  Using the 2D multi-group, flux-limited diffusion version of the code
VULCAN/2D, that also incorporates rotation, we have calculated the collapse,
bounce, shock formation, and early post-bounce evolutionary phases of a
core-collapse supernova for a variety of initial rotation rates. This is the
first series of such multi-group calculations undertaken in supernova theory
with fully multi-D tools. We find that though rotation generates
pole-to-equator angular anisotropies in the neutrino radiation fields, the
magnitude of the asymmetries is not as large as previously estimated. Moreover,
we find that the radiation field is always more spherically symmetric than the
matter distribution, with its plumes and convective eddies. We present the
dependence of the angular anisotropy of the neutrino fields on neutrino
species, neutrino energy, and initial rotation rate. Only for our most rapidly
rotating model do we start to see qualitatively different hydrodynamics, but
for the lower rates consistent with the pre-collapse rotational profiles
derived in the literature the anisotropies, though interesting, are modest.
This does not mean that rotation does not play a key role in supernova
dynamics. The decrease in the effective gravity due to the centripetal effect
can be quite important. Rather, it means that when a realistic mapping between
initial and final rotational profiles and 2D multi-group
radiation-hydrodynamics are incorporated into collapse simulations the
anisotropy of the radiation fields may be only a secondary, not a pivotal
factor, in the supernova mechanism.
