Scaling Laws for Dark Matter Halos in Late-Type and Dwarf Spheroidal Galaxies

Dark matter (DM) halos of Sc–Im and dwarf spheroidal (dSph) galaxies satisfy scaling laws: halos in lower-luminosity galaxies have smaller core radii, higher central densities, and smaller velocity dispersions. These results are based on maximum-disk rotation curve decompositions for giant galaxies and Jeans equation analysis for dwarfs. (1) We show that spiral, Im, and Sph galaxies with absolute magnitudes M V > −18 form a sequence of decreasing baryon-to-DM surface density with decreasing luminosity. We suggest that this is a sequence of decreasing baryon retention versus supernova-driven losses or decreasing baryon capture after cosmological reionization. (2) The structural differences between S+Im and Sph galaxies are small. Both are affected mostly by the physics that controls baryon depletion. (3) There is a linear correlation between the maximum rotation velocities of baryonic disks and the outer circular velocities V circ of test particles in their DM halos. Baryons become unimportant at V circ = 42 ± 4 km s −1 . Smaller galaxies are dim or dark. (4) We find that, absent baryon "depletion" and with all baryons converted into stars, dSph galaxies would be brighter by ∼4.6 mag and dIm galaxies would be brighter by ∼3.5 mag. Both have DM halos that are massive enough to help to solve the "too big to fail" problem with DM galaxy formation. (5) We suggest that there exist many galaxies that are too dark to be discovered by current techniques, as required by cold DM theory. (6) Central surface densities of DM halos are constant from M B ∼ −5 to −22. This implies a Faber–Jackson law with halo mass M ∝ (halo dispersion) 4 .