at M∗>10^12 M⊙, but resolution effects persist; resolved predictions generally match observations, with passive fractions too low at the highest masses and sizes generally overestimated.Passive fractions and sizes become resolution-sensitive above the stellar-mass-function calibration limit; the sSFR and passive-fraction upturns and metallicity downturn at low masses are numerical effects.Source: §6.2 · pp. 24, 25, 27, Figure 14 · p. 26

6.3 Cluster scaling relations

  • Cluster scaling relations are converged and agree excellently with observations; X-ray luminosity relations are sensitive to gas fractions but largely insensitive to cosmology, stellar mass function, and feedback implementation at fixed gas fraction.The fiducial gas-fraction model best fits the data, while more extreme gas-fraction variations disagree more strongly.Source: §6.3 · pp. 27–28, Figure 15 · p. 28

6.4 Large-scale structure

  • The y–κ cross-spectrum converges across resolutions at fixed box size, while the 1 Gpc volume misses some power; switching to the lensing LS8 cosmology reduces its amplitude by ≈30%.The 2.8 Gpc Limber calculation agrees well with the map-based result, cosmic variance matters at ℓ≲500, and massive neutrinos and feedback variations also affect the spectrum.Source: §6.4 · pp. 29–30, Figure 17 · p. 30
  • The cross-spectrum is more sensitive to explored cosmological than feedback variations; smaller cluster gas fractions raise power at ℓ<600 and lower it on smaller scales.This scale-dependent response is consistent with stronger-feedback results from BAHAMAS simulations (McCarthy et al. 2018) and suggests sensitivity to both gas ejection and where outflows stall.Source: §6.4 · p. 30
  • Hill & Spergel (2014) cross-spectrum measurements were rescaled down by 20% for estimated residual CIB contamination of 20% ± 10%, and converted from y-φ to y-κ.The conversion uses φ_ℓ = 2κ_ℓ/(ℓ(ℓ + 1)).Source: §6.4 · p. 31
  • Current data cannot distinguish feedback variations, but weakly prefer a low-S8 or high-neutrino-mass cosmology.This preference is consistent with recent large-scale-structure findings, including Amon et al. 2023.Source: §6.4 · p. 31
  • Forthcoming Advanced Atacama Cosmology Telescope and Simons Observatory measurements are expected to improve precision, potentially enabling competitive cosmology and astrophysics constraints.The cited observatories are De Bernardis et al. 2016 and Ade et al. 2019, respectively.Source: §6.4 · p. 31

7 HALO MASS FUNCTION

FLAMINGO predicts substantial, mass-dependent baryonic changes to the halo mass function (HMF), while its simulations show strong convergence over relevant cluster masses. The effects vary with calibrated cluster gas fractions and, more modestly, with stellar-mass assumptions and feedback implementation.

7 HALO MASS FUNCTION

  • DMO HMF resolution deviations remain below 5% down to haloes of 100 particles, while literature predictions can differ substantially beyond Poisson errors.Magneticum and MiraTitan agree at the percent level over 10^13 ≲ M200c/M⊙ ≲ 10^14; the broader discrepancies are likely dominated by differing halo definitions.Source: §7 · pp. 31–32, Figure 19 · p. 31
  • The L2p8_m9 hydrodynamical run contains 4.1 × 10^6 haloes above 10^13 M⊙, 3.4 × 10^5 above 10^14 M⊙, and 4.6 × 10^3 above 10^15 M⊙ at z=0.It also contains 4.7 × 10^4 haloes above 10^14 M⊙ at z=1 and 1.4 × 10^3 at z=2.Source: §7 · p. 32
  • Hydrodynamical HMFs converge nearly perfectly across box sizes up to 10^15 M⊙ and across resolutions for cluster masses, but diverge at lower masses.For 11.7 < log10 M200m/M⊙ < 13.0, resolution differences are <5%; below that range, intermediate-resolution haloes may not have formed stars.Source: §7 · p. 32
  • Baryons reduce the HMF by more than 5% below 7 × 10^11 M⊙ and from 2 × 10^12 to 1 × 10^14 M⊙, with an ≈18% maximum at 2 × 10^13 M⊙.At 10^12 M⊙ the HMF is nearly unchanged, and at masses ≫10^14 M⊙ the hydrodynamical and DMO HMFs converge; low- and high-mass suppression are attributed to stellar and AGN feedback, respectively.Source: §7 · p. 32
  • The baryonic effect on the HMF is insensitive to tested cosmologies, although the simulations do not vary the universal baryon fraction.That fraction may have the largest impact absent subgrid recalibration.Source: §7 · p. 32
  • For M200m > 10^13 M⊙, smaller calibrated cluster gas fractions produce stronger HMF suppression; the smallest-gas-fraction model exceeds 5% suppression up to 10^15 M⊙.Source: §7 · p. 32
  • Reducing observed stellar masses by 0.14 dex strengthens suppression by 5–10% near 10^12 M⊙, while Jet feedback weakens it for 10^13–10^14 M⊙ haloes.At this resolution, AGN implementation has little HMF effect when models reproduce the same halo gas fractions; uncertainty between gas-fraction variants implies ∼10% HMF uncertainty at 10^14 M⊙.Source: §7 · p. 32, Figure 20 · p. 33
  • For masses ≫10^13 M⊙, cosmo-OWLS brackets fiducial FLAMINGO, while Magneticum agrees well at 10^14–10^15 M⊙; failing to model baryonic effects can bias cluster-count cosmology.At lower masses, cosmo-OWLS and Magneticum predict stronger suppression than FLAMINGO variations.Source: §7 · p. 32, Figure 20 · p. 33

