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

We study the evolution of the observed correlation between central stellar velocity dispersion σe and stellar mass M∗ of massive (M∗ ≿ 3 × 1010 M☉) early-type galaxies (ETGs) out to redshift z ≈ 2.5, taking advantage of a Bayesian hierarchical inference formalism. Collecting ETGs from state-of-the-art literature samples, we build a fiducial sample (0 ≾ z ≾ 1), which is obtained with homogeneous selection criteria, but also a less homogeneous extended sample (0 ≾ z ≾ 2.5). Based on the fiducial sample, we find that at z ≾ 1 the M∗-σe relation is well represented by σe ∝ M∗β(1 + z)ζ, with β ≃ 0.18 independent of redshift and ζ ≃ 0.4 (at a given M∗, σe decreases for decreasing z, for instance by a factor of ≈1.3 from z = 1 to z = 0). When the slope β is allowed to evolve, we find it increasing with redshift: β(z) ≃ 0.16 + 0.26log (1 + z) describes the data as well as constant β ≃ 0.18. The intrinsic scatter of the M∗-σe relation is ≃0.08 dex in σe at given M∗, independent of redshift. Our results suggest that, on average, the velocity dispersion of individual massive (M∗ ≿ 3 × 1011M☉) ETGs decreases with time while they evolve from z ≈ 1 to z ≈ 0. The analysis of the extended sample, over the wider redshift range 0 ≾ z ≾ 2.5, leads to results similar to that of the fiducial sample, with slightly stronger redshift dependence of the normalization (ζ ≃ 0.5) and weaker redshift dependence of the slope (dβ/dlog (1 + z) ≃ 0.18) when β varies with time. At z = 2 ETGs with M∗ ≈ 1011 M☉ have, on average, ≈1.7 higher σe than ETGs of similar stellar mass at z = 0.