Lambda CDM halo density profiles: where do actual halos converge to NFW ones?

Aims. We present an analysis of 37 high-quality extended rotation curves that highlights the existence of a new discrepancy (or a new aspect of an old discrepancy) between the density profiles predicted by the Lambda Cold Dark Matter (LambdaCDM) theory and the actual distribution of dark matter in galaxies. Methods. We compare the predicted face-value density vs. enclosed mass relationship, at large distances, to the observational data at the last measured radii of the rotation curves and in two whole rotation curves of high quality. A further analysis is performed by studying a relation, inbuilt in LambdaCDM, that links at radius R, the enclosed halo mass M(R) and its density rho(R) in a way that is independent of the mass of the virialised object. Results. We find that the predicted density vs. enclosed mass relationship has a systematic offset with respect to the observational data. In test case extended rotation curves, at their last measured point, the predicted NFW densities are up to a factor 3 lower than those derived from the kinematics. Moreover, the abovementioned relation, inbuilt in LambdaCDM, does not hold for the objects of our sample. Such a new outer discrepancy is different and maybe complementary with respect to the core/cusp issue, for which the NFW densities turn out to be higher than those observed and it seems to imply a global mass rearrangement of a pristine NFW-LambdaCDM halo