Redshift evolution of the Fundamental Plane relation in the IllustrisTNG simulation

We investigate the Fundamental Plane (FP) evolution of early-type galaxies in the IllustrisTNG-100 simulation (TNG100) from redshift z = 0 to z = 2. We find that a tight plane relation already exists as early as z = 2. Its scatter stays as low as ∼0.08 dex across this redshift range. Both slope parameters b and c (where R ∝ σ^bI^c with R, σ, and I being the typical size, velocity dispersion, and surface brightness) of the plane evolve mildly since z = 2, roughly consistent with observations. The FP residual Res (≡ a + b log σ + c log I - log R, where a is the zero-point of the FP) is found to strongly correlate with stellar age, indicating that stellar age can be used as a crucial fourth parameter of the FP. However, we find that 4c + b + 2 = δ, where δ ∼ 0.8 for FPs in TNG, rather than zero as is typically inferred from observations. This implies that a tight power-law relation between the dynamical mass-to-light ratio M_dyn/L and the dynamical mass M_dyn (where M_dyn ≡ 5σ²R/G, with G being the gravitational constant) is not present in the TNG100 simulation. Recovering such a relation requires proper mixing between dark matter and baryons, as well as star formation occurring with correct efficiencies at the right mass scales. This represents a powerful constraint on the numerical models, which has to be satisfied in future hydrodynamical simulations.