  We present self-consistent, axisymmetric core-collapse supernova simulations
performed with the Prometheus-Vertex code for 18 pre-supernova models in the
range of 11-28 solar masses, including progenitors recently investigated by
other groups. All models develop explosions, but depending on the progenitor
structure, they can be divided into two classes. With a steep density decline
at the Si/Si-O interface, the arrival of this interface at the shock front
leads to a sudden drop of the mass-accretion rate, triggering a rapid approach
to explosion. With a more gradually decreasing accretion rate, it takes longer
for the neutrino heating to overcome the accretion ram pressure and explosions
set in later. Early explosions are facilitated by high mass-accretion rates
after bounce and correspondingly high neutrino luminosities combined with a
pronounced drop of the accretion rate and ram pressure at the Si/Si-O
interface. Because of rapidly shrinking neutron star radii and receding shock
fronts after the passage through their maxima, our models exhibit short
advection time scales, which favor the efficient growth of the standing
accretion-shock instability. The latter plays a supportive role at least for
the initiation of the re-expansion of the stalled shock before runaway. Taking
into account the effects of turbulent pressure in the gain layer, we derive a
generalized condition for the critical neutrino luminosity that captures the
explosion behavior of all models very well. We validate the robustness of our
findings by testing the influence of stochasticity, numerical resolution, and
approximations in some aspects of the microphysics.
