  Star formation begins with the gravitational collapse of a dense core inside
a molecular cloud. As the collapse progresses, the centre of the core begins to
heat up as it becomes optically thick. The temperature and density in the
centre eventually reach high enough values where fusion reactions can ignite;
the protostar is born. This sequence of events entail many physical processes,
of which radiative transfer is of paramount importance. Many simulations of
protostellar collapse make use of a grey treatment of radiative transfer
coupled to the hydrodynamics. However, interstellar gas and dust opacities
present large variations as a function of frequency. In this paper, we
follow-up on a previous paper on the collapse and formation of Larson's first
core using multigroup radiation hydrodynamics (Paper I) by extending the
calculations to the second phase of the collapse and the formation of Larson's
second core. We have made the use of a non-ideal gas equation of state as well
as an extensive set of spectral opacities in a spherically symmetric fully
implicit Godunov code to model all the phases of the collapse of a 0.1, 1 and
10 solar mass cloud cores. We find that, for a same central density, there are
only small differences between the grey and multigroup simulations. The first
core accretion shock remains supercritical while the shock at the second core
border is found to be strongly subcritical with all the accreted energy being
transfered to the core. The size of the first core was found to vary somewhat
in the different simulations (more unstable clouds form smaller first cores)
while the size, mass and temperature of the second cores are independent of
initial cloud mass, size and temperature. Our simulations support the idea of a
standard (universal) initial second core size of 0.003 AU and mass 0.0014 solar
masses.
