  In ultra-central heavy-ion collisions, anisotropic hydrodynamic flow is
generated by density fluctuations in the initial state rather than by geometric
overlap effects. For a given centrality class, the initial fluctuation spectrum
is sensitive to the method chosen for binning the events into centrality
classes. We show that sorting events by total initial entropy or by total final
multiplicity yields event classes with equivalent statistical fluctuation
properties, in spite of viscous entropy production during the fireball
evolution. With this initial entropy-based centrality definition we generate
several classes of ultra-central Pb+Pb collisions at LHC energies and evolve
the events using viscous hydrodynamics with non-zero shear but vanishing bulk
viscosity. Comparing the predicted anisotropic flow coefficients for charged
hadrons with CMS data we find that both the Monte Carlo Glauber (MC-Glb) and
Monte Carlo Kharzeev-Levin-Nardi (MC-KLN) models produce initial fluctuation
spectra that are incompatible with the measured final anisotropic flow power
spectrum, for any choice of the specific shear viscosity. In spite of this
failure, we show that the hydrodynamic model can qualitatively explain, in
terms of event-by-event fluctuations of the anisotropic flow coefficients and
flow angles, the breaking of flow factorization for elliptic, triangular and
quadrangular flow measured by the CMS experiment. For elliptic flow, this
factorization breaking is large in ultra-central collisions. We conclude that
the bulk of the experimentally observed flow factorization breaking effects are
qualitatively explained by hydrodynamic evolution of initial-state
fluctuations, but that their quantitative description requires a better
understanding of the initial fluctuation spectrum.
