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We expand our previous analytical and numerical studies of the family ofS\'ersic models, routinely used to describe early-type galaxies and the bulgesof spiral galaxies. In particular, we focus on the total energy budget, animportant dynamical property that has not been discussed in detail in previousworks. We use two different methods to calculate the total energy for theS\'ersic model family, resulting in two independent expressions that can beused along the entire sequence of S\'ersic models. We use these expressions toinvestigate whether the Spitzer concentration index is a reliable measure forthe intrinsic 3D concentration of galaxies, and we conclude that it is not avery useful measure for the central concentration. The popular Third GalaxyConcentration index, on the other hand, is shown to be a reliable measure forthe intrinsic 3D concentration, even though it is based on the surfacebrightness distribution and not on the intrinsic 3D density.

Stellar systems following the $R^{1/m}$ luminosity law. IV. The total energy and the central concentration of galaxies