On the shape of the light profiles of early type galaxies – II. The $(D_\text n/A_\text e)-\langle\mu\rangle_\text e$ diagram

Abstract

We present new evidence against the universality of the de Vaucouleurs $$r^{1/4}$$ law, considered to be the best empirical formula for fitting the light profiles of elliptical galaxies, through the analysis of the properties of the $$(D_\text n/A_\text e)-\langle\mu\rangle_\text e$$ diagram for a volume-limited sample of early-type galaxies that are members of the Virgo and Fornax clusters. The $$r^{1/4}$$ law turns out to be only a particular case of the more general $$r^{1/m}$$ law, where the exponent m is found to correlate with the effective radius of the galaxy. We compare our sample of early-type galaxies with that studied by Burstein et al., and find that the observed differences can be explained in terms of procedures and methodologies adopted for measuring the global photometric parameters such as total luminosities, effective radii, effective surface brightnesses and $$D_\text n$$ diameters.