  A set of eight self-consistent, time-dependent supernova (SN) simulations in
three spatial dimensions (3D) for 9 solar-mass and 20 solar-mass progenitors is
evaluated for the presence of dipolar asymmetries of the electron lepton-number
emission as discovered by Tamborra et al. and termed lepton-number emission
self-sustained asymmetry (LESA). The simulations were performed with the
Aenus-Alcar neutrino/hydrodynamics code, which treats the energy- and
velocity-dependent transport of neutrinos of all flavors by a two-moment scheme
with algebraic M1 closure. For each of the progenitors, results with fully
multi-dimensional (FMD) neutrino transport and with ray-by-ray-plus (RbR+)
approximation are considered for two different grid resolutions. While the 9
solar-mass models develop explosions, the 20 solar-mass progenitor does not
explode with the employed version of simplified neutrino opacities. In all 3D
models we observe the growth of substantial dipole amplitudes of the
lepton-number (electron neutrino minus antineutrino) flux with stable or slowly
time-evolving direction and overall properties fully consistent with the LESA
phenomenon. Models with RbR+ transport develop LESA dipoles somewhat faster and
with temporarily higher amplitudes, but the FMD calculations exhibit cleaner
hemispheric asymmetries with a far more dominant dipole. In contrast, the RbR+
results display much wider multipole spectra of the neutrino-emission
anisotropies with significant power also in the quadrupole and higher-order
modes. Our results disprove speculations that LESA is a numerical artifact of
RbR+ transport. We also discuss LESA as consequence of a dipolar convection
flow inside of the nascent neutron star and establish, tentatively, a
connection to Chandrasekhar's linear theory of thermal instability in spherical
shells.
