APOSTLE/EAGLE Cosmological Simulations

Updated 1 April 2026

APOSTLE/EAGLE simulations are a suite of cosmological hydrodynamical projects that model galaxy formation and evolution using state-of-the-art SPH methods and empirically tuned feedback processes.
The projects integrate large-volume and targeted zoom-in simulations to capture detailed dynamics from group environments to Local Group analogues with high resolution and calibrated subgrid physics.
These simulations also enable realistic synthetic experiments—such as strong lensing and satellite dynamics studies—providing actionable insights into the interplay between baryonic and dark matter.

The APOSTLE and EAGLE projects constitute a comprehensive suite of cosmological hydrodynamical simulations designed to model galaxy formation and evolution across a broad range of scales, environments, and physical conditions. EAGLE (Evolution and Assembly of GaLaxies and their Environments) delivers a set of large-volume periodic simulations focused on field and group galaxies, while APOSTLE (A Project Of Simulating The Local Environment) implements targeted zoom-in simulations to investigate the Local Group—specifically, analogues of the Milky Way, Andromeda, and their satellite populations—using identical subgrid physics and numerical methods. Both projects employ the “ANARCHY” pressure-entropy SPH formulation, advanced subgrid models for stellar and AGN feedback, and rigorous calibration to key low-redshift observables. Extensions such as C-EAGLE target rich cluster environments, while pipelines such as SEAGLE enable observationally realistic synthetic lensing experiments. Together, the APOSTLE/EAGLE simulations enable detailed, self-consistent modeling of galaxy populations, internal structures, and the interplay between baryonic and dark matter on cosmological scales.

1. Simulation Frameworks and Computational Setup

EAGLE

EAGLE simulations employ volumes of 25, 50, or 100 cMpc with particle numbers up to $2 \times 1504^3$ in the largest boxes. The reference run Ref-L100N1504, for example, utilizes a $100$ cMpc box with baryonic particle mass $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ and dark matter mass $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ , with comoving Plummer-equivalent softening of $2.66$ ckpc, capped at $0.7$ pkpc for $z < 2.8$ (Schaye et al., 2014, McAlpine et al., 2015). The adopted cosmology closely follows Planck 2013: $\Omega_\mathrm{m}=0.307,\ \Omega_\Lambda=0.693,\ \Omega_\mathrm{b}=0.04825,\ h=0.6777,\ \sigma_8=0.8288,\ n_s=0.9611$ .

The hydrodynamics scheme is the ANARCHY SPH formulation, featuring a pressure-entropy approach (Hopkins 2013), Wendland $C^2$ kernel, a time-step limiter (Durier & Dalla Vecchia 2012), and improved viscosity/conduction switches. Subgrid physics includes element-by-element cooling in a UV/X-ray background, pressure-dependent star formation following the Kennicutt–Schmidt law (Schaye & Dalla Vecchia 2008), stochastic thermal stellar feedback, and Bondi-limited black-hole accretion with thermal AGN feedback (Schaye et al., 2014, McAlpine et al., 2015, Schaller et al., 2015). Free parameters governing feedback and AGN heating ( $f_\mathrm{th}$ , $100$0, $100$1) are empirically calibrated to match the $100$2 stellar mass function, galaxy sizes, and black hole mass–stellar mass relation.

APOSTLE

APOSTLE employs zoom-in regions extracted from a $100$3 parent N-body simulation (WMAP-7 cosmology), with a focus on environments mimicking the observed kinematics and environment of the Local Group (Fattahi et al., 2015, Sawala et al., 2015). Twelve paired-halo volumes are selected according to separation, mass, approach and tangential velocities, and Hubble flow constraints, targeting a total system mass $100$4–$100$5 with a median $100$6.

The APOSTLE re-simulations are performed at three mass resolutions (L1: $100$7, $100$8 pc; L2: $100$9, $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 0 pc; L3: $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 1, $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 2 pc), with the same hydrodynamical and subgrid physics as EAGLE (Sawala et al., 2015, Oman, 2017). This allows resolution of satellite galaxies down to $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 3 and self-consistent modeling of baryonic processes relevant for dwarf galaxies and satellites.

2. Subgrid Physics, Calibration, and Hydrodynamics

Both projects implement identical subgrid physics, with all hydrodynamical runs using the pressure–entropy ANARCHY SPH (Schaller et al., 2015). Key ingredients include:

Radiative Cooling/Heating: Tabulated, element-by-element cooling rates with a uniform UV/X-ray background, accounting for hydrogen reionization at $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 4 with an imposed heat boost.
Star Formation: Stochastic, pressure-law-based star formation imposed above a metallicity-dependent density threshold: $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 5 cm $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 6, calibrated to reproduce the Kennicutt–Schmidt relation (Sawala et al., 2015, McAlpine et al., 2015).
Stellar Feedback: Thermal injection of energy into ISM by newly formed stars with a temperature jump $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 7 K, with a feedback efficiency $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 8 that varies with local gas density and metallicity, bounded by $m_\mathrm{gas} = 1.81 \times 10^6\,M_\odot$ 9 (Schaye et al., 2014).
Black Hole Growth and AGN Feedback: Seeded in haloes above $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 0, gas accretion with a viscosity-limited Bondi prescription, and thermal AGN feedback heating neighboring gas particles by $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 1 K (EAGLE Ref), or $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 2 K (AGNdT9/C-EAGLE), with feedback efficiency $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 3 (Schaye et al., 2014, Barnes et al., 2017).

Calibration is achieved using the $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 4 GSMF, galaxy size–mass relations, and black hole scaling relations. "Weak convergence" is adopted: subgrid parameter values are re-tuned if resolution changes outside an empirically determined 'converged window' (Ludlow et al., 2019).

