We introduce the Virgo Consortium's EAGLE project, a suite of hydrodynamical simulations that follow the formation of galaxies and supermassive black holes in cosmologically representative volumes of a standard ΛCDM universe. 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 decouple 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 present-day galaxy stellar mass function and the amplitude of the galaxy-central black hole mass relation, also taking galaxy sizes into account. The observed galaxy stellar mass function is reproduced to < ∼ 0.2 dex over the full resolved mass range, 10 8 < M * /M < ∼ 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 C iv and O vi. While the mass-metallicity relations for gas and stars are consistent with observations for M * > ∼ 10 9 M (M * > ∼ 10 10 M at intermediate resolution), they are insufficiently steep at lower masses. For the reference model the gas fractions and temperatures are too high for clusters of galaxies, but for galaxy groups these discrepancies can be resolved by adopting a higher heating temperature in the subgrid prescription for AGN feedback. The EAGLE simulation suite, which also includes physics variations and higher-resolution zoomed-in volumes described elsewhere, constitutes a valuable new resource for studies of galaxy formation.

We present results from thirteen cosmological simulations that explore the parameter space of the "Evolution and Assembly of GaLaxies and their Environments" (EAGLE) simulation project. Four of the simulations follow the evolution of a periodic cube L = 50 cMpc on a side, and each employs a different subgrid model of the energetic feedback associated with star formation. The relevant parameters were adjusted so that the simulations each reproduce the observed galaxy stellar mass function at z = 0.1. Three of the simulations fail to form disc galaxies as extended as observed, and we show analytically that this is a consequence of numerical radiative losses that reduce the efficiency of stellar feedback in high-density gas. Such losses are greatly reduced in the fourth simulation -the EAGLE reference model -by injecting more energy in higher density gas. This model produces galaxies with the observed size distribution, and also reproduces many galaxy scaling relations. In the remaining nine simulations, a single parameter or process of the reference model was varied at a time. We find that the properties of galaxies with stellar mass M (the "knee" of the galaxy stellar mass function) are largely governed by feedback associated with star formation, while those of more massive galaxies are also controlled by feedback from accretion onto their central black holes. Both processes must be efficient in order to reproduce the observed galaxy population. In general, simulations that have been calibrated to reproduce the low-redshift galaxy stellar mass function will still not form realistic galaxies, but the additional requirement that galaxy sizes be acceptable leads to agreement with a large range of observables. the regime where those outcomes are determined primarily by gravitational forces, have been corroborated by a diverse range of observational tests. These include, but are not limited to, cosmic shear induced by large-scale structure (e.g. Fu et al. 2008), the abundance of brightest cluster galaxies (BCGs, e.g. Rozo et al. 2010), tests of the cosmic expansion rate (e.g. Blake et al. 2011a) and the distanceredshift relation (e.g. Blake et al. 2011b), redshift-space distortions of the 2-point correlation function (e.g. Beutler et al. 2012) and the luminosity-distance relation of type Ia supernovae (e.g. Suzuki et al. 2012).The formation and evolution of galaxies is governed ulti-arXiv:1501.01311v2 [astro-ph.GA] 3 Apr 2015 1 We refer to losses on these scales as "subgrid losses". Losses induced by processes acting on scales that are resolved by cosmological simulations can also be significant, and dependent upon the subgrid implementation; we term these "macroscopic losses". 2 See also http://eagle.strw.leidenuniv.nl and http://icc.dur.ac.uk/Eagle 3 S15 also introduced a third model that better reproduces the observed properties of intragroup gas at intermediate resolution by adopting a higher AGN heating temperature ("AGNdT9").

We use a combination of three large N‐body simulations to investigate the dependence of dark matter halo concentrations on halo mass and redshift in the Wilkinson Microwave Anisotropy Probe year 5 (WMAP5) cosmology. The median relation between concentration and mass is adequately described by a power law for halo masses in the range 1011–1015 h−1 M⊙ and redshifts z < 2, regardless of whether the halo density profiles are fitted using Navarro, Frenk & White or Einasto profiles. Compared with recent analyses of the Millennium Simulation, which uses a value of σ8 that is higher than allowed by WMAP5, z= 0 halo concentrations are reduced by factors ranging from 23 per cent at 1011 h−1 M⊙ to 16 per cent at 1014 h−1 M⊙. The predicted concentrations are much lower than inferred from X‐ray observations of groups and clusters.

We investigate the physics driving the cosmic star formation (SF) history using the more than fifty large, cosmological, hydrodynamical simulations that together comprise the OverWhelmingly Large Simulations (OWLS) project. We systematically vary the parameters of the model to determine which physical processes are dominant and which aspects of the model are robust. Generically, we find that SF is limited by the build-up of dark matter haloes at high redshift, reaches a broad maximum at intermediate redshift, then decreases as it is quenched by lower cooling rates in hotter and lower density gas, gas exhaustion, and self-regulated feedback from stars and black holes. The higher redshift SF is therefore mostly determined by the cosmological parameters and to a lesser extent by photo-heating from reionization. The location and height of the peak in the SF history, and the steepness of the decline towards the present, depend on the physics and implementation of stellar and black hole feedback. Mass loss from intermediate-mass stars and metal-line cooling both boost the SF rate at late times. Galaxies form stars in a self-regulated fashion at a rate controlled by the balance between, on the one hand, feedback from massive stars and black holes and, on the other hand, gas cooling and accretion. Paradoxically, the SF rate is highly insensitive to the assumed SF law. This can be understood in terms of self-regulation: if the SF efficiency is changed, then galaxies adjust their gas fractions so as to achieve the same rate of production of massive stars. Self-regulated feedback from accreting black holes is required to match the steep decline in the observed SF rate below redshift two, although more extreme feedback from SF, for example in the form of a top-heavy IMF at high gas pressures, can help.Comment: Accepted for publication in MNRAS, 27 pages and 18 figures. Revised version: minor change

