Find in Library

We have analyzed the distribution of early-type galaxies (ETGs) in the effective surface intensity vs. effective radius (<inline-formula><math display="inline"><semantics><mrow><msub><mi>I</mi><mi>e</mi></msub><mo>−</mo><msub><mi>R</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula>) plane and in the total luminosity vs. central stellar velocity dispersion (<inline-formula><math display="inline"><semantics><mrow><mi>L</mi><mo>−</mo><mi>σ</mi></mrow></semantics></math></inline-formula>) 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 <inline-formula><math display="inline"><semantics><mrow><mi>L</mi><mo>=</mo><msub><mi>L</mi><mn>0</mn></msub><msup><mi>σ</mi><mi>α</mi></msup></mrow></semantics></math></inline-formula>, in which the parameters <inline-formula><math display="inline"><semantics><msub><mi>L</mi><mn>0</mn></msub></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> are confined in a small range of possible values, is incompatible with the distribution observed in the <inline-formula><math display="inline"><semantics><mrow><msub><mi>I</mi><mi>e</mi></msub><mo>−</mo><msub><mi>R</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> 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 <inline-formula><math display="inline"><semantics><mrow><mi>L</mi><mo>=</mo><msubsup><mi>L</mi><mn>0</mn><mo>′</mo></msubsup><msup><mi>σ</mi><mi>β</mi></msup></mrow></semantics></math></inline-formula> law proposed by D’Onofrio et al. in 2020, in which both <inline-formula><math display="inline"><semantics><msubsup><mi>L</mi><mn>0</mn><mo>′</mo></msubsup></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> 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 <inline-formula><math display="inline"><semantics><mrow><mi>L</mi><mo>=</mo><msubsup><mi>L</mi><mn>0</mn><mo>′</mo></msubsup><msup><mi>σ</mi><mi>β</mi></msup></mrow></semantics></math></inline-formula> law and confirm the prediction of the Zone of Exclusion (ZoE) originating from the intersection of the virial law with the <inline-formula><math display="inline"><semantics><mrow><mi>L</mi><mo>=</mo><msubsup><mi>L</mi><mn>0</mn><mo>′</mo></msubsup><msup><mi>σ</mi><mi>β</mi></msup></mrow></semantics></math></inline-formula> relation. The ZoE is the region in the <inline-formula><math display="inline"><semantics><mrow><msub><mi>I</mi><mi>e</mi></msub><mo>−</mo><msub><mi>R</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>e</mi></msub><mo>−</mo><msub><mi>M</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula> 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.