The Sersic Virial Hyperplane

Early type galaxies (ETGs) are known to possess a number of quite useful scaling relations among their photometric and/or kinematical quantities. We propose a unified picture reducing both the fundamental plane and the photometric plane to suitable projections of a single relation. Modelling the ETG as a two component system, made out of a luminous Sersic profile and a NFW dark halo, and applying the virial theorem, we are able to express the velocity dispersion σ0 as a function of the effective intensity 〈Ie〉, the effective radius Re and the Sersic index n. In a log log plot, this relation reduces to a hyperplane (i.e., a plane in a four dimensional configuration space) which we dubbed the Sersic Virial Hyperplane (SVH). The tilt of the SVH can be fully explained in terms of a power law scaling of the stellar (rather than the global) mass to light ratio Υ⋆ with the total luminosity LT , while the scatter is determined by those on the c − Mvir relation between the concentration c and the virial mass Mvir of the dark halo component. In order to test whether such the observed SVH is consistent with the theoretical assumptions, we perform a detailed simulation of a large ETGs sample reproducing the same photometric properties of a SDSS low redshift ETGs catalog. It turns out that the simulated SVH is fully consistent with the observed one thus validating our theoretical approach.