This paper updates our derivation (Kormendy 1988, 1990; Kormendy & Freeman 1996) of scaling laws for DM halos of Sc - Im and dwarf spheroidal (dSph) galaxies. We show that DM halos in less luminous galaxies have smaller core radii rc, higher central densities 0, and smaller central velocity dispersions . These scaling laws are analogous to the fundamental plane relations for elliptical galaxies (Djorgovski & Davis 1986, 1987; Faber et al. 1987; Dressler et al. 1987; Djorgovski, de Carvalho, & Han 1988; see Kormendy & Djorgovski 1989 for a review), and they are interesting for the same reason: they provide new constraints on galaxy formation and evolution. Simple conclusions are discussed in Section 4. A detailed discussion will be published in Kormendy & Freeman (2003).
Halo parameters for giant galaxies are derived by decomposing rotation curves V(r) into visible matter and DM contributions (van Albada et al. 1985). At galaxy absolute magnitudes MB >> - 14, rotation curve decomposition becomes impossible as V decreases (Tully & Fisher 1977) and becomes similar to the velocity dispersion of the gas. Pressure-supported galaxies are not flat. DM central densities can still be derived, e.g., by fitting King (1966) models to the density and velocity dispersion profiles of dSph galaxies. But DM rc and can no longer be measured. In this paper, we combine these data to investigate the systematic properties of DM halos over a large range of galaxy luminosities.
Only Sc - Im and dwarf spheroidal (dSph) galaxies are included. Galaxies of type E - Sbc are omitted for two reasons that result from their bulge components. (1) Rotation curve decomposition must deal with two visible-matter components that have different unknown mass-to-light ratios. Therefore it is less reliable. (2) Gravitational compression of the DM by the baryons has substantially modified the halo when the visible mass density is high. Many Sa - Sbc galaxies satisfy the DM correlations, but others deviate in the direction of small rc and large 0 (Kormendy 1988, 1990). This is consistent with baryonic compression. Further evidence for baryonic compression is presented in Athanassoula, Bosma, & Papaioannou (1987, hereafter ABP). Baryonic compression corrections are omitted here but will be included in Kormendy & Freeman (2003).