  We have recently shown that the 3-parameter density-profile model from
Prugniel & Simien provides a better fit to simulated, galaxy- and
cluster-sized, dark matter halos than an NFW-like model with arbitrary inner
profile slope gamma (Paper I). By construction, the parameters of the
Prugniel-Simien model equate to those of the Sersic R^{1/n} function fitted to
the projected distribution. Using the Prugniel-Simien model, we are therefore
able to show that the location of simulated (10^{12} M_sun) galaxy-sized dark
matter halos in the <mu>_e-log(R_e) diagram coincides with that of brightest
cluster galaxies, i.e., the dark matter halos appear consistent with the
Kormendy relation defined by luminous elliptical galaxies. These objects are
also seen to define the new, and equally strong, relation log(rho_e) = 0.5 -
2.5log(R_e), in which rho_e is the internal density at r=R_e. Simulated
(10^{14.5} M_sun) cluster-sized dark matter halos and the gas component of real
galaxy clusters follow the relation log(rho_e) = 2.5[1 - log(R_e)]. Given the
shapes of the various density profiles, we are able to conclude that while
dwarf elliptical galaxies and galaxy clusters can have dark matter halos with
effective radii of comparable size to the effective radii of their baryonic
component, luminous elliptical galaxies can not. For increasingly large
elliptical galaxies, with increasingly large profile shapes `n', to be dark
matter dominated at large radii requires dark matter halos with increasingly
large effective radii compared to the effective radii of their stellar
component.
