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 _ { \ast } ( 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 \pm 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 \alpha = 0.18 \pm 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 \alpha = 0.20 \pm 0.05 .
These results leave little room for the recently claimed universality of ( dark and stellar ) column density .