  Radiative shocks play a dominant role in star formation. The accretion shocks
on the first and second Larson's cores involve radiative processes and are thus
characteristic of radiative shocks. In this study, we explore the formation of
the first Larson's core and characterize the radiative and dynamical properties
of the accretion shock, using both analytical and numerical approaches. We
develop both numerical RHD calculations and a semi-analytical model that
characterize radiative shocks in various physical conditions, for radiating or
barotropic fluids. Then, we perform 1D spherical collapse calculations of the
first Larson's core, using a grey approximation for the opacity of the
material. We consider three different models for radiative transfer, namely:
the barotropic approximation, the FLD approximation and the more complete M1
model. We investigate the characteristic properties of the collapse and of the
first core formation. Comparison between the numerical results and our
semi-analytical model shows that this latter reproduces quite well the core
properties obtained with the numerical calculations. The accretion shock on the
first Larson core is found to be supercritical, implying that all the accretion
shock energy on the core is radiated away. The FLD approximation is found to
agree quite well with the results based on the M1 model, and is thus
appropriate to study the star formation process. In contrast, the barotropic
approximation does not correctly describe the thermal properties of the gas
during the collapse. We show that a consistent treatment of radiation and
hydrodynamics is mandatory to correctly handle the cooling of the gas during
the core formation and thus to obtain the correct mechanical and thermal
properties for this latter.
