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 gravitationa l systems and therefore they also have a quasi-constant specific entropy. A ssuming that light traces mass, these two laws imply that in the space defi ned by the three Sersic law parameters (intensity Sigma (0), scale a and sh ape v), elliptical galaxies are distributed on two intersecting 2-manifolds : the Entropic Surface and the Energy-Mass Surface. Using a sample of 132 g alaxies belonging to three nearby clusters, we have verified that elliptica ls indeed follow these laws. This also implies that they are distributed al ong the intersection line (the Energy-Entropy line), thus they constitute a one-parameter family. These two physical laws (separately or combined), al low to find the theoretical origin of several observed photometrical relati ons, such as the correlation between absolute magnitude and effective surfa ce brightness, and the fact that ellipticals are located on a surface in th e [log R-eff, -2:5 log Sigma (0); log v] space. The fact that elliptical ga laxies are a one-parameter family has important implications for cosmology and galaxy formation and evolution models. Moreover, the Energy-Entropy lin e could be used as a distance indicator.