Density Fluctuation Effects on Collective Neutrino Oscillations in
  O-Ne-Mg Core-Collapse Supernovae
  We investigate the effect of matter density fluctuations on supernova
collective neutrino flavor oscillations. In particular, we use full
multi-angle, 3-flavor, self-consistent simulations of the evolution of the
neutrino flavor field in the envelope of an O-Ne-Mg core collapse supernova at
shock break-out (neutrino neutronization burst) to study the effect of the
matter density "bump" left by the He-burning shell. We find a seemingly
counterintuitive increase in the overall electron neutrino survival probability
created by this matter density feature. We discuss this behavior in terms of
the interplay between the matter density profile and neutrino collective
effects. While our results give new insights into this interplay, they also
suggest an immediate consequence for supernova neutrino burst detection: it
will be difficult to use a burst signal to extract information on fossil
burning shells or other fluctuations of this scale in the matter density
profile. Consistent with previous studies, our results also show that the
interplay of neutrino self-coupling and matter fluctuation could cause a
significant increase in the electron neutrino survival probability at very low
energy
