Context. The Λ cold dark matter (ΛCDM) scenario is able to describe the Universe at large scales, but clearly shows some serious difficulties at small scales. The core-cusp question is one of these difficulties: the inner dark matter (DM) density profiles of spiral galaxies generally appear to be cored, without the r-1 profile that is predicted by N-body simulations in the above scenario. Aims. It is well known that in a more physical context, the baryons in the galaxy might backreact and erase the original cusp through supernova explosions. Before the efficiency and the presence of this effect is 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. Methods. We used more than 3200 quite extended rotation curves (RCs) of good quality and high resolution of disk systems that included normal and dwarf spirals as well as low surface brightness galaxies. The curves cover all magnitude ranges. All 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 the contribution of the stellar disk. Results. The fits are generally poor in all the 26 cases: in several cases, we find χred2 > 2. Moreover, the best-fitting values of three parameters of the model (c, MD, and Mvir) combined with those of their 1σ uncertainty clearly contradict well-known expectations of the ΛCDM scenario. We also tested the scaling relations that exist in spirals with the outcome of the current mass modeling: the modeling does not account for these scaling relations. Conclusions. The results of testing the NFW profile in disk systems indicate that this DM halo density law cannot account for the kinematics of the whole family of disk galaxies. It is therefore mandatory for the success of the ΛCDM scenario in any disk galaxy of any luminosity or maximum rotational velocity to transform initial cusps into the observed cores.
