There has long been evidence that low-mass galaxies are systematically larger in radius , of lower central stellar mass density , and of lower central phase-space density , than are star clusters of the same luminosity .
The larger radius , at a comparable value of central velocity dispersion , implies a larger mass at similar luminosity , and hence significant dark matter , in dwarf galaxies , compared to no dark matter in star clusters .
We present a synthesis of recent photometric and kinematic data for several of the most dark-matter dominated galaxies .
There is a bimodal distribution in half-light radii , with stable star clusters always being smaller than \sim 30 pc , while stable galaxies are always larger than \sim 120 pc .
We extend the previously known observational relationships and interpret them in terms of a more fundamental pair of intrinsic properties of dark matter itself : dark matter forms cored mass distributions , with a core scale length of greater than about 100pc , and always has a maximum central mass density with a narrow range .
The dark matter in dSph galaxies appears to be clustered such that there is a mean volume mass density within the stellar distribution which has the very low value of about 0.1 M _ { \odot } pc ^ { -3 } ( about 5GeV/c ^ { 2 } cm ^ { -3 } ) .
All dSphs have velocity dispersions equivalent to circular velocities at the edge of their light distributions of \sim 15 km s ^ { -1 } .
In two dSphs there is evidence that the density profile is shallow ( cored ) in the inner regions , and so far none of the dSphs display kinematics which require the presence of an inner cusp .
The maximum central dark matter density derived is model dependent , but is likely to have a mean value ( averaged over a volume of radius 10 pc ) of \sim 0.1 M _ { \odot } pc ^ { -3 } ( about 5 GeV/c ^ { 2 } cm ^ { -3 } ) for our proposed cored dark mass distributions ( where it is similar to the mean value ) , or \sim 60 M _ { \odot } pc ^ { -3 } ( about 2 TeV/c ^ { 2 } cm ^ { -3 } ) if the dark matter density distribution is cusped .
Galaxies are embedded in dark matter halos with these properties ; smaller systems containing dark matter are not observed .
These values provide new information into the nature of the dominant form of dark matter .