Abstract
We have analyzed the distribution of early-type galaxies (ETGs) in the effective surface intensity vs. effective radius (Ie−Re) plane and in the total luminosity vs. central stellar velocity dispersion (L−σ) diagram, with the aim of studying the physical variables that allow the transformation of one space-parameter into the other. We find that the classical Faber–Jackson relation L=L0σα, in which the parameters L0 and α are confined in a small range of possible values, is incompatible with the distribution observed in the Ie−Re plane. The two distributions become mutually consistent only if luminosity is not considered a pure proxy of mass but a variable tightly dependent on the past history of mass assembling and star formation and on the present evolutionary state of the stellar content of a galaxy. The solution comes by considering the L=L0′σβ law proposed by D’Onofrio et al. in 2020, in which both L0′ and β can vary considerably from galaxy to galaxy. We will also show that the data of the Illustris numerical simulation prove the physical foundation of the L=L0′σβ law and confirm the prediction of the Zone of Exclusion (ZoE) originating from the intersection of the virial law with the L=L0′σβ relation. The ZoE is the region in the Ie−Re and Re−Ms diagrams avoided by real galaxies, and the border of which marks the condition of ‘full’ virial equilibrium with no recent significant merger events and no undergoing star formation.
Highlights
The plan of the paper is as follows: In Section 2, we describe the data used in our study; in Section 3, we provide a brief theoretical introduction aimed at demonstrating that the Ie − Re and L − σ relations can be linked with each other; in Section 4, we prove that the Ie − Re plane cannot be derived from the classical Faber and Jackson (FJ) relation taking into account the uncertainties on L0 and α nor considering the possibility that the FJ is a bi- or threesegmented relation with different values for L0 and α passing from low to high luminosity
We have demonstrated above that the Ie − Re and L − σ distributions are only mutually compatible if we accept the idea that luminosity and velocity dispersion of each individual galaxy are related by the L = L00 σ β law, where L00 and β vary from galaxy to galaxy and over the course of time
The distribution observed in the Ie − Re plane originates from the L = L00 σ β relation, in particular, on the spectrum of values attained by β and L00 that each galaxy can experience during its evolution; The distribution does not depend on the definition of Re and Ms but only on the history of mass assembly, mass removal, star formation and evolution of the stellar content; All the scaling relations based on the effective radius Re can be interpreted as originating from the combination of the Virial Theorem (VT) and the L = L00 σ β distribution
Summary
The scaling relations (SRs) are the chief tool at our disposal to decipher the physical properties of galaxies and their past history of formation and evolution. They are often represented by mathematical expressions that are fit of observed distributions in a parameters space. Luminosity might increase/decrease for different reasons related to the star formation activity and/or the mass accumulation/stripping during merger events and the passive stellar evolution. This makes L a parameter that is not a simple proxy of mass but conceals the non-linear history of a galaxy growth. In some SRs, luminosity enters as a proxy of mass, while in others, it displays its full physical background
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