Navarro-Frenk-White dark matter profile and the dark halos around disk
  systems
  The $\Lambda$ cold dark matter ($\Lambda$CDM) scenario well describes the
Universe at large scales, but shows some serious difficulties at small scales:
the inner dark matter (DM) density profiles of spiral galaxies generally appear
to be cored, without the $r^{-1}$ predicted by N-body simulations in the above
scenario.
  In a more physical context, the baryons in the galaxy might backreact and
erase the original cusp through supernova explosions. Before that this effect
be investigated, it is important to determine how wide and frequent the
discrepancy between observed and N-body predicted profiles is and what its
features are. We used more than 3200 quite extended rotation curves (RCs) of
good quality and high resolution of disk systems. The curves cover all
magnitude ranges. These RCs were condensed into 26 coadded RCs, each of them
built with individual RCs of galaxies of similar luminosity and morphology. We
performed mass models of these 26 RCs using the Navarro-Frenk-White (NFW)
profile for the contribution of the DM halo to the circular velocity and the
exponential Freeman disk for that of the stellar disk. The fits are generally
poor in all the 26 cases: in several cases, we find $\chi^2_{red}>2$. Moreover,
the best-fitting values of three parameters of the model ($c$, $M_D$, and
$M_{vir}$) combined with those of their 1$\sigma$ uncertainty clearly
contradict well-known expectations of the $\Lambda$CDM scenario. We also tested
the scaling relations that exist in spirals with the fitting outcome: the
modeling does not account for these scaling relations.
  Therefore, NFW halo density law cannot account for the kinematics of the
whole family of disk galaxies. It is therefore mandatory for the $\Lambda CDM$
scenario in any disk galaxy of any luminosity to transform initial cusps into
the observed cores.
