Suppression of the multi-azimuthal-angle instability in dense neutrino
  gas during supernova accretion phase
  It has been recently pointed out that removing the axial symmetry in the
"multi-angle effects" associated with the neutrino-neutrino interactions for
supernova (SN) neutrinos, a new multi-azimuthal-angle (MAA) instability would
arise. In particular, for a flux ordering $F_{\nu_e} > F_{\bar\nu_e} >
F_{\nu_x}$, as expected during the SN accretion phase, this instability occurs
in the normal neutrino mass hierarchy. However, during this phase the ordinary
matter density can be larger than the neutrino one, suppressing the
self-induced conversions. At this regard, we investigate the matter suppression
of the MAA effects, performing a linearized stability analysis of the neutrino
equations of motion, in the presence of realistic SN density profiles. We
compare these results with the numerical solution of the SN neutrino non-linear
evolution equations. Assuming axially symmetric distributions of neutrino
momenta we find that the large matter term strongly inhibits the MAA effects.
In particular, the hindrance becomes stronger including realistic
forward-peaked neutrino angular distributions. As a result, in our model for a
$10.8$ $M_{\odot}$ iron-core SNe, MAA instability does not trigger any flavor
conversion during the accretion phase. Instead, for a $8.8$ $M_{\odot}$ O-Ne-Mg
core SN model, with lower matter density profile and less forward-peaked
angular distributions, flavor conversions are possible also at early times.
