The Distribution of Dark Matter in Galaxies: the Core Radius Issue

I review the up-to-date status on the properties of the Dark Matter density distribution around Galaxies. The rotation curves of spirals all conform to a same Universal profile which can be uniquely decomposed as the sum of an exponential thin stellar disk and a dark halo with a flat density core. From dwarfs to giants galaxies, the halos embedding the stellar component feature a constant density region of size $r_0$ and value $\rho_0$, which are inversely correlated. The fine structure of dark halos in the region of the stellar disk has been derived for a number of low--luminosity disk galaxies: the halo circular velocity increases almost linearly with radius out to the edge of the stellar disk, implying, up there, an almost constant dark matter density. This sets a serious discrepancy between the cuspy density distribution predicted by N-body simulations of $\Lambda$CDM cosmology, and those actually detected around galaxies. The small scatter around the Fundamental Plane (FP) of elliptical galaxies constraints the distribution of dark and luminous matter in these systems. The measured central velocity dispersion $\sigma_0$ in the FP is linked to both photometric and dynamical properties of luminous and dark matter. As a consequence, the well-known features of the FP imply that, inside the effective radius $R_e$, the stellar spheroid must dominate over the dark matter, in contrast with $\Lambda$CDM predictions