Sersic fit to low luminosity elliptical (NGC 4464) showing near-nuclear excess. This is termed a "Power Law" or "Coreless" galaxy. [Figures from Kormendy et al 2009 o-link]
Sersic fit to high luminosity elliptical (NGC 4649) showing near-nuclear loss. This is termed a "Core" galaxy.
Central profiles matched near the break radius. There is a clear division into those with (cuspy, not flat) cores, and those without (power laws). Notes M32 and M87 are the two prototypes shown with dashed lines.
The central luminosity density (in Lsun/pc3 at 0.1 arcsec) is much higher for the power-law Ellipticals than for he Core Ellipticals. By definition, the innermost slopes are less in the Core Ellipticals. This illustrates the current (HST) limits of distance probed. [Figure from Lauer et al (1995 o-link) ]