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 } \simeq - 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 } \simeq - 7.6 to Sc I galaxies with M _ { B } \simeq - 22.4 .

2 – The high DM densities in dSph galaxies are normal for such tiny galaxies .
Since virialized density depends on collapse redshift z _ { coll } , \rho _ { 0 } \propto ( 1 + z _ { coll } ) ^ { 3 } , the smallest dwarfs formed at least \Delta z _ { coll } \simeq 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 can not 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 } \propto k ^ { n } of primordial density fluctuations .
Our preliminary results not yet corrected for baryonic compression of DM give n \simeq - 1.9 \pm 0.2 .
This is consistent with cold DM theory .