On the origin of the Fundamental Plane and Faber-Jackson relations: consequences for the star formation problem

TL;DR

This paper proposes that the Fundamental Plane of early-type galaxies originates from a fine-tuned relationship between star formation rates and galaxy structure, explaining observed properties and linking star formation to initial conditions and galaxy parameters.

Contribution

It introduces a model with two virtual planes in galaxy parameter space, connecting star formation rates to the Fundamental Plane and explaining its tilt, scatter, and the Zone of Exclusions.

Findings

The model explains the tilt and scatter of the FP.

It accounts for the Zone of Exclusions in FP projections.

Links star formation history to galaxy structural properties.

Abstract

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 $<SFR>$ 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 $<SFR>$ 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 $L\sim\sigma\sqrt{<SFR>}$ 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).