The EAGLE project: Simulating the evolution and assembly of galaxies and their environments

TL;DR

<3-5 sentence high-level summary> The paper addresses the challenge of modeling galaxy formation in cosmological volumes with hydrodynamics by introducing the EAGLE project, a suite of simulations that calibrate subgrid feedback to reproduce the local GSMF and BH–stellar mass relation. It employs stochastic thermal feedback for stars and a single-mode thermal AGN feedback, conducted in a Planck-consistent cosmology across multiple volumes and resolutions, to achieve broad agreement with a wide range of observables beyond the calibration set. The results show that GSMF, galaxy sizes, Tully–Fisher trends, and ISM/IGM metallicities are well reproduced, while certain discrepancies remain at low masses and in the intracluster medium, which can be addressed by adjusting AGN heating or resolution. Overall, EAGLE provides a robust, physically interpretable resource for studying galaxy formation and its gaseous environments, while highlighting the importance of calibration and the nuanced meaning of convergence in subgrid-dominated regimes.

Abstract

We introduce the Virgo Consortium's EAGLE project, a suite of hydrodynamical simulations that follow the formation of galaxies and black holes in representative volumes. We discuss the limitations of such simulations in light of their finite resolution and poorly constrained subgrid physics, and how these affect their predictive power. One major improvement is our treatment of feedback from massive stars and AGN in which thermal energy is injected into the gas without the need to turn off cooling or hydrodynamical forces, allowing winds to develop without predetermined speed or mass loading factors. Because the feedback efficiencies cannot be predicted from first principles, we calibrate them to the z~0 galaxy stellar mass function and the amplitude of the galaxy-central black hole mass relation, also taking galaxy sizes into account. The observed galaxy mass function is reproduced to $\lesssim 0.2$ dex over the full mass range, $10^8 < M_*/M_\odot \lesssim 10^{11}$, a level of agreement close to that attained by semi-analytic models, and unprecedented for hydrodynamical simulations. We compare our results to a representative set of low-redshift observables not considered in the calibration, and find good agreement with the observed galaxy specific star formation rates, passive fractions, Tully-Fisher relation, total stellar luminosities of galaxy clusters, and column density distributions of intergalactic CIV and OVI. While the mass-metallicity relations for gas and stars are consistent with observations for $M_* \gtrsim 10^9 M_\odot$, they are insufficiently steep at lower masses. The gas fractions and temperatures are too high for clusters of galaxies, but for groups these discrepancies can be resolved by adopting a higher heating temperature in the subgrid prescription for AGN feedback. EAGLE constitutes a valuable new resource for studies of galaxy formation.

Figures (17)

• Figure 1: A $100\times 100\times 20$ cMpc slice through the Ref-L100N1504 simulation at $z=0$. The intensity shows the gas density while the colour encodes the gas temperature using different colour channels for gas with $T<10^{4.5}\,{\rm K}$ (blue), $10^{4.5}\,{\rm K}<T<10^{5.5}\,{\rm K}$ (green), and $T>10^{5.5}\,{\rm K}$ (red). The insets show regions of 10 cMpc and 60 ckpc on a side and zoom into an individual galaxy with a stellar mass of $3\times 10^{10}\,{{\rm M}_\odot}$. The 60 ckpc image shows the stellar light based on monochromatic u, g and r band SDSS filter means and accounting for dust extinction. It was created using the radiative transfer code skirtBaes2011SKIRT.
• Figure 2: Examples of galaxies taken from simulation Ref-L100N1504 illustrating the $z=0$ Hubble sequence of galaxy morphologies. The images were created with the radiative transfer code skirtBaes2011SKIRT. They show the stellar light based on monochromatic u, g and r band SDSS filter means and accounting for dust extinction. Each image is 60 ckpc on a side. For disc galaxies both face-on and edge-on projections are shown. Except for the 3rd elliptical from the left, which has a stellar mass of $1\times 10^{11}\,{{\rm M}_\odot}$, and the merger in the bottom-left, which has a total stellar mass of $8\times 10^{10}\,{{\rm M}_\odot}$, all galaxies shown have stellar masses of 5--$6\times 10^{10}\,{{\rm M}_\odot}$.
• Figure 3: The evolution of the supernova Ia rate density. Data points show observations from SDSS Stripe 82 Dilday2010SNIa, SDSS-DR7 Graur2013SNIa, SNLS Perrett2012SNIa, GOODS Dahlen2008SNIa, SDF Graur2011SNIa, and CLASH Graur2014SNIa, as compiled by Graur2014SNIa. Only data classified by Graur2014SNIa as the "most accurate and precise measurements" are shown. The $1\sigma$ error bars account for both statistical and systematic uncertainties. The simulations assume that the rate is a convolution of the star formation rate density with an exponential delay time distribution (eq. \ref{['eq:snia']}) with e-folding time $\tau = 2~$Gyr, normalised to yield $\nu = 2\times 10^{-3}\,{{\rm M}_\odot}^{-1}$ supernovae Ia per unit stellar mass when integrated over all time.
• Figure 4: The galaxy stellar mass function at $z=0.1$ for the EAGLE simulations Ref-L100N1504 (blue), AGNdT9-L050N0752 (red), and Recal-L025N0752 (green-blue). The curves switch from solid to dashed at the high-mass end when there are fewer than 10 objects per (0.2 dex) stellar mass bin. At the low-mass end the curves become dotted when the stellar mass falls below that corresponding to 100 baryonic particles. Data points show measurements with $1\sigma$ error bars from the GAMA survey (open circles; $z<0.06$; Baldry2012GSMF) and from SDSS (filled circles; $z\sim 0.07$; Li2009GSMF). The high-resolution model Recal-L025N0752 is noisier because of its small box size. The intermediate-resolution models slightly underestimate the galaxy number density at the knee of the mass function and slightly overestimate the abundance at $M_\ast \sim 10^{8.5}\,{{\rm M}_\odot}$. The galaxy number density agrees with the data to $\la 0.2$ dex.
• Figure 5: Comparisons of the GSMF from EAGLE's Ref-L100N1504 with the semi-analytic models of Gonzalez-Perez2014Galform, Henriques2013SAM, and Porter2014SAM (left panel) and with the large hydrodynamical simulations of Oppenheimer2010GSMF, Puchwein2013GSMF, the Illustris simulation Vogelsberger2014Illustris, and the MassiveBlack-II simulation Khandai2014MassiveBlack (right panel). All models are for a Chabrier IMF (Gonzalez-Perez2014Galform and Khandai2014MassiveBlack have been converted from Kennicutt and Salpeter IMFs, respectively). The EAGLE curve is dotted when galaxies contain fewer than 100 stellar particles and dashed when there are fewer than 10 galaxies per stellar mass bin. Except for Oppenheimer2010GSMF, all simulations include AGN feedback. Apart from MassiveBlack-II, all models were calibrated to the data (the Galform semi-analytic model of Gonzalez-Perez2014Galform was calibrated to fit the K-band galaxy luminosity function). The agreement with the data is relatively good for both EAGLE and the semi-analytic models, but EAGLE fits the data substantially better than the other hydrodynamical simulations do.