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HST photometry of dwarf elliptical galaxies in Coma, and an explanation for the alleged structural dichotomy between dwarf and bright elliptical galaxies

We have analyzed archival HST F606W images of 18 dwarf elliptical (dE) galaxy candidates in the Coma Cluster. We model the full radial extent of their light-profiles by simultaneously fitting a PSF-convolved Sersic R^(1/n) model and, when necessary, either a central point-source or a central PSF-convolved Gaussian. The luminosities of the central component L_nuc scale with the host galaxy luminosity L_gal such that L_nuc = 10^(4.76 +/- 0.10)*(L_gal/10^7)^(0.87 +/- 0.26). The underlying host galaxies display systematic departures from an exponential model that are correlated with the model-independent host galaxy luminosity and are not due to biasing from the nuclear component. The Pearson correlation coefficient between log(n) and central galaxy surface brightness mu_0 (excluding the flux from extraneous central components) is -0.83 at a significance level of 99.99%. The Pearson correlation coefficient between the logarithm of the Sersic index `n' and the host galaxy magnitude is -0.77 at a significance of 99.9%. We explain the observed relationship between dE galaxy luminosity and inner logarithmic profile slope (gamma-prime) as a by-product of the correlation between luminosity and Sersic index n. Including, from the literature, an additional 232 dE and E galaxies spanning 10 mag in absolute magnitude (M), the dE galaxies are shown to display a continuous sequence with the brighter E galaxies such that mu_0 brightens linearly with M until core formation causes the most luminous (M_B < -20.5 mag) E galaxies to deviate from this relation. The different behavior of dE and E galaxies in the M-mu_e (and M-<mu>_e) diagram, and the <mu>_e-log(R_e) diagram have nothing to do with core formation, and are in fact expected from the continuous and linear relation between M and mu_0 and M and log(n).