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 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.

Upcoming weak lensing surveys, such as LSST, EUCLID and WFIRST, aim to measure the matter power spectrum with unprecedented accuracy. In order to fully exploit these observations, models are needed that, given a set of cosmological parameters, can predict the non‐linear matter power spectrum at the level of 1 per cent or better for scales corresponding to comoving wavenumbers 0.1 ≲k≲ 10 h Mpc−1. We have employed the large suite of simulations from the OverWhelmingly Large Simulations (OWLS) project to investigate the effects of various baryonic processes on the matter power spectrum. In addition, we have examined the distribution of power over different mass components, the back‐reaction of the baryons on the cold dark matter and the evolution of the dominant effects on the matter power spectrum. We find that single baryonic processes are capable of changing the power spectrum by up to several tens of per cent. Our simulation that includes AGN feedback, which we consider to be our most realistic simulation as, unlike those used in previous studies, it has been shown to solve the overcooling problem and to reproduce optical and X‐ray observations of groups of galaxies, predicts a decrease in power relative to a dark matter only simulation ranging, at z= 0, from 1 per cent at k≈ 0.3 h Mpc−1 to 10 per cent at k≈ 1 h Mpc−1 and to 30 per cent at k≈ 10 h Mpc−1. This contradicts the naive view that baryons raise the power through cooling, which is the dominant effect only for k≳ 70 h Mpc−1. Therefore, baryons, and particularly AGN feedback, cannot be ignored in theoretical power spectra for k≳ 0.3 h Mpc−1. It will thus be necessary to improve our understanding of feedback processes in galaxy formation, or at least to constrain them through auxiliary observations, before we can fulfil the goals of upcoming weak lensing surveys.