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The S\'ersic or $R^{1/m}$ model has become the de facto standard model todescribe the surface brightness profiles of early-type galaxies and the bulgesof spiral galaxies. The photometric, intrinsic, and dynamical properties ofthis model have been investigated, but mainly for fairly large S\'ersic indices$m$. For small values of $m$, appropriate for low-mass and dwarf ellipticals, adetailed investigation of these properties is still lacking. In this study, weused a combination of numerical and analytical techniques to investigate theS\'ersic model over the entire range of S\'ersic parameters, focussing on thesmall $m$ regime, where a number of interesting and surprising properties arefound. For all values $m<1$, the model is characterised by a finite centralluminosity density, and for $m<\tfrac12$, even a central depression in theluminosity density profile. This behaviour translates to the dynamicalproperties: we show that all S\'ersic models with $m \geqslant\tfrac12$ can besupported by an isotropic velocity dispersion tensor, and that these isotropicmodels are stable to both radial and non-radial perturbations. The models with$m < \tfrac12$, on the other hand, cannot be supported by an isotropic velocitydispersion tensor.

Stellar systems following the $R^{1/m}$ luminosity law. III. Photometric, intrinsic, and dynamical properties for all S\'ersic indices