Context : 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 .
Simulated collapsing cores without radiative transfer rapidly become thermally supported before reaching high enough temperatures and densities , preventing the formation of stars .

Aims : 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 , which can potentially be overlooked by grey models and lead to significantly different results .
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 .

Methods : 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 { M } _ { \odot } cloud cores .

Results : 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 .

Conclusions : Our simulations support the idea of a standard ( universal ) initial second core size of \sim 3 \times 10 ^ { -3 } AU and mass \sim 1.4 \times 10 ^ { -3 } { M } _ { \odot } .
The grey approximation for radiative transfer appears to perform well in one-dimensional simulations of protostellar collapse , most probably because of the high optical thickness of the majority of the protostar-envelope system .
A simple estimate of the characteristic timescale of the second core suggests that the effects of using multigroup radiative transfer may be more important in the long term evolution of the proto-star .