Dark Matter Scaling Relations

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Abstract
We investigate the structure of dark matter halos by means of the kinematics of a very large sample of spiral galaxies of all luminosities. The observed rotation curves show a universal profile which is the sum of an exponential thin disk term and a spherical halo term with a flat density core. We find that the Burkert profile proposed to describe the dark matter halo density distribution of dwarf galaxies also provides an excellent mass model for the dark halos around disk systems up to 100 times more massive. Moreover, we find that spiral dark matter core densities ρ0 and core radii r0 lie in the same scaling relation ρ0 = 4.5 × 10-2(r0/kpc)-2/3 M☉ pc-3 of dwarf galaxies with core radii up to 10 times smaller. At the highest masses ρ0 decreases with r0 faster than the - power law, implying a lack of objects with disk masses greater than 1011 M☉ and central densities greater than 1.5 × 10-2(r0/kpc)-3 M☉ pc-3 that can be explained by the existence of a maximum mass of about 2 × 1012 M☉ for a halo hosting a spiral galaxy.
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