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

Abstract

We study the evolution of the observed correlation between central stellar velocity dispersion ${\sigma }_{\mathrm{e}}$ and stellar mass $M_{\ast }$ of massive ($M_{\ast }\gtrsim 3\times 10^{10}{\mathrm{M}}_{\odot }$) 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 $M_{\ast }$-${\sigma }_{\mathrm{e}}$ relation is well represented by ${\sigma }_{\mathrm{e}}\propto M_{\ast }^{\beta }(1+z{)}^{\zeta }$, with $\beta \simeq 0.18$ independent of redshift and $\zeta \simeq 0.4$ (at given $M_{\ast }$, ${\sigma }_{\mathrm{e}}$ decreases for decreasing $z$, for instance by a factor of $\approx 1.3$ 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 $M_{\ast }$-${\sigma }_{\mathrm{e}}$ relation is $\simeq 0.08$ dex in ${\sigma }_{\mathrm{e}}$ at given $M_{\ast }$, independent of redshift. Our results suggest that, on average, the velocity dispersion of $individual$ massive ($M_{\ast }\gtrsim 3\times 10^{11}{M}_{\odot }$) 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 ($\mathrm{d}\beta /\mathrm{d}\log (1+z)\simeq 0.18$) when $\beta$ varies with time. At $z=2$ ETGs with $M_{\ast }\approx 10^{11}{M}_{\odot }$ have, on average, $\approx 1.7$ higher ${\sigma }_{\mathrm{e}}$ than ETGs of similar stellar mass at $z=0$.

26 pages, 15 figures, accepted for publication in MNRAS