8 MATTER POWER SPECTRA

FLAMINGO finds that baryons leave large-scale matter power nearly unchanged, suppress it at intermediate scales, and boost it at small scales. The magnitude and scale dependence vary with gas fractions and AGN feedback, while cluster baryon fractions predict power suppression accurately over a limited range of scales.

8 MATTER POWER SPECTRA

  • Gas suppression dominates over k∼1–10^2 h Mpc−1, while condensed gas and stars boost power at very small scales, with stellar contributions dominant above k≫10 h Mpc−1.Gas ejection from low-mass clusters is associated with suppression at k≲10 h Mpc−1 and from groups at k≳10 h Mpc−1.Source: §8 · pp. 33–34, Figure 21 · p. 34
  • Baryons trace total matter on large scales, suppress power on intermediate scales, and boost it on small scales.The ratio Phydro/ PDMO is approximately 1, below 1, and above 1 across those respective regimes.Source: §8 · p. 34, Figure 22 · p. 35
  • Baryonic effects converge across box sizes, but resolution differences exceed 1% beyond k>3 h Mpc−1 for L1_m10 and k>20 h Mpc−1 for L1_m9 relative to L1_m8.Source: §8 · p. 34
  • BAHAMAS predicts stronger suppression than fiducial FLAMINGO, which the authors suggest may indicate gas is ejected to larger distances; the reason for its scale-dependent difference is not explained by the compared fractions.Source: §8 · p. 34
  • The baryonic effect appears insensitive to tested cosmologies, but the simulations do not explore large variations in cosmic baryon fraction.Such variations might have the strongest interaction with galaxy-formation physics.Source: §8 · p. 34
  • Gas fractions within R500c do not fully constrain baryonic suppression: equal-SMF models with smaller cluster gas fractions suppress power more, but BAHAMAS differs despite fractions closer to fiducial FLAMINGO.The fgas−2σ and fgas+2σ models are not necessarily bounds on suppression; BAHAMAS can reach suppression as strong as fgas−4σ or fgas−8σ models.Source: §8 · p. 34
  • Jet feedback changes the scale dependence, producing relatively stronger suppression on larger scales; at fixed gas fraction, AGN implementation retains a residual effect.Differences are small in percentage points where large-scale power itself is only a few percent below DMO; SMF uncertainties matter mainly for k≳10 h Mpc−1.Source: §8 · p. 34, Figure 22 · p. 35
  • At k=1 h Mpc−1, the Van Daalen et al. (2020) relation predicts nearly all simulations’ matter power spectra to ∼1% accuracy from their DMO power and cluster mean baryon fraction.The same holds at k=0.5 and 2.0 h Mpc−1, while deviations and resolution effects are larger at k=10 h Mpc−1.Source: §8 · pp. 34–36, Figure 23 · p. 36

9 SUMMARY

FLAMINGO provides large-volume hydrodynamical simulations with machine-learning-calibrated galaxy-formation models and variations specified through observable shifts. Its converged predictions reproduce calibration data and show that baryonic effects alter halo abundances and matter clustering, while some galaxy properties remain unresolved or discrepant.

