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 ({Lambda}CDM) 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-to-fail 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 {Lambda}CDM. 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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