Opening Reionization: Quantitative Morphology of the Epoch of
  Reionization and Its Connection to the Cosmic Density Field
  We introduce a versatile and spatially resolved morphological
characterisation of binary fields, rooted in the opening transform of
mathematical morphology. We subsequently apply it to the thresholded ionization
field in simulations of cosmic reionization and study the morphology of ionized
regions. We find that an ionized volume element typically resides in an ionized
region with radius $\sim8\,h^{-1}\mathrm{cMpc}$ at the midpoint of reionization
($z\approx7.5$) and follow the bubble size distribution even beyond the overlap
phase. We find that percolation of the fully ionized component sets in when 25%
of the universe is ionized and that the resulting infinite cluster incorporates
all ionized regions above $\sim8\,h^{-1}\mathrm{cMpc}$. We also quantify the
clustering of ionized regions of varying radius with respect to matter and on
small scales detect the formation of superbubbles in the overlap phase. On
large scales we quantify the bias values of the centres of ionized and neutral
regions of different sizes and not only show that the largest ones at the
high-point of reionization can reach $b\approx 30$, but also that early small
ionized regions are positively correlated with matter and large neutral regions
and late small ionized regions are heavily anti-biased with respect to matter,
down to $b\lesssim-20$.
