EAGLE Cosmological Simulations

• EAGLE Cosmological Simulations are a suite of advanced hydrodynamical models that simulate galaxy formation and evolution with state-of-the-art SPH methods.
• They employ a modified GADGET-3 code with the ANARCHY SPH scheme and detailed subgrid physics to accurately model star formation, AGN feedback, and chemical enrichment.
• The simulations achieve benchmark consistency with observed galaxy stellar mass functions and black hole scaling relations, supported by publicly accessible data products.

The EAGLE (Evolution and Assembly of GaLaxies and their Environments) cosmological simulation suite is a flagship set of cosmological, hydrodynamical simulations designed for comprehensive modeling of galaxy formation and evolution. Utilizing a modified version of GADGET-3 with the “ANARCHY” smoothed-particle hydrodynamics (SPH) implementation, EAGLE incorporates a broad array of subgrid physics models, rigorously calibrated to reproduce pivotal low-redshift galaxy observables. Operating at mass resolutions sufficient to marginally resolve the Jeans mass at star formation threshold, EAGLE leverages Planck cosmology and tracks the coupled evolution of dark matter, gas, stars, and supermassive black holes (SMBHs) across $\sim$12 to 100 comoving Mpc volumes with particle masses on the order of $10^6\,M_\odot$ (gas) and $10^7\,M_\odot$ (dark matter). The suite has established benchmark results for the present-day galaxy stellar mass function, SMBH mass function, galaxy clustering statistics, chemical enrichment, outflow rates, and environmental dependencies (Artale et al., 2016Rosas-Guevara et al., 2016Barnes et al., 2017Rossi et al., 2018McAlpine et al., 2015Furlong et al., 2014).

1. Numerical Framework and Physical Models

EAGLE simulations are based on a heavily modified GADGET-3 architecture, featuring the ANARCHY SPH scheme with a pressure-entropy formulation, Wendland C2 kernel (58 neighbours), advanced viscosity switch, and time-step limiter. The gravitational solver employs TreePM algorithms, and the cosmology is set to Planck Collaboration 2013/2014 values: $\Omega_{\rm m}=0.307$, $\Omega_\Lambda=0.693$, $\Omega_{\rm b}=0.04825$, $h=0.6777$, $\sigma_8=0.8288$, $n_s=0.9611$, $Y=0.248$.

Subgrid physics encompasses:

• Radiative cooling and heating: element-by-element with CLOUDY-based tables and a dynamic Haardt & Madau UV/X-ray background [Wiersma et al. 2009].
• Star formation: follows a pressure-law Kennicutt–Schmidt relation above a metallicity-dependent density threshold, $$n_{\rm H}^*(Z)=0.1~\mathrm{cm^{-3}} (Z/0.002)^{-0.64}$$, with an imposed polytropic equation of state ($P\propto\rho^{4/3}$) [Schaye & Dalla Vecchia 2008].
• Stellar evolution and enrichment: tracks yields (AGB, SN II, SN Ia, 11 elements) via mass loss prescriptions [Wiersma et al. 2009].
• Stellar feedback: thermal injection, stochastically raising the temperature of neighbour gas particles by $\Delta T = 10^{7.5}\,\mathrm{K}$ with injected energy per Chabrier-IMF star formation event modulated by local metallicity and density dependent feedback efficiency $f_{\rm th}$.
• Black hole physics: seeds inserted in halos $M_{200} > 10^{10}~M_\odot$, Bondi-Hoyle accretion with angular-momentum limiters and a fixed radiative efficiency ($\epsilon_r=0.1$), and AGN feedback via thermal stochastic heating with $\Delta T_{\rm AGN}=10^{8.5}-10^{9}\,\mathrm{K}$, coupling efficiency $\epsilon_f=0.15$.

Gravitational softening is comoving ($\epsilon_{\rm com}=2.66~\mathrm{kpc}$) down to $z=2.8$ then fixed proper ($\epsilon_{\rm phys}=0.7~\mathrm{kpc}$).

2. Calibration, Resolution, and Model Variants

EAGLE models are stringently calibrated to replicate:

• The galaxy stellar mass function (GSMF) at $z\approx0.1$ [Baldry et al. 2012].
• Present-day galaxy half-light sizes [Shen et al. 2003].
• The $M_{\rm BH}$–$M_*$ relation.

Resolution strategy ensures marginal Jeans mass resolution ($\sim8\times$ SPH smoothing masses at threshold density). The Reference run “Ref-L100N1504” corresponds to a $100~\mathrm{cMpc}$ cube with $2\times1504^3$ particles, $m_{\rm gas}=1.81\times10^6~M_\odot$, and $m_{\rm DM}=9.7\times10^6~M_\odot$.

Thirteen runs explore the subgrid-physics parameter space, including models with fixed feedback efficiency (FBconst), logistic metallicity or velocity-dispersion scaling (FBZ, FBσ), variable AGN heating temperature (AGNdT8/9), and density/polytropic ISM variations (Crain et al., 2015). High-resolution recalibrated runs (“Recal-L025N0752”) employ $m_{\rm gas}\approx2.26\times10^5~M_\odot$.

3. Clustering, Halo-Galaxy Connection, and Quenching

Small-scale ($r_p \lesssim 4~h^{-1}\,\mathrm{Mpc}$) galaxy clustering statistics in EAGLE closely match those of the GAMA survey when binned by $M_*$, color, or luminosity. The projected correlation function $w_p(r_p)$ is computed via Landy–Szalay estimators and measured against a canonical power law, $$w_p^{\rm ref}(r_p) \propto r_p\left(\frac{r_0}{r_p}\right)^\gamma$$, where $r_0=5.33~h^{-1}\,\mathrm{Mpc},\ \gamma=1.8$.

