  Neutrinos are densely populated deep inside the core of massive stars after
their gravitational collapse to produce supernova explosions and form compact
stars such as neutron stars (NS) and black holes (BH). It has been considered
that they may change their flavor identities through so-called fast-pairwise
conversions induced by mutual forward scatterings. If that is really the case,
the dynamics of supernova explosion will be influenced, since the conversion
may occur near the neutrino sphere, from which neutrinos are effectively
emitted. In this paper, we conduct a pilot study of such possibilities based on
the results of fully self-consistent, realistic simulations of a core-collapse
supernova explosion in two spatial dimensions under axisymmetry. As we solved
the Boltzmann equations for neutrino transfer in the simulation not as a
post-process but in real time, the angular distributions of neutrinos in
momentum space for all points in the core at all times are available, a
distinct feature of our simulations. We employ some of these distributions
extracted at a few selected points and times from the numerical data and apply
linear analysis to assess the possibility of the conversion. We focus on the
vicinity of the neutrino sphere, where different species of neutrinos move in
different directions and have different angular distributions as a result. This
is a pilot study for a more thorough survey that will follow soon. We find no
positive sign of conversion unfortunately at least for the spatial points and
times we studied in this particular model. We hence investigate rather in
detail the condition for the conversion by modifying the neutrino distributions
rather arbitrarily by hand.
