  We study the structure of vacuum entanglement for two complimentary segments
of a linear harmonic chain, applying the modewise decomposition of entangled
gaussian states discussed in \cite {modewise}. We find that the resulting
entangled mode shape hierarchy shows a distinctive layered structure with well
defined relations between the depth of the modes, their characteristic
wavelength, and their entanglement contribution. We re-derive in the strong
coupling (diverging correlation length) regime, the logarithmic dependence of
entanglement on the segment size predicted by conformal field theory for the
boson universality class, and discuss its relation with the mode structure. We
conjecture that the persistence of vacuum entanglement between arbitrarily
separated finite size regions is connected with the localization of the highest
frequency innermost modes.
