The velocity dispersion function of early-type galaxies and its redshift evolution: the newest results from lens redshift test

The redshift distribution of galactic-scale lensing systems provides a laboratory to probe the velocity dispersion function (VDF) of early-type galaxies (ETGs) and measure the evolution of ETGs at redshift z ~ 1. Through the statistical analysis of the currently largest sample of ETG gravitational lenses, we conclude that the VDF inferred solely from strong lensing systems is well consistent with the measurements of SDSS DR5 data in the local Universe. In particular, our results strongly indicate a decline in the number density of lenses by a factor of two and a 20 per cent increase in the characteristic velocity dispersion for the ETG population at z ~ 1. Such VDF evolution is in perfect agreement with the ΛCDM paradigm (i.e. the hierarchical build-up of mass structures over cosmic time) and different from 'stellar mass-downsizing' evolutions obtained by many galaxy surveys. Meanwhile, we also quantitatively discuss the evolution of the VDF shape in a more complex evolution model, which reveals its strong correlation with the number density and velocity dispersion of ETGs. Finally, we evaluate if future missions such as LSST can be sensitive enough to place the most stringent constraints on the redshift evolution of ETGs, based on the redshift distribution of available gravitational lenses.