Weak homology of elliptical galaxies

Studies of the Fundamental Plane of early{type galaxies, from small to intermediate redshifts, are generally carried out under the guiding principle that the Fundamental Plane reflects the existence of an underlying mass{luminosity relation for such galaxies, in a scenario where galaxies are homologous systems in dynamical equilibrium. In this paper we re-examine the question of whether a systematic non{homology could be partly responsible for the correlations that dene the Fundamental Plane. We start by studying a small set of objects characterized by photometric proles that have been pointed out to deviate signicantly from the standard R 1=4 law. For these objects we conrm that a generic R 1=n law, with n a free parameter, can provide superior ts (the best-t value of n can be lower than 2.5 or higher than 10), better than those that can be obtained by a pure R 1=4 law, by an R 1=4 + exponential model, and by other dynamically justied self{consistent models. Therefore, strictly speaking, elliptical galaxies should not be considered homologous dynamical systems. Still, a case for weak homology, useful for the interpretation of the Fundamental Plane, could be made if the best-t parameter n, as often reported, correlates with galaxy luminosity L, provided the underlying dynamical structure also follows a systematic trend with luminosity. We demonstrate that this statement may be true even in the presence of signicant scatter in the correlation n(L). Preliminary indications provided by a set of \data points" associated with a sample of 14 galaxies suggest that neither the strict homology nor the constant stellar mass{ to{light solution are a satisfactory explanation of the observed Fundamental Plane. These conclusions await further extensions and clarications, because the class of low{luminosity early{type galaxies, which contribute signicantly to the Fundamental Plane, falls outside the simple dynamical framework considered here and because dynamical considerations should be supplemented with other important constraints derived from the evolution of stellar populations.