As part of a research program exploring how and why dwarf elliptical ( dE ) galaxies depart from the Fundamental Plane defined by luminous elliptical ( E ) galaxies , we have analyzed archival Hubble Space Telescope F606W images of a sample of 18 dE galaxy candidates in the Coma Cluster .
We model the full radial extent of their light-profiles by simultaneously fitting a PSF-convolved Sérsic R ^ { 1 / n } 
model and , when necessary , either a central point-source or a central PSF-convolved Gaussian .
Nucleation was detected in all but two of our final sample of 15 dE galaxies .
When detected , the luminosities of the central component L _ { nuc } 
scale with the host galaxy luminosity L _ { gal } such that L _ { nuc } = 10 ^ { 4.76 \pm 0.10 } \left ( L _ { gal } / 10 ^ { 7 } \right ) ^ { 0.87 \pm 0.26 } .
We confirm that the light-profiles of 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 % .
Excluding one outlier , the Pearson correlation coefficient between the logarithm of the Sérsic 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 the inner logarithmic profile slope \gamma \prime as a by-product of the correlation between luminosity and Sérsic 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 } \lesssim - 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 ) .