The relationship between the Sérsic law profiles measured along the major and minor axes of elliptical galaxies

In this paper we discuss the reason why the parameters of the Sérsic model best-fitting the major axis light profile of elliptical galaxies can differ significantly from those derived for the minor axis profile. We show that this discrepancy is a natural consequence of the fact that the isophote eccentricity varies with the radius of the isophote and present a mathematical transformation that allows the minor axis Sérsic model to be calculated from the major axis model, provided that the elliptical isophotes are aligned and concentric and that their eccentricity can be represented by a well behaved, though quite general, function of the radius. When there is no variation in eccentricity only the effective radius changes in the Sérsic model, while for radial-dependent eccentricity the transformation which allows the minor axis Sérsic model to be calculated from the major axis model is given by the Lerch Φ transcendental function. The proposed transformation was tested using photometric data for 28 early-type galaxies.