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.

The Local Group of galaxies offer some of the most discriminating tests of models of cosmic structure formation. For example, observations of the Milky Way (MW) and Andromeda satellite populations appear to be in disagreement with N-body simulations of the "Lambda Cold Dark Matter" (ΛCDM) model: there are far fewer satellite galaxies than substructures in cold dark matter halos (the "missing satellites" problem); dwarf galaxies seem to avoid the most massive substructures (the "too-big-tofail" problem); and the brightest satellites appear to orbit their host galaxies on a thin plane (the "planes of satellites" problem). Here we present results from Apostle (A Project Of Simulating The Local Environment), a suite of cosmological hydrodynamic simulations of twelve volumes selected to match the kinematics of the Local Group (LG) members. Applying the Eagle code to the LG environment, we find that our simulations match the observed abundance of LG galaxies, including the satellite galaxies of the MW and Andromeda. Due to changes to the structure of halos and the evolution in the LG environment, the simulations reproduce the observed relation between stellar mass and velocity dispersion of individual dwarf spheroidal galaxies without necessitating the formation of cores in their dark matter profiles. Satellite systems form with a range of spatial anisotropies, including one similar to that of the MW, confirming that such a configuration is not unexpected in ΛCDM. Finally, based on the observed velocity dispersion, size, and stellar mass, we provide new estimates of the maximum circular velocity for the halos of nine MW dwarf spheroidals.

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