1. MOTIVATION

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 r_c, 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 M_B >> - 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 r_c 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 r_c 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).