Early-type galaxies (ETGs) are observed to be more compact, on average, at z>2 than at z~0, at fixed stellar mass. Such evolution could be at least partly driven by an underlying evolution of the host dark-matter haloes where the new galaxies form. We explore this hypothesis by studying the distribution of halo central velocity dispersion and half-mass radius as functions of halo mass M and redshift z, in a cosmological Lambda-CDM N-body simulation. In the range 0<z<2.5, we find sigma_0 proportional to M^{0.31-0.37} and r_h proportional to M^{0.28-0.32}, close to the values expected for homologous virialized systems. At fixed mass in the range 10^11 M_sun < M < 5.5 x 10^14 M_sun we find sigma_0 proportional to (1+z)^0.35 and r_h proportional to(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 sigma_0 proportional to M^0.2 and r_h proportional to 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: we find that the resulting galaxies evolve consistently with the observed size evolution of ETGs up to z~2, but the model has difficulty reproducing the fast evolution observed at z>2. We conclude that up to z~2 a substantial fraction of the size evolution of ETGs can be ascribed to that of the underlying halo population.

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Date added: Thu, 10 Oct 13

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