3. Local Group, Satellite, and Cluster Zooms

Local Group (APOSTLE)

APOSTLE directly addresses the formation, internal structure, and dynamical properties of satellite systems in MW- and M31-mass haloes. Realistic populations of satellites and their kinematics are reproduced for primary halo masses $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 5– $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 6 (Sawala et al., 2015). Simulated satellite abundance, stellar mass functions, velocity dispersions, and spatial anisotropies are in concordance with both the observed MW and M31 systems. “Missing satellite”, “too-big-to-fail”, and “planes of satellites” issues are resolved once the effects of baryon-induced subhalo mass loss and reionization-driven suppression of star formation in low-mass haloes are included (Sawala et al., 2015, Lovell et al., 2016).

LMC analogues are found to be more frequent in Local Group-like environments, with eccentric first-infall orbits and associated companions distributed along their orbital planes. Only a mild contribution to the total satellite population is found from these Magellanic analogues: $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 7 satellites with $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 8 per LMC-like object (Santos-Santos et al., 2020).

Cluster Environment (C-EAGLE)

C-EAGLE simulates 30 galaxy clusters ( $m_\mathrm{DM} = 9.70 \times 10^6\,M_\odot$ 9–$2.66$0) using the AGNdT9 EAGLE variant, featuring enhanced AGN feedback heating ($2.66$1 K). Global properties such as temperature–mass, $2.66$2–mass, stellar and black hole scaling relations, and integrated ICM metallicities are well-reproduced (Barnes et al., 2017). However, clusters remain systematically gas-rich relative to X-ray and Sunyaev–Zel'dovich measurements (by $2.66$3), and show large, high-entropy, non-cool ICM cores, reflecting the limitations of efficient but non-directional AGN feedback in massive, high-redshift progenitors.

4. Key Scientific Results and Applications

Star Formation, Scaling Relations, and Metallicity

EAGLE and APOSTLE accurately reproduce:

The galaxy stellar mass function at $2.66$4 over $2.66$5–$2.66$6 ($2.66$7 dex residual) (Schaye et al., 2014).
The stellar mass–halo mass relation, with peak galaxy formation efficiency near $2.66$8.
Projected half-mass radii for disc galaxies, Tully–Fisher relation, mass–metallicity relations for both gas and stars above $2.66$9 (McAlpine et al., 2015).
Specific star formation rates and passive fractions matched to GAMA, SDSS and other low-redshift surveys.

Principal component analysis reveals a robust 'fundamental plane of star formation' defined by neutral gas fraction, $0.7$0, and SFR, with negligible scatter and redshift evolution (Lagos et al., 2015).

Satellite Dynamics and Internal Kinematics

The observed velocity dispersion–stellar mass relation for dwarf spheroidals is reproduced without requiring DM cores (Sawala et al., 2015).
Cusp–core tension in rotation curve data is shown to be largely attributable to non-circular motions; factoring these in removes the need for exotic DM physics or core formation (Oman, 2017).
The suppression of satellite formation in sterile neutrino WDM cosmologies tracks the reduction in low-mass subhalo concentrations, providing a direct test for WDM particle models (Lovell et al., 2016).

Strong Lensing and SEAGLE Pipeline

The SEAGLE program exploits EAGLE (and by extension, APOSTLE) outputs to create synthetic strong lens images via GLAMER ray-tracing, followed by realistic forward-modeling and mass model inference using LENSED. Comparative analysis of lensing observables indicates that EAGLE early-type galaxies have a mean 3D density slope $0.7$1 (rms), steeper than observed samples (SL2S: $0.7$2, SLACS: $0.7$3). Model degeneracies, notably a strong shear–ellipticity correlation ($0.7$4), are highlighted (Mukherjee et al., 2018).

5. Resolution, Numerical Convergence, and Public Data Infrastructure

Convergence studies show that hydrodynamical galaxy formation runs are strongly sensitive to gravitational softening: robust predictions for star formation, GSMF, and galaxy sizes are achieved only within a narrow window ($0.7$5–$0.7$6 calibration value) for $0.7$7, with both excessive and insufficient softening yielding artifacts in star formation, feedback, and structural parameters (Ludlow et al., 2019).

EAGLE’s data products, including both integrated galaxy catalogs and full particle-level snapshots, follow a well-documented relational schema, supporting advanced queries and cross-redshift merger trees (McAlpine et al., 2015, team, 2017). APOSTLE data are less universally public but follow analogous storage and analysis conventions.

6. Extensions and Thematic Studies

Variable IMF models (e.g., bottom- and top-heavy variations) have been implemented and calibrated within the EAGLE framework, showing that only bottom-heavy IMF variations can simultaneously satisfy dynamical, chemical, and observational constraints for early-type galaxies, while top-heavy models overproduce SFRs, gas fractions, and galaxy sizes at high mass (Barber et al., 2018).
EAGLE has been exploited to study the weak dependence of global star formation efficiency and galaxy formation on the cosmological constant, with important implications for anthropic explanations in the multiverse context (Barnes et al., 2018).
Systematic predictions for DM decay fluxes and line widths have been generated for galaxies and clusters (including APOSTLE and C-EAGLE runs), supporting observational strategies for X-ray searches for decaying DM (Lovell et al., 2018).

The APOSTLE/EAGLE simulations represent an advanced, empirically validated platform for cosmological hydrodynamics, galaxy formation, and environmental structure studies, supporting diverse investigations ranging from Local Group satellite dynamics and strong lensing to galaxy clusters and beyond (Schaye et al., 2014, Sawala et al., 2015, Santos-Santos et al., 2020, Lagos et al., 2015, Mukherjee et al., 2018, Barnes et al., 2017, Ludlow et al., 2019).