A new model for Clausius' virial maximum theory: explanation of galaxy Fundamental Plane tilt.

The theory of the Clausius' virial maximum proposed by Secco (2000, 2001, 2005) is based on the existence of a maximum in the Clausius' Virial potential energy of a baryonic component when it is completely embedded inside a dark matter (DM) halo. When this maximum is reached the baryonic inner component acquires a scale length in its own gravity field due to the induced effect on it from the dark matter gravitation. The existence of this special configuration among the infinity number of those an inner component may assume inside an outer DM halo is able to explain the typical scale relationships observed for the early type galaxies (ETGs) which derive from their lying on the Fundamental Plane (FP). To prove that we model an ETG in the following way: an inner baryonic component of stellar kind built-up by a King-model with a cut-off and a DM halo with a cored power law density profile. The two components, which are gravitationally interacting, settle on virial equilibrium after violent relaxation. The new improved model allows us to understand more deeply the dynamical reason of the FP existence and in particular why it has a tilt. The main puzzle may be also fully understood that is why the FP is degenerated with respect to the initial density perturbation spectrum in a CDM hierarchical clustering cosmological scenario