Empirical Models for Dark Matter Halos. III. The Kormendy Relation and the log�?_<i>e</i>?log�<i>R</i>_<i>e</i>Relation

Abstract

We have recently shown that the 3-parameter density-profile model from Prugniel &amp;amp; Simien provides a better fit to simulated, galaxy- and cluster-sized, dark matter halos than an NFWlike model with arbitrary inner profile slope γ (Paper I). By construction, the parameters of the Prugniel-Simien model equate to those of the Sérsic 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⊙) galaxy-sized dark matter halos in the 〈µ〉e–log Re 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 important, relation log(ρe) = 0.5 − 2.5 log(Re), in which ρe is the internal density at r = Re. Simulated (10 14.5 M⊙) cluster-sized dark matter halos and the gas component of real galaxy clusters follow the relation log(ρe) = 2.5[1 − log(Re)]. 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,