Is the shape of the luminosity profile of dwarf elliptical galaxies an useful distance indicator?

The shape of the surface brightness profile of dE galaxies, quantified by parameter n of Sersic's generalized profile law, has recently been put forward as new extragalactic distance indicator (Young & Currie 1994). Its application to the Virgo cluster has subsequently led to the claim that the Virgo dEs are not lying in the cluster core but are distributed in a prolate structure stretching from 8 to 20 Mpc distance (Young & Currie 1995). This claim is refuted here. We have fitted a Sersic law to the surface brightness profiles of 128 Virgo cluster dEs and dS0s from the photometry of Binggeli & Cameron (1991). The dispersion of the n - M relation is indeed large (sigma_rms ~ 0.9 mag). However, we argue that this scatter is not due to the depth of the Virgo cluster, but is essentially intrinsic. Contrary to what one would expect from the cluster depth hypothesis, there is no clear velocity-``distance'' relation for a sample of 43 Virgo dEs and dS0s with known redshifts. The analysis of Young & Currie (1995) is hampered by the use of low-resolution photometry and flawed by the assumption that the n - M and n - R relations can be used independently. By combining different Sersic law parameters, the scatter of the scaling relations can be reduced somewhat, but never below sigma_rms ~ 0.7 mag, at least for the Virgo cluster. For the purpose of distance measurements, this falls short of the well-established Tully-Fisher and D_n - sigma methods, and it is comparable to what one can get already from the < mu >_eff - M relation for dEs, which does not require any profile modelling.