- ... transport
^{} - Appendices are only available in electronic form at http://www.edpsciences.org
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...
^{} *Present address*: Rechenzentrum der Max-Planck-Gesellschaft am Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, 85748 Garching, Germany.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...
EoS
^{} - The error in the -particle mass fraction that was
recently discoved in the EoS of Lattimer & Swesty (1991) was tested to have no
important influence on our simulations; for details see Buras et al. (2006).
In some models, we replaced the Lattimer & Swesty EoS below a density
of 10
^{11}g cm^{-3}, i.e. in the regime of possible -particle presence after bounce, by our low-density EoS without discovering any significant dynamical differences.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... (PNS)
^{} - For
simplicity, we identify the PNS mass and radius with the mass and
radius enclosed by the electron neutrinosphere,
and
,
respectively. Throughout this paper, neutrinospheres
are defined as "transport spheres'', using the opacities for momentum
transfer between neutrinos and stellar medium in calculating
optical depths, as given in Eq. (28) of Buras et al. (2006).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...
^{} - Note that in 2D simulations the
"enclosed mass'' is not a Lagrangian coordinate but corresponds
to the sphere which contains a certain amount of mass at a given
time.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... level
^{} - The large values of
between the neutrinosphere and the gain radius
in case of Model s112_64, which can be inferred from
Fig. 23, are a consequence of our choice of periodic
boundary conditions at both lateral boundaries of the 90
wedge
used in this model, see Sect. 3.1.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... failure
^{} - In this
context it is interesting to note that for an
progenitor from Woosley et al. (2002), which has a less steep density
profile exterior to the iron core, Burrows et al. (2006) did not find an
explosion before about 0.5 s after bounce. Besides a different
progenitor, there were, however, also other differences. They, e.g.,
performed purely
Newtonian simulations and used a flux-limited diffusion treatment
for the neutrino transport, in which energy bin coupling by
Doppler shifts and neutrino-electron scattering were ignored.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... exists
^{} - The Monte Carlo calculations by
Janka & Mönchmeyer (1989b) did not make use of such
simplifications, assumed, however, that the transport in different
lateral directions of the 2D environment can be approximated by
a "ray-by-ray'' approach, in which the neutrino flux at a given
latitude is assumed to be radial and can be calculated by the
transport in a spherical background with a radial structure as it is
present in the 2D model at this latitude.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... trapping
^{} - Note that the small
differences in
and in
after trapping disappear
completely, and those in entropy remain slightly larger, when the
simulations are done with the sophisticated implementation of electron
captures on nuclei of Langanke et al. (2003).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...
shock
^{} - Technically this moment is determined by taking the
time of maximum luminosity at 400 km minus the time of flight between
the neutrinosphere and this radius.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .