As found in Secco (2000, 2001), the presence of a (non-baryonic) dark halo in large-scale celestial objects, can induce a scale length on the luminous spheroid through the occurrence of an unexpected maximum in the virial potential energy (Clausius Virial, CV). The above mentioned investigations were grounded on two cored power law density profiles, but the same result is shown to hold for more refined and realistic models.