  During the stalled-shock phase of our 3D hydrodynamical core-collapse
simulations with energy-dependent, 3-flavor neutrino transport, the
lepton-number flux (nue minus antinue) emerges predominantly in one hemisphere.
This novel, spherical-symmetry breaking neutrino-hydrodynamical instability is
termed LESA for "Lepton-number Emission Self-sustained Asymmetry." While the
individual nue and antinue fluxes show a pronounced dipole pattern, the
heavy-flavor neutrino fluxes and the overall luminosity are almost spherically
symmetric. Initially, LESA seems to develop stochastically from convective
fluctuations, it exists for hundreds of milliseconds or more, and it persists
during violent shock sloshing associated with the standing accretion shock
instability. The nue minus antinue flux asymmetry originates mainly below the
neutrinosphere in a region of pronounced proto-neutron star (PNS) convection,
which is stronger in the hemisphere of enhanced lepton-number flux. On this
side of the PNS, the mass-accretion rate of lepton-rich matter is larger,
amplifying the lepton-emission asymmetry, because the spherical stellar infall
deflects on a dipolar deformation of the stalled shock. The increased shock
radius in the hemisphere of less mass accretion and minimal lepton-number flux
(antinue flux maximum) is sustained by stronger convection on this side, which
is boosted by stronger neutrino heating because the average antinue energy is
higher than the average nue energy. Asymmetric heating thus supports the global
deformation despite extremely nonstationary convective overturn behind the
shock. While these different elements of LESA form a consistent picture, a full
understanding remains elusive at present. There may be important implications
for neutrino-flavor oscillations, the neutron-to-proton ratio in the
neutrino-heated supernova ejecta, and neutron-star kicks, which remain to be
explored.
