The cosmic evolution of the stellar mass$-$velocity dispersion relation of early-type galaxies

TL;DR

This study investigates how the relationship between stellar mass and velocity dispersion in early-type galaxies evolves from redshift 2.5 to 0, revealing a decrease in velocity dispersion over time and a mild evolution in the relation's slope.

Contribution

It introduces a Bayesian hierarchical inference method to analyze the evolution of the stellar mass-velocity dispersion relation across a wide redshift range using homogeneous and extended galaxy samples.

Findings

Velocity dispersion decreases with decreasing redshift for massive ETGs.

The $M_*$-$\sigma_e$ relation's normalization evolves with redshift, with higher dispersions at earlier times.

The intrinsic scatter of the relation remains approximately constant at 0.08 dex.

Abstract

We study the evolution of the observed correlation between central stellar velocity dispersion $\sigma_\mathrm{e}$ and stellar mass $M_*$ of massive ($M_*\gtrsim 3\times 10^{10}\,\mathrm{M_\odot}$) early-type galaxies (ETGs) out to redshift $z\approx 2.5$, exploiting a Bayesian hierarchical inference formalism. Collecting ETGs from state-of-the-art literature samples, we build a $fiducial$ sample ($0\lesssim z\lesssim 1$), which is obtained with homogeneous selection criteria, but also a less homogeneous $extended$ sample ($0\lesssim z\lesssim 2.5$). Based on the fiducial sample, we find that the $M_*$-$\sigma_\mathrm{e}$ relation is well represented by $\sigma_\mathrm{e}\propto M_*^{\beta}(1+z)^{\zeta}$, with $\beta\simeq 0.18$ independent of redshift and $\zeta\simeq 0.4$ (at given $M_*$, $\sigma_\mathrm{e}$ decreases for decreasing $z$, for instance by a factor of $\approx1.3$ from $z=1$ to $z=0$). When the slope $\beta$ is allowed to evolve, we find it increasing with redshift: $\beta(z)\simeq 0.16+0.26\log(1+z)$ describes the data as well as constant $\beta\simeq 0.18$. The intrinsic scatter of the $M_*$-$\sigma_\mathrm{e}$ relation is $\simeq0.08$ dex in $\sigma_\mathrm{e}$ at given $M_*$, independent of redshift. Our results suggest that, on average, the velocity dispersion of $individual$ massive ($M_*\gtrsim 3\times 10^{11}\,M_\odot$) ETGs decreases with time while they evolve from $z\approx 1$ to $z\approx 0$. The analysis of the extended sample leads to results similar to that of the fiducial sample, with slightly stronger redshift dependence of the normalisation ($\zeta\simeq 0.5$) and weaker redshift dependence of the slope (${\rm d} \beta/{\rm d} \log (1+z)\simeq 0.18$) when $\beta$ varies with time. At $z=2$ ETGs with $M_*\approx 10^{11}\,M_\odot$ have, on average, $\approx1.7$ higher $\sigma_\mathrm{e}$ than ETGs of similar stellar mass at $z=0$.