Published mass models fitted to galaxy rotation curves are used to study the systematic properties of dark matter (DM) halos in late-type and dwarf spheroidal (dSph) galaxies. Halo parameters are derived by fitting non-singular isothermals to (V(2) - V(vis)(2))(1/2), where V(r) is the observed rotation curve and V(vis) is the rotation curve of the visible matter. The latter is calculated from the surface brightness assuming that the mass-to-light ratio M/L is constant with radius. "Maximum disk" values of M/L are adjusted to fit as much of the inner rotation curve as possible without making the halo have a hollow core. Rotation curve decomposition becomes impossible fainter than absolute magnitude M(B) similar or equal to -14, where V becomes comparable to the velocity dispersion of the gas. To increase the luminosity range further, we include dSph galaxies, which are physically related to spiral and irregular galaxies. Combining the data, we find that DM halos satisfy well defined scaling laws analogous to the "fundamental plane" relations for elliptical galaxies. Halos in less luminous galaxies have smaller core radii r(c), higher central densities rho(0), and smaller central velocity dispersions sigma. Scaling laws provide new and detailed constraints on the nature of DM and on galaxy formation and evolution. Some simple implications include: 1 - A single, continuous physical sequence of increasing mass extends from dSph galaxies with M(B) similar or equal to -7.6 to ScI galaxies with M(B) similar or equal to -22.4. 2 - The high DM densities in dSph galaxies are normal for such tiny galaxies. Since virialised density depends on collapse redshift z(coll), rho(0) proportional to (1 + z(coll))(3), the smallest dwarfs formed at least Deltaz(coll) similar or equal to 7 earlier than the biggest spirals. 3 - The high DM densities of dSphs implies that they are real galaxies formed from primordial density fluctuations. They are not tidal fragments. Tidal dwarfs cannot retain even the low DM densities of their giant-galaxy progenitors. In contrast, dSphs have higher DM densities than do giant-galaxy progenitors. 4 - The fact that, as luminosity decreases, dwarf galaxies become much more numerous and also more nearly dominated by DM raises the possibility that there exists a large population of objects that are completely dark. Such objects are a canonical prediction of cold DM theory. If they exist, "empty halos" are likely to be small and dense - that is, darker versions of Draco and UMi. 5 - The slopes of the DM parameter correlations provide a measure on galactic mass scales of the slope n of the power spectrum |delta(k)|(2) proportional to V of primordial density fluctuations. Our preliminary results, not yet corrected for baryonic compression of DM, give n similar or equal to -1.9 +/- 0.2. This is consistent with cold DM theory.
