Energy, entropy and mass scaling relations for elliptical galaxies. Towards a physical understanding of their photometric properties

In the present paper, we show that elliptical galaxies (Es) obey a scaling relation between potential energy and mass. Since they are relaxed systems in a post violent-relaxation stage, they are quasi-equilibrium gravitational systems and therefore they also have a quasi-constant specific entropy. Assuming that light traces mass, these two laws imply that in the space defined by the three S\'ersic law parameters (intensity Sigma_0, scale a and shape nu), elliptical galaxies are distributed on two intersecting 2-manifolds: the Entropic Surface and the Energy-Mass Surface. Using a sample of 132 galaxies belonging to three nearby clusters, we have verified that ellipticals indeed follow these laws. This also implies that they are distributed along the intersection line (the Energy-Entropy line), thus they constitute a one-parameter family. These two physical laws (separately or combined), allow to find the theoretical origin of several observed photometrical relations, such as the correlation between absolute magnitude and effective surface brightness, and the fact that ellipticals are located on a surface in the [log R_eff, -2.5 log Sigma_0, log nu] space. The fact that elliptical galaxies are a one-parameter family has important implications for cosmology and galaxy formation and evolution models. Moreover, the Energy-Entropy line could be used as a distance indicator.