We present a method that self‐consistently tracks the growth of supermassive black holes (BHs) and the feedback from active galactic nuclei (AGN) in cosmological, hydrodynamical simulations. Our model is a substantially modified version of the one introduced by Springel, Di Matteo & Hernquist implemented in a significantly expanded version of the gadget III code, which contains new prescriptions for star formation, supernova feedback, radiative cooling and chemodynamics. We simulate the growth of BHs from an initial seed state via Eddington‐limited accretion of the surrounding gas, and via mergers with other BHs. Because cosmological simulations at present lack both the resolution and the physics to model the multiphase interstellar medium, they tend to strongly underestimate the Bondi–Hoyle accretion rate. To allow low‐mass BHs to grow, it is therefore necessary to increase the predicted Bondi–Hoyle rates in star‐forming gas by large factors, either by explicitly multiplying the accretion rate by a numerical correction factor or by using an unresolved, subgrid model for the gas close to the BH. We explore the physical regimes where the use of such multiplicative factors is reasonable, and through this introduce a new prescription for gas accretion by BHs. Feedback from AGN is modelled by coupling a fraction of the rest‐mass energy of the accreted gas thermally into the surrounding medium. We describe the implementation as well as the limitations of the model in detail and motivate all the changes relative to previous work. We demonstrate how general physical considerations can be used to choose many of the parameters of the model and demonstrate that the fiducial model reproduces observational constraints. We employ a large suite of cosmological simulations, in which the parameters of the BH model are varied away from their fiducial values, to investigate the robustness of the predictions for the cosmic star formation history and the redshift zero cosmic BH density, BH scaling relations and galaxy‐specific star formation rates. We find that the freedom introduced by the need to increase the predicted accretion rates by hand, the standard procedure in the literature, is the most significant source of uncertainty. Our simulations demonstrate that supermassive BHs are able to regulate their growth by releasing a fixed amount of energy for a given halo mass, independent of the assumed efficiency of AGN feedback, which sets the normalization of the BH scaling relations. Regardless of whether BH seeds are initially placed above or below the BH scaling relations, they grow on to the same scaling relations. AGN feedback efficiently suppresses star formation in high‐mass galaxies.

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Radiative cooling is central to a wide range of astrophysical problems. Despite its importance, cooling rates are generally computed using very restrictive assumptions, such as collisional ionization equilibrium and solar relative abundances. We simultaneously relax both assumptions and investigate the effects of photoionization of heavy elements by the metagalactic ultraviolet (UV)/X‐ray background and of variations in relative abundances on the cooling rates of optically thin gas in ionization equilibrium. We find that photoionization by the metagalactic background radiation reduces the net cooling rates by up to an order of magnitude for gas densities and temperatures typical of the shock‐heated intergalactic medium and proto‐galaxies (104 K ≲T≲ 106 K, ρ/〈ρ〉≲ 100). In addition, photoionization changes the relative contributions of different elements to the cooling rates. We conclude that photoionization by both the ionizing background and heavy elements needs to be taken into account in order for the cooling rates to be correct to an order of magnitude. Moreover, if the rates need to be known to better than a factor of a few, then departures of the relative abundances from solar need to be taken into account. We propose a method to compute cooling rates on an element‐by‐element basis by interpolating pre‐computed tables that take photoionization into account. We provide such tables for a popular model of the evolving UV/X‐ray background radiation, computed using the photoionization package cloudy.

We present an implementation of stellar evolution and chemical feedback for smoothed particle hydrodynamics simulations. We consider the timed release of individual elements by both massive (Type II supernovae and stellar winds) and intermediate‐mass stars (Type Ia supernovae and asymptotic giant branch stars). We illustrate the results of our method using a suite of cosmological simulations that include new prescriptions for radiative cooling, star formation and galactic winds. Radiative cooling is implemented element‐by‐element, in the presence of an ionizing radiation background, and we track all 11 elements that contribute significantly to the radiative cooling. While all simulations presented here use a single set of physical parameters, we take specific care to investigate the robustness of the predictions of chemodynamical simulations with respect to the ingredients, the methods and the numerical convergence. A comparison of nucleosynthetic yields taken from the literature indicates that relative abundance ratios may only be reliable at the factor of 2 level, even for a fixed initial mass function. Abundances relative to iron are even more uncertain because the rate of Type Ia supernovae is not well known. We contrast two reasonable definitions of the metallicity of a resolution element and find that while they agree for high metallicities, there are large differences at low metallicities. We argue that the discrepancy is indicative of the lack of metal mixing caused by the fact that metals are stuck to particles. We argue that since this is a (numerical) sampling problem, solving it by using a poorly constrained physical process such as diffusion could have undesired consequences. We demonstrate that the two metallicity definitions result in redshift z= 0 stellar masses that can differ by up to a factor of 2, because of the sensitivity of the cooling rates to the elemental abundances. Finally, we use several 5123 particle simulations to investigate the evolution of the distribution of heavy elements, which we find to be in reasonably good agreement with available observational constraints. We find that by z= 0 most of the metals are locked up in stars. The gaseous metals are distributed over a very wide range of gas densities and temperatures. The shock‐heated warm–hot intergalactic medium has a relatively high metallicity of ∼10−1 Z⊙ that evolves only weakly, and is therefore an important reservoir of metals. Any census aiming to account for most of the metal mass will have to take a wide variety of objects and structures into account.