Title: Galaxies' properties in the Fundamental Plane across time

Abstract: Context: Using the Illustris-1 and IllustrisTNG-100 simulations we investigate the properties of the Fundamental Plane (FP), that is the correlation between the effective radius Re, the effective surface intensity Ie and the central stellar velocity dispersion (sigma) of galaxies, at different cosmic epochs.
Aims: Our aim is to study the properties of galaxies in the FP and its projections across time, adopting samples covering different intervals of mass. We would like to demonstrate that the position of a galaxy in the FP space strongly depends on its degree of evolution, that might be represented by the beta and L'_0 parameters entering the L-sigma^beta(t) law.
Methods: Starting from the comparison of the basic relations among the structural parameters of artificial and real galaxies at low redshift, we obtain the fit of the FP and its coefficients at different cosmic epochs for samples of different mass limits. Then, we analyze the dependence of the galaxy position in the FP space as a function of the beta parameter and the star formation rate (SFR).
Results: We find that: 1) the coefficients of the FP change with the mass range of the galaxy sample; 2) the low luminous and less massive galaxies do not share the same FP of the bright massive galaxies; 3) the scatter around the fitted FP is quite small at any epoch and increases when the mass interval increases; 4) the distribution of galaxies in the FP space strongly depends on the $\beta$ values (i.e. on the degree of virialization and the star formation rate).
Conclusions: The FP is a complex surface that is well approximated by a plane only when galaxies share similar masses and condition of virialization.