The fundamental Plane as a consequence of Clausius' virial minimum

In order to explain the main features of the Fundamental Plane for pressure-supported, elliptical galaxies, we analysed the virialized state, at Clausius' virial minimum, of a bright component which is completely embedded inside a dark halo. It was assumed that the two subsystems are concentric and coaxial, similar, heterogeneous spheroids, with two different, power-law density distributions. The peculiarities of Clausius' virial minimum are: (i) it provides an induced scale length for the luminous structure, which, at given mass distributions, corresponds to the maximum virial dimension with minimal random kinetic energy; (ii) it shares in almost equal amounts, tidal-potential energy due to a dark halo, and self-potential energy. These properties and the structure of dark matter halo, which allows the existence of the virial minimum, turn out to be the key for understanding the observed properties of FP. A universal, dark matter distribution of exponent /d~=0.5 inside the luminous subsystem, seems to be required when comparing with the observed tilt of FP.