9 SUMMARY

  • FLAMINGO combines three resolutions, flagship 1 and 2.8 Gpc boxes, and 12 additional intermediate-resolution simulations varying cosmology and galaxy-formation physics; the largest run follows 2.8 × 10^11 particles.Lightcones are generated on the fly for up to eight observers, and each hydrodynamical run has a dark-matter-only counterpart.Source: §9 · p. 36
  • Machine-learning emulators calibrate subgrid models separately by resolution to observed stellar mass functions, cluster gas fractions, and the black-hole–stellar-mass relation, accounting for observational errors and biases.Variants shift stellar mass functions and/or gas fractions relative to calibration data, while two models use jet-like rather than thermal isotropic AGN feedback.Source: §9 · pp. 36–37
  • The fiducial models reproduce the calibration data within converged mass ranges, and cluster gas-fraction agreement extends beyond the calibration range to over an order of magnitude higher cluster masses for the high-resolution model.At stellar masses ≳10^12 M⊙, SMFs differ substantially across simulations and from calibration data; aperture and intracluster-light systematics complicate comparisons.Source: §9 · p. 37
  • Galaxy predictions reproduce cosmic star-formation history and generally agree with observations for converged sSFR, passive fraction, and metallicity, but passive fractions at ≳10^12 M⊙ and galaxy sizes show discrepancies.Jet models improve the passive-fraction comparison but still do not quench star formation sufficiently in very massive galaxies; sizes are generally overestimated except in the high-resolution simulation at high mass.Source: §9 · p. 37
  • The fiducial model agrees excellently with low-redshift cluster scaling-relation data, while thermal-SZE/CMB-lensing cross-correlations agree well with data that are slightly better fit by low-S8 and high-neutrino-mass cosmologies.X-ray relations respond to gas fractions but not to the investigated cosmology, stellar-mass-function, or AGN-feedback variations; cross-correlation predictions show observer-to-observer cosmic variance on large scales.Source: §9 · p. 37
  • Baryonic effects reduce the halo mass function by ≈20 per cent for low-mass clusters near 10^13 M⊙, while the difference is below 5 per cent near 10^15 M⊙ for fiducial gas fractions.Gas fraction is the main factor determining cluster-mass suppression; its observational uncertainty translates into ∼10 per cent uncertainty in the halo mass function at 10^14 M⊙.Source: §9 · p. 37
  • The matter power spectrum is suppressed at 1 ≲ k ≲ 10 h Mpc−1 and boosted at k ≳ 10^2 h Mpc−1, with suppression exceeding 10 per cent near k ∼ 10 h Mpc−1.Smoother gas drives suppression on these scales, while stars mainly drive the boost at higher k; the fiducial model’s large-scale suppression is smaller than in fiducial BAHAMAS, and the simulations follow the Van Daalen et al. (2020) relation.Source: §9 · pp. 37–38
  • The paper documents FLAMINGO methods and basic galaxy and cluster results, and previews applications including baryonic corrections to dark-matter-only simulations and future large-scale-structure emulation.The planned emulation suite is intended to vary cosmology and baryonic effects jointly.Source: §9 · p. 38

APPENDIX A: LIGHTCONE DATA

The simulation code produces full-sky lightcone particle output and HEALPix maps for specified quantities and redshift intervals. Observer placement differs between the 1 Gpc and larger simulation boxes.

APPENDIX A: LIGHTCONE DATA

  • The Swift code outputs particles crossing one or more observers’ past full-sky lightcones and generates HEALPix maps for user-specified quantities and redshift intervals.This functionality was added for the FLAMINGO project.Source: Appendix A · p. 40
  • The 1 Gpc boxes use two observers at opposite quarter-box coordinates, while larger boxes use eight observers at all ±L/4 coordinate combinations.The positions are specified relative to the box centre.Source: Appendix A · p. 40

A1.1 Implementation

The implementation identifies particles that may cross an observer’s lightcone during each time step, including periodic copies. Particle output thresholds and observer counts are summarized in Table A1.

A1.1 Implementation

  • At each time step, a shell around each observer bounds possible lightcone crossings, with an inner boundary layer accounting for particle motion under the assumption that particles travel below light speed.The shell is set from the earliest and latest times particles may be drifted in that step.Source: A1.1 Implementation · p. 40
  • Table A1 lists observer counts and maximum output redshifts by particle type, including filtered-gas thresholds described in the appendix.For simulations with two lightcones, individual particles are output only for the first lightcone.Source: Table A1 · p. 41
  • Periodic copies of the simulation volume overlapping the shell are checked during particle drift, and crossed particles are interpolated to their crossing redshift and buffered for output.A cell-based optimization restricts checks to periodic replications that particles in the current cell may cross.Source: A1.1 Implementation · p. 41

A1.2 Redshift limits

Lightcone redshift limits vary by particle type, with separate thresholds for all gas and filtered gas. Gas filtering uses temperature and density cuts selected through experimentation with X-ray observables.

