Stellar systems following the R1/m luminosity law: III. Photometric, intrinsic, and dynamical properties for all Sérsic indices

The Sersic or R 1/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 Sersic 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 Sersic model over the entire range of Sersic parameters, focussing on the small m regime, where a number of interesting and surprising properties are found. For all values m  <  1, the model is characterised by a finite central luminosity density, and for , even a central depression in the luminosity density profile. This behaviour translates to the dynamical properties: we show that all Sersic models with 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 , on the other hand, cannot be supported by an isotropic velocity dispersion tensor.