Tidal interactions between neighboring objects span across the wholeadmissible range of lengths in nature: from, say, atoms to clusters of galaxiesi.e. from micro to macrocosms. According to current cosmological theories,galaxies are embedded within massive non-baryonic dark matter (DM) halos, whichaffects their formation and evolution. It is therefore highly rewarding tounderstand the role of tidal interaction between the dark and luminous matterin galaxies. The current investigation is devoted to Early-Type Galaxies(ETGs), looking in particular at the possibility of establishing whether thetidal interaction of the DM halo with the luminous baryonic component may be atthe origin of the so-called "tilt" of the Fundamental Plane (FP). The extensionof the tensor virial theorem to two-component matter distributions implies thecalculation of the self potential energy due to a selected subsystem, and thetidal potential energy induced by the other one. The additional assumption ofhomeoidally striated density profiles allows analytical expressions of theresults for some cases of astrophysical interest. The current investigationraises from the fact that the profile of the (self + tidal) potential energy ofthe inner component shows maxima and minima, suggesting the possible existenceof preferential scales for the virialized structure, i.e. a viable explanationof the so called "tilt" of the FP. It is found that configurations related tothe maxima do not suffice, by themselves, to interpret the FP tilt, and someother relation has to be looked for.
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