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 Claus ius' virial minimum, of a bright component which is completely embedded ins ide a dark halo. It was assumed that the two subsystems are concentric and coaxial, similar, heterogeneous spheroids, with two different, power-law de nsity 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, tida l-potential energy due to a dark halo, and self-potential energy. These pro perties and the structure of dark matter halo, which allows the existence o f the virial minimum, turn out to be the key for understanding the observed properties of FP. A universal, dark matter distribution of exponent d simi lar or equal to 0.5 inside the luminous subsystem, seems to be required whe n comparing with the observed tilt of FP. (C) 2001 Elsevier Science B.V. Al l rights reserved.