  The spectacular recent development of modern high-energy density laboratory
facilities which concentrate more and more energy in millimetric volumes allows
the astrophysical community to reproduce and to explore, in millimeter-scale
targets and during very short times, astrophysical phenomena where radiation
and matter are strongly coupled. The astrophysical relevance of these
experiments can be checked from the similarity properties and especially
scaling laws establishment, which constitutes the keystone of laboratory
astrophysics. From the radiating optically thin regime to the so-called
optically thick radiative pressure regime, we present in this paper, for the
first time, a complete analysis of the main radiating regimes that we
encountered in laboratory astrophysics with the same formalism based on the
Lie-group theory. The use of the Lie group method appears as systematic which
allows to construct easily and orderly the scaling laws of a given problem.
This powerful tool permits to unify the recent major advances on scaling laws
and to identify new similarity concepts that we discuss in this paper and which
opens important applications for the present and the future laboratory
astrophysics experiments. All these results enable to demonstrate theoretically
that astrophysical phenomena in such radiating regimes can be explored
experimentally thanks to powerful facilities. Consequently the results
presented here are a fundamental tool for the high-energy density laboratory
astrophysics community in order to quantify the astrophysics relevance and
justify laser experiments. Moreover, relying on the Lie-group theory, this
paper constitutes the starting point of any analysis of the self-similar
dynamics of radiating fluids.
