  Following a simulation approach of recent publications we explore the
viability of the neutrino-heating explosion mechanism in dependence on the
spatial dimension. Our results disagree with previous findings. While we also
observe that two-dimensional (2D) models explode for lower driving neutrino
luminosity than spherically symmetric (1D) models, we do not find that
explosions in 3D occur easier and earlier than in 2D. Moreover, we find that
the average entropy of matter in the gain layer hardly depends on the dimension
and thus is no good diagnostic quantity for the readiness to explode. Instead,
mass, integrated entropy, total neutrino-heating rate, and nonradial kinetic
energy in the gain layer are higher when models are closer to explosion.
Coherent, large-scale mass motions as typically associated with the standing
accretion-shock instability (SASI) are observed to be supportive for explosions
because they drive strong shock expansion and thus enlarge the gain layer.
While 2D models with better angular resolution explode clearly more easily, the
opposite trend is seen in 3D. We interpret this as a consequence of the
turbulent energy cascade, which transports energy from small to large spatial
scales in 2D, thus fostering SASI activity. In contrast, the energy flow in 3D
is in the opposite direction, feeding fragmentation and vortex motions on
smaller scales and thus making the 3D evolution with finer grid resolution more
similar to 1D. More favorable conditions for explosions in 3D may therefore be
tightly linked to efficient growth of low-order SASI modes including
nonaxisymmetric ones.
