In fact, the points representative of these active galaxies are spread in the plot over the discrete sources line and around the diffuse gas line (see Fig.\[X3\], left side). In the L$_X$–L$_{FIR}$ diagram (Fig.\[X3\], right side) the spread is similar to that of early-type galaxies plotted in Fig.\[X2\], but we separately plotted the active galaxies because of the particular nature of their X-ray emission, due to the nuclear contribution.

Modelling $L_{X}$, $L_{B}$ and $L_{FIR}$ of early-type galaxies {#Modelling}
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To cast light on the nature of the relations observed between $L_{X}$, **$L_{B}$** and $L_{FIR}$ for early-type galaxies, one has to consider the various components of a galaxy (stars, gas and dust) and to understand their mutual interactions as far as the spectral energy distribution (SED) is concerned. There are two basic schemes to model the formation and evolution of early type galaxies: (1) the semi-analytical models on which a great deal of our understanding of the chemo-spectro-photometric properties is derived, and (2) the N-Body Tree-SPH simulations which, in contrast, have been only occasionally used to study spectro-photometric properties of early type galaxies. In the following part of this section we will proceed as follows. First we will analyse the drawbacks 