On the Origin of the Fundamental Plane and Faber–Jackson Relations: Implications for the Star Formation Problem

The aim of this work is to show that the origin of the Fundamental Plane (FP) relation for early-type galaxies (ETGs) can be traced back to the existence of a fine-tuning between the average star formation rate $ $ of galaxies and their structural and dynamical characteristics. To get such result it is necessary to imagine the existence of two distinct "virtual planes" for each galaxy in the $\log(R_e)-\log(I_e)-\log(\sigma)$ space. The first one (named Virial Plane VP) represents the total galaxy mass using the scalar Virial Theorem and the mass-to-light ratio $M/L$, while the second plane comes from an expression of the total galaxy luminosity as a function of the mean star formation rate $ $ and the velocity dispersion $\sigma$, through a relation $L=L'_0 \sigma^{-2}$ (named here pseudo-Faber-Jackson (PFJ)) which is a mathematical convenient way for expressing the independency of light from the virial equilibrium. Its validity can be connected to the mutual correlation $L\sim\sigma\sqrt{ }$ observed for all ETGs. A posteriori it is possible to see that this approach permits to explain the observed properties of the FP (tilt and scatter) and the Zone of Exclusions (ZOE) visible in the FP projections. Furthermore, the link between the properties of the FP and the SFR of galaxies provides a new idea of the star formation, as a phenomenon driven by the initial conditions of proto-galaxies and regulated across the whole cosmic history by the variation of the main galaxy parameters (mass, luminosity, structural shape and velocity dispersion).