Surface Density of dark matter haloes on galactic and cluster scales

In this paper, in the framework of the secondary infall model, the correlation between the central surface density and the halo core radius of galaxy, and cluster of galaxies, dark matter haloes was analyzed, this having recently been studied on a wide range of scales. We used Del Popolo (2009) secondary infall model taking into account ordered and random angular momentum, dynamical friction, and dark matter (DM) adiabatic contraction to calculate the density profile of haloes, and then these profiles are used to determine the surface density of DM haloes. The main result is that $r_∗$ (the halo characteristic radius) is not an universal quantity as claimed by Donato et al. (2009) and Gentile et al. (2009). On the contrary, we find a correlation with the halo mass $M_200$ in agreement with Cardone & Tortora (2010), Boyarsky at al. (2009) and Napolitano et al. (2010), but with a significantly smaller scatter, namely $0.16 ± 0.05$. We also consider the baryon column density finding this latter being indeed a constant for low mass systems such as dwarfs, but correlating with mass with a slope $α= 0.18 ± 0.05$. In the case of the surface density of dark matter for a system composed only of dark matter, as in dissipationless simulations, we get $α=0.20 ± 0.05$. These results leave little room for the recently claimed universality of (dark and stellar) column density.