The fundamental plane in the hierarchical context

Abstract

Context. The fundamental plane (FP) relation and the distribution of early-type galaxies (ETGs) in the FP projections cannot be easily explained in the hierarchical framework, where galaxies grow up by merging and as a result of star formation episodes. Aims. We want to show here that both the FP and its projections arise naturally from the combination of the virial theorem (VT) and a new time-dependent relation, describing how luminosity and stellar velocity dispersion change during galaxy evolution. This relation has the form of the Faber-Jackson relation, but a different physical meaning: the new relation is L = L0′(t)σβ(t), where its coefficients L0′ and β are time-dependent and can vary considerably from object to object, at variance with those obtained from the fit of the L − σ plane. Methods. By combining the VT and L = L0′(t)σβ(t) law, we derived an equation for each galaxy that is identical in form to the FP, but with coefficients depending on β. This allowed us to extract the solutions for β as a function of the structural parameters of ETGs and consequently calculate the coefficients of the FP-like equations. Results. We demonstrate that the observed properties of ETGs in the FP and its projections can be understood in terms of variations of β and L0′. These two parameters encrypt the history of galaxy evolution across the cosmic epochs and determine the future aspect of the FP and its projections. In particular, we show that the FP coefficients are simple averages of those in the FP-like equations valid for each galaxy, and that the variations of β naturally explain the distributions of ETGs observed in the FP projections and the direction of the border of the Zone of Exclusion.