Supermassive black holes in the EAGLE Universe. Revealing the
  observables of their growth
  We investigate the evolution of supermassive black holes in the `Evolution
and Assembly of GaLaxies and their Environments' (EAGLE) cosmological
hydrodynamic simulations. The largest of the EAGLE volumes covers a $(100 \,\rm
cMpc)^3$ and includes state-of-the-art physical models for star formation and
black hole growth that depend only on local gas properties. We focus on the
black hole mass function, Eddington ratio distribution and the implied duty
cycle of nuclear activity. The simulation is broadly consistent with
observational constraints on these quantities. In order to make a more direct
comparison with observational data, we calculate the soft and hard X-ray
luminosity functions of the active galactic nuclei (AGN). Between redshifts $0$
and $1$, the simulation is in agreement with data. At higher redshifts, the
simulation tends to underpredict the luminosities of the brightest observed
AGN. This may be due to the limited volume of the simulation, or a fundamental
deficiency of the underlying model. It seems unlikely that additional
unresolved variability can account for this difference. The simulation shows a
similar `downsizing' of the AGN population as seen in observational surveys.
