--- title: APOSTLE/EAGLE Cosmological Simulations url: https://www.emergentmind.com/topics/apostle-eagle-cosmological-hydrodynamical-simulations type: topic --- # APOSTLE/EAGLE Cosmological Simulations 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 $z < 2.8$ [1407.7040, 1510.01320]. 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 [1407.7040, 1510.01320, 1509.05056]. Free parameters governing feedback and AGN heating ($f_\mathrm{th}$, $C_\mathrm{visc}$, $\Delta T_\mathrm{AGN}$) are empirically calibrated to match the $z\approx 0$ stellar mass function, galaxy sizes, and black hole mass–stellar mass relation. ### APOSTLE APOSTLE employs zoom-in regions extracted from a $100^3\,\mathrm{Mpc}^3$ parent N-body simulation (WMAP-7 cosmology), with a focus on environments mimicking the observed kinematics and environment of the Local Group [1507.03643, 1511.01098]. Twelve paired-halo volumes are selected according to separation, mass, approach and tangential velocities, and Hubble flow constraints, targeting a total system mass $M_{200,\rm MW}+M_{200,\rm M31}\sim 1.6$–$3.6\times10^{12}\,M_\odot$ with a median $2.3\times10^{12}\,M_\odot$. The APOSTLE re-simulations are performed at three mass resolutions (L1: $m_\mathrm{gas}=1\times10^4\,M_\odot$, $\epsilon_\mathrm{max}=134$ pc; L2: $1.2\times10^5\,M_\odot$, $307$ pc; L3: $1.5\times10^6\,M_\odot$, $711$ pc), with the same hydrodynamical and subgrid physics as EAGLE [1511.01098, 1712.02562]. This allows resolution of satellite galaxies down to $M_*\sim10^5\,M_\odot$ 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 [1509.05056]. Key ingredients include: - **Radiative Cooling/Heating**: Tabulated, element-by-element cooling rates with a uniform UV/X-ray background, accounting for hydrogen reionization at $z=11.5$ with an imposed heat boost. - **Star Formation**: Stochastic, pressure-law-based star formation imposed above a metallicity-dependent density threshold: $n_\mathrm{H,th}(Z)=0.1\,(Z/0.002)^{-0.64}$ cm$^{-3}$, calibrated to reproduce the Kennicutt–Schmidt relation [1511.01098, 1510.01320]. - **Stellar Feedback**: Thermal injection of energy into ISM by newly formed stars with a temperature jump $\Delta T=10^{7.5}$ K, with a feedback efficiency $f_\mathrm{th}$ that varies with local gas density and metallicity, bounded by $0.3\leq f_\mathrm{th}\leq 3$ [1407.7040]. - **Black Hole Growth and AGN Feedback**: Seeded in haloes above $10^{10}\,M_\odot$, gas accretion with a viscosity-limited Bondi prescription, and thermal AGN feedback heating neighboring gas particles by $\Delta T_\mathrm{AGN}=10^{8.5}$ K (EAGLE Ref), or $10^9$ K (AGNdT9/C-EAGLE), with feedback efficiency $\epsilon_f=0.15$ [1407.7040, 1703.10907]. Calibration is achieved using the $z\approx 0$ 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' [1908.05019]. ## 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 $M_{200}\sim0.5$–$1.5\times10^{12}\,M_\odot$ [1511.01098]. 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 [1511.01098, 1611.00010]. 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: $\sim1.8\pm0.9$ satellites with $M_*>10^5\,M_\odot$ per LMC-like object [2011.13500]. ### Cluster Environment (C-EAGLE) C-EAGLE simulates 30 galaxy clusters ($10^{14}$–$10^{15.4}\,M_\odot$) using the AGNdT9 EAGLE variant, featuring enhanced AGN feedback heating ($\Delta T_\mathrm{AGN}=10^9$ K). Global properties such as temperature–mass, $L_\mathrm{X}$–mass, stellar and black hole scaling relations, and integrated ICM metallicities are well-reproduced [1703.10907]. However, clusters remain systematically gas-rich relative to X-ray and Sunyaev–Zel'dovich measurements (by $\sim30\%$), 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 $z\sim0.1$ over $10^8$–$10^{11}\,M_\odot$ ($<0.2$ dex residual) [1407.7040]. - The stellar mass–halo mass relation, with peak galaxy formation efficiency near $M_{200}\sim10^{12}\,M_\odot$. - Projected half-mass radii for disc galaxies, Tully–Fisher relation, mass–metallicity relations for both gas and stars above $M_*\gtrsim10^{9.5}\,M_\odot$ [1510.01320]. - 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, $M_*$, and SFR, with negligible scatter and redshift evolution [1510.08067]. ### Satellite Dynamics and Internal Kinematics - The observed velocity dispersion–stellar mass relation for dwarf spheroidals is reproduced without requiring DM cores [1511.01098]. - 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 [1712.02562]. - 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 [1611.00010]. ### 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 $\langle t \rangle = 2.26\pm0.25$ (rms), steeper than observed samples (SL2S: $t\approx2.16$, SLACS: $t\approx2.08$). Model degeneracies, notably a strong shear–ellipticity correlation ($\gamma\simeq\epsilon/4$), are highlighted [1802.06629]. ## 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 ($\approx0.5$–$2\times$ calibration value) for $\epsilon_{0}$, with both excessive and insufficient softening yielding artifacts in star formation, feedback, and structural parameters [1908.05019]. 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 [1510.01320, 1706.09899]. 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 [1804.09079]. - 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 [1801.08781]. - 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 [1810.05168]. --- 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 [1407.7040, 1511.01098, 2011.13500, 1510.08067, 1802.06629, 1703.10907, 1908.05019]. Source: https://www.emergentmind.com/topics/apostle-eagle-cosmological-hydrodynamical-simulations