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

¹ Instituto de Astrofísica de Andalucía (C.S.I.C.), Apartado 3004, 18080 Granada, Spain
² Instituto Astronômico e Geofísico/USP, Av. Miguel Stefano 4200, São Paulo/SP, Brazil
³ Instituto Nacional de Pesquisas Espaciais, São José dos Campos/SP, Brazil
⁴ Institut d'Astrophysique de Paris, CNRS, 98bis Bld Arago, 75014 Paris, France
⁵ DAEC, Observatoire de Paris, Université Paris VII, CNRS (UA 173), 92195 Meudon Cedex, France
⁶ Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy

Corresponding author: I. Márquez, isabel@iaa.es

Received: 22 December 2000
Accepted: 18 September 2001

Abstract

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 Sérsic law parameters (intensity , scale a and shape ν), 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 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.