# Redshift Evolution of the Fundamental Plane Relation in the IllustrisTNG Simulation

## TL;DR

This study examines the evolution of the fundamental plane of early-type galaxies in the IllustrisTNG-100 simulation from redshift 2 to 0, revealing its early formation, mild evolution, and the importance of stellar age as a parameter.

## Contribution

It demonstrates that the fundamental plane exists at high redshift with low scatter and highlights the discrepancy in the mass-to-light ratio relation, providing constraints for future simulations.

## Key findings

- The fundamental plane exists at z=2 with low scatter (~0.08 dex).
- The FP parameters evolve mildly since z=2, consistent with observations.
- A tight relation between M_dyn/L and M_dyn is not present in TNG100.

## Abstract

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 $\sim 0.08$ dex across this redshift range. Both slope parameters $b$ and $c$ (where $R \propto \sigma^b I^c$ with $R$, $\sigma$, 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 $\rm Res$ ($\equiv\,a\,+\,b\log \sigma\,+\,c\log I\,-\,\log R$, 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 $4c+b+2=\delta$, where $\delta \sim 0.8$ 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 $M_{\rm dyn}/L$ and the dynamical mass $M_{\rm dyn}$ (where $M_{\rm dyn}\equiv 5\sigma^2R/G$, 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.