Velocity dispersion function evolution from strong lensing statistics

The redshift and size distributions of galaxy-scale strong lenses depend on the evolution of early-type galaxies. We use this dependence to constrain the velocity dispersion function (VDF) evolution from the Strong Lensing Legacy Survey sample of lenses in the redshift range 0.25 less than or similar to z less than or similar to 0.75. Our modelling of the lens population includes lens identifiability given survey parameters, and constrains the evolution of the VDF based on the redshift distributions of sources and lenses as well as the distribution of Einstein radii. We consider five different assumptions for the reference VDF at redshift zero and two sets of scaling relations for the VDF. We find that in all cases the observed lens sample favours a slow evolution of both the VDF normalization factor and the VDF characteristic velocity with redshift which is consistent with a VDF that is constant in redshift for z less than or similar to 0.75