Clausius' virial vs. total potential energy in a two-heterogeneous component system

As underlined in a previous paper (Secco 2000), in a double gravitational bound system in virial equilibrium the Clausius' virial of one subcomponent is not, in general, equal to the total potential energy of the same component as it occurs in a single system without external forces. This is the main reason for the presence, in the cases of two non-coinciding concentric spheroidal subsystems, of a minimum (in absolute value) in the Clausius' virial trend of the inner component B, as its dimension decreases at fixed size and shape of the outer D component, instead of a monotonic absolute increasing trend usually obtained for the total potential energy of the same subsystem. That has been already proved in the case of two heterogeneous homothetic oblate spheroids of spheroidal, similar strata with two power-law density profiles and surely in some cases of non-similar components (Caimmi and Secco 2000). As the minimum appears it leads to the definition of a tidal scale length induced from the outer system on the inner one. What may be the relevance of this scale length in some aspects of the galaxy dynamics we have already investigated (see, e.g., Secco 2001). A new physical insight may be get by looking at the location of this special length inside the plot of the total potential energies of both subsystems separately and of the whole system taking into account also the trend of the antisymmetric residual-energy that is the difference between the tidal and the interaction-energy of each component