The imprint of dark matter haloes on the size and velocity dispersion evolution of early-type galaxies

Early-type galaxies (ETGs) are observed to be more compact, on average, at z > 2 than at z=0, at fixed stellar mass. Recent observational works suggest that such size evolution could reflect the similar evolution of the host dark matter halo density as a function of the time of galaxy quenching. We explore this hypothesis by studying the distribution of halo central velocity dispersion (sigmazero) and half-mass radius (rh) as functions of halo mass M and redshift z, in a cosmological LambdaCDM N-body simulation. In the range 0<z<2.5, we find sigmazero~M^{0.31-0.37} and rh~M^{0.28-0.32}, close to the values expected for homologous virialized systems. At fixed M in the range 10^11Msun <M< 5.5x10^14Msun we find sigmazero~(1+z)^0.35 and rh~(1+z)^{-0.7}. We show that such evolution of the halo scaling laws is driven by individual haloes growing in mass following the evolutionary tracks sigmazero~M^0.2 and rh~M^0.6, consistent with simple dissipationless merging models in which the encounter orbital energy is accounted for. We compare the N-body data with ETGs observed at 0<z<3 by populating the haloes with a stellar component under simple but justified assumptions: the resulting galaxies evolve consistently with the observed ETGs up to z=2, but the model has difficulty reproducing the fast evolution observed at z>2. We conclude that a substantial fraction of the size evolution of ETGs can be ascribed to a systematic dependence on redshift of the dark matter haloes structural properties.