On galaxy mass-radius relationship

In the Clausius' virial maximum theory (TCV) [Secco and Bindoni, NewA 14, 567 (2009)] to explain the galaxy Fundamental Plane (FP) a natural explanation follows about the observed relationship between stellar mass and effective radius, M ∗ - r e , for early type galaxies (ETGs). The key of this correlation lies in the deep link which has to exist between cosmology and the existence of the FP. The general strategy consists in using the two-component tensor virial theorem to describe the virial configuration of the baryonic component of mass M B ≃ M ∗ embedded in a dark matter (DM) halo of mass M D at the end of relaxation phase. In a ΛCDM flat cosmology, starting from variance at equivalence epoch, we derive some preliminary theoretical relationships, M ∗ - r e , which are functions of mass ratio m = M D / M B . They appear to be in agreement with the trends extracted from the data of galaxy sample used by [Tortora et al., MNRAS 396, 1132 (2009)].