Stellar systems following the R 1/m luminosity law: III. Photometric, intrinsic, and dynamical properties for all Sérsic indices

The Sérsic or R1/m model has become the de facto standard model to describe the surface brightness profiles of early-Type galaxies and the bulges of spiral galaxies. The photometric, intrinsic, and dynamical properties of this model have been investigated, but mainly for fairly large Sérsic indices m. For small values of m, appropriate for low-mass and dwarf ellipticals, a detailed investigation of these properties is still lacking. In this study, we used a combination of numerical and analytical techniques to investigate the Sérsic model over the entire range of Sérsic parameters, focussing on the small m regime, where a number of interesting and surprising properties are found. For all values mâ < â 1, the model is characterised by a finite central luminosity density, and for m < 1/2, even a central depression in the luminosity density profile. This behaviour translates to the dynamical properties: we show that all Sérsic models with m ≥ 1/2 can be supported by an isotropic velocity dispersion tensor, and that these isotropic models are stable to both radial and non-radial perturbations. The models with m < 1/2, on the other hand, cannot be supported by an isotropic velocity dispersion tensor.