A1.2 Redshift limits

  • All gas is output below its listed redshift limit, while filtered gas additionally requires T > 10^5 K and nH > 10^-6(1 + z)^4 cm−3.The temperature and density thresholds were chosen based on experimentation with X-ray observables.Source: A1.2 Redshift limits · p. 41
  • Dark matter, neutrinos, and unfiltered gas are output to z = 0.25 in 1 Gpc boxes and z = 0.78 in 2.8 Gpc boxes, approximately corresponding to box size.Gas contributing significantly to X-ray and SZE observations is stored to z = 0.5; black holes are stored below z = 15.Source: A1.2 Redshift limits · p. 41

A2 HEALPix maps

FLAMINGO creates on-the-fly HEALPix maps by accumulating particle contributions into redshift-shell maps for each observer. The method smooths gas contributions where needed and distributes map work across compute nodes.

A2 HEALPix maps

  • Lightcone quantities are accumulated into full-sky HEALPix maps for concentric shells, with shell boundaries and maximum redshifts varying across box sizes and observers.The maps cover 68 shells to z=5 before using wider-spaced boundaries at higher redshift.Source: A2 HEALPix maps · pp. 41–42

A2.1 Smoothing the HEALPix maps

  • Gas smoothing converts each particle’s SPH smoothing length and observer distance into an angular search radius, then distributes contributions across pixels using projected-kernel weights when needed.Particles with search radii below the maximum pixel radius contribute wholly to their position pixel; the projected kernel uses the Wendland C2 kernel.Source: A2.1 Smoothing the HEALPix maps · p. 42

A2.2 Parallelisation scheme

  • Maps are distributed across compute nodes by contiguous HEALPix ring-pixel ranges, while shells are written and deallocated as particles pass through them.Usually only one or two shell maps are in memory at a time, regardless of the total number of shells.Source: A2.2 Parallelisation scheme · p. 42, Table A2 · p. 42

A2.3 Quantities stored in HEALPix maps

The lightcone maps record particle masses and star formation, alongside smoothed gas observables including X-ray, Sunyaev–Zel'dovich, and dispersion-measure signals. Some maps exclude recently AGN-heated gas, and implementation bugs required approximate corrections to the kinematic-SZE and dispersion-measure maps.

A2.3 Quantities stored in HEALPix maps

  • Mass maps include all particle types and individual species except black holes, while star-formation-rate maps accumulate each crossing gas particle’s rate without smoothing.Gas mass is stored both unsmoothed and SPH-smoothed.Source: A2.3 Quantities stored in HEALPix maps · p. 42
  • Smoothed X-ray energy and photon-flux maps cover three observer-frame bands, excluding gas recently and directly heated by AGN when its temperature falls within the stated feedback-related range.The bands are eROSITA 0.2–2.3 keV, eROSITA 2.3–8.0 keV, and ROSAT 0.5–2.0 keV.Source: A2.3 Quantities stored in HEALPix maps · p. 42
  • Thermal-SZE Compton-y maps are smoothed, and gas whose temperature was affected by recent direct AGN feedback is excluded.The map accumulates a dimensionless quantity derived from particle mass, pixel solid angle, and angular-diameter distance.Source: A2.3 Quantities stored in HEALPix maps · pp. 42–43
  • Kinematic-SZE Doppler-b maps exclude recently AGN-heated particles, and an extra scale-factor bug was approximately corrected using each shell’s midpoint expansion factor.The maps can be corrected precisely from particle lightcone outputs where those outputs were stored.Source: A2.3 Quantities stored in HEALPix maps · p. 43
  • Dispersion-measure maps exclude recently AGN-heated gas, and a missing scale factor was approximately corrected by multiplying by the shell-midpoint expansion factor.Precise correction is possible from particle lightcone outputs where available.Source: A2.3 Quantities stored in HEALPix maps · p. 43

APPENDIX B: THE CHOICE OF THE LINEAR PHASES FOR THE INITIAL CONDITIONS

The FLAMINGO initial conditions use updated Panphasia phases, with descriptors specifying phases for simulation volumes and their future zooms. The authors describe the initial conditions as an advance for CDM, baryons, and neutrinos.

APPENDIX B: THE CHOICE OF THE LINEAR PHASES FOR THE INITIAL CONDITIONS

  • The FLAMINGO Gaussian phases use an updated Panphasia field with sixth-order polynomials and the ThreeFry4x64 pseudo-random generator.These replace the S8 scheme and a multiple linear congruence generator, respectively.Source: Appendix B · p. 43
  • The authors characterize the initial conditions as a significant accuracy advance for cosmological CDM, baryon, and neutrino simulations, with no known code matching their zoom accuracy across all three components.DMO zoom initial conditions for FLAMINGO volumes can be generated with the latest IC_Gen code.Source: Appendix B · p. 43
  • Table A3 descriptors specify phases for different box sizes and, in principle, define phases for future zoom simulations; variations within a volume share a descriptor.Both the public and FLAMINGO versions of monofonIC can use the new descriptors.Source: Appendix B · p. 43, Table A3 · p. 44
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