At fixed $M_*$, red galaxies exhibit stronger clustering than blue counterparts, consistent with environmental and ram-pressure quenching. EAGLE reproduces halo occupation distributions: central galaxies of $M_*\sim10^{9.5-10}~h^{-2}~M_\odot$ reside in $M_h\sim10^{11.2-12.5}~h^{-1}~M_\odot$ halos; satellites of the same $M_*$ preferentially inhabit $M_h\gtrsim10^{12}~h^{-1}~M_\odot$ (Artale et al., 2016).

Principal component analysis (PCA) demonstrates a robust co-evolution axis ($M_{\rm halo}$–$M_*$–SFR), an environmental quenching axis (anti-correlation of $M_{\rm halo}$ and SFR), and a mass-quenching regime above $M_*\sim10^{10}~M_\odot$, persistent to $z=4$ (Cochrane et al., 2018).

4. Black Hole Growth, AGN Feedback, and Galaxy–Halo Scaling

SMBH physics are tightly aligned with observed $z=0$ mass functions. The local SMBH mass function is consistent within $\sim0.2~\mathrm{dex}$ of indirect observational estimates, and the present-day SMBH mass density $$\rho_{\rm BH}=2.6\times10^5~M_\odot~\mathrm{Mpc}^{-3}$$. Eddington ratio distributions reveal an AGN duty cycle of $\sim1\%$ at $z=0.1$—in line with quasar lifetime estimates. The $M_{\rm BH}$–$M_{200}$ relation transitions from sub-seed masses at $M_{200}\sim10^{11.6}~M_\odot$ to rapid growth and then flattens (Rosas-Guevara et al., 2016).

AGN feedback efficiency and energy per event ($\Delta T_{\rm AGN}$) critically determine massive galaxy quenching and the high-mass cutoff of the GSMF. Higher AGN heating ($10^9~\mathrm{K}$) suppresses metallicity and flattens the $M_*$–$Z_*$ relation at high mass. The integrated star formation efficiency exhibits weak dependence on $\Lambda$ up to large multiples of the observed value, limiting anthropic constraints on the cosmological constant from galaxy formation alone (Barnes et al., 2018).

5. Outflows, Gas Recycling, and ICM Properties

Outflow dynamics in EAGLE manifest as mass loading factors $\eta\propto V_c^{-3/2}$ for stellar feedback–dominated galaxies, with an AGN-driven upturn for halo masses $>10^{12}~M_\odot$. The ratio of CGM/halo-scale to ISM-scale outflow rates increases with halo mass (up to $\sim10$ at $M_{200}\sim10^{13}~M_\odot$), indicating significant entrainment and propagation effects. Wind recycling onto galaxies is generally inefficient: first-time gas infall dominates over recycled flows except at $M_{200}\sim10^{12}~M_\odot$, with galaxy-scale recycling efficiencies $\eta_{\rm rec,gal}\ll1$ and return timescales $\sim$Hubble time. This suppresses star formation in low-mass and high-mass systems via strong preventative feedback (Mitchell et al., 2019Mitchell et al., 2020).

Cluster-scale C-EAGLE zoom simulations (AGNdT9 model) reproduce bulk stellar and BH scaling relations, X-ray and Sunyaev–Zel'dovich properties, but systematically overpredict gas fractions and central entropy, highlighting limitations in AGN feedback efficiency at high $z$ and the need for more bursty/anisotropic implementations (Barnes et al., 2017).

6. Chemical Evolution and J–M–f_{atm} Relations

A well-defined $M_*$–$Z_*$ sequence is observed in EAGLE, with $Z_*\approx0.02-0.12$ over $M_*\approx10^9-10^{11}~M_\odot$, and a strong anti-correlation with gas fraction $$\partial\log_{10}Z_*/\partial\log_{10}f_{\rm SF,gas}\approx-0.57$$. AGN feedback at high mass reduces stellar metallicity via star formation quenching and metal-enriched gas ejection. This relation evolves weakly with redshift ($|\Delta\alpha|<0.05$ over $0Rossi et al., 2018).

The joint plane in $(j_{\rm bar}, M_{\rm bar}, f_{\rm atm})$ space is tightly constrained for $f_{\rm atm}>0.01$, with EAGLE yielding $$j_{\rm bar}\propto M_{\rm bar}^{0.94} f_{\rm atm}^{0.90}$$ (scatter $\sigma=0.25$ dex). For gas-poor systems ($f_{\rm atm}<0.01$), EAGLE galaxies can retain high $j$ values, indicating a breakdown of the disc stability ansatz (Hardwick et al., 2023).

7. Data Products, Access, and Scientific Impact

EAGLE simulation outputs are publicly available as SQL-accessible catalogues containing galaxy/halo properties at 29 snapshots from $z=20$ to $z=0$, with merger-tree indexing and synthetic photometry/images (McAlpine et al., 2015). The particle data (HDF5 format, Peano–Hilbert indexing) enable spatially resolved studies of stellar/gas/DM/BH properties, with recommended best practices for region selection and parallel reading (team, 2017). Cosmological applications include synthetic FRB dispersion measures as a function of redshift, with robust statistical prescriptions for DM(z) and scatter (python API in FRUITBAT) (Batten et al., 2020).

Comparisons to other major hydrodynamical suites (Illustris, Magneticum, Horizon-AGN, FIRE, Auriga) underline EAGLE’s distinct strategy: locally-calibrated pressure-law star formation, stochastic thermal feedback (no explicit wind velocity/mass loading), and extended validation against diverse observational data. Systematic differences in outflow propagation, recycling efficiency, and clustering slopes remain active areas for cross-simulation analysis. EAGLE’s calibrated, transparent physical prescriptions, and full public catalogue access have redefined standards for cosmological simulation-based astrophysical inference.