Galaxy evolution from strong lensing statistics: the differential evolution of the velocity dispersion function and connection with mass functions

We study galaxy evolution from z = 1 to z = 0 as a function of velocity dispersion σ for galaxies with σ & 95 km s based on the measured and Monte Carlo realised local velocity dispersion functions (VDFs) of galaxies and the revised statistical properties of 30 strongly-lensed sources from the Cosmic Lens All-Sky Survey (CLASS), the PMN-NVSS Extragalactic Lens Survey (PANELS) and the Hubble Space Telescope Snapshot survey. We assume that the total (luminous plus dark) mass profile of a galaxy is isothermal in the optical region for 0 6 z 6 1. This study is the first to investigate the evolution of the VDF shape as well as the overall number density. It is also the first to study the evolution of the total and the late-type VDFs in addition to the early-type VDF. For the evolutionary behaviours of the VDFs we find that: (1) the number density of massive (mostly early-type) galaxies with σ & 200 km s evolves differentially in the way that the number density evolution is greater at a higher velocity dispersion; (2) the number density of intermediate and low mass early-type galaxies (95 km s . σ . 200 km s) is nearly constant; (3) the late-type VDF transformed from the Monte Carlo realised circular velocity function is consistent with no evolution in its shape or integrated number density consistent with galaxy survey results. The evolution of the VDF is shown to match well the ΛCDM halo mass function through a simple abundance matching analysis, supporting in a straightforward fashion the hierarchical assembly of structures. We infer the galaxy stellar mass function (SMF) from the VDF through an abundance matching at z = 0 and toy evolution models of σ(Mstars) motivated from observed structural evolutions of galaxies. We find that the inferred SMF is in line with predictions of more recent semi-analytic models of galaxy formation but is marginally discrepant with “mass-downsizing” SMFs from many galaxy surveys. We discuss the VDF evolution in the context of current cosmological observations including the SMF evolution, structural evolutions of galaxies (such as size and velocity dispersion evolutions) and galaxy merging rates. From the point of view of this work evidence for mass-downsizing is weak at best but there is a promising agreement between the VDF evolution and the ΛCDM hierarchical assembly of galaxies.