Stellar systems following the R^1/m luminosity law

IV. The total energy and the central concentration of galaxies

¹ Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000 Gent, Belgium
e-mail: maarten.baes@ugent.be
² Dipartimento di Fisica e Astronomia, Università di Bologna, Via Piero Gobetti 93/2, Bologna, Italy

Received: 22 July 2019
Accepted: 2 September 2019

Abstract

We expand our previous analytical and numerical studies of the family of Sérsic models, which are routinely used to describe early-type galaxies and the bulges of spiral galaxies. In particular, we focus on the total energy budget, an important dynamical property that has not been discussed in detail in previous works. We use two different methods to calculate the total energy for the Sérsic model family that result in two independent expressions that can be used along the entire sequence of Sérsic models. We use these expressions to investigate whether the Spitzer concentration index is a reliable measure for the intrinsic 3D concentration of galaxies, and we conclude that it is not a very useful measure for the central concentration. The popular Third Galaxy Concentration index, on the other hand, is shown to be a reliable measure for the intrinsic 3D concentration, even though it is based on the surface brightness distribution and not on the intrinsic 3D density.