Size and velocity-dispersion evolution of early-type galaxies in a Lambda cold dark matter universe

Early-type galaxies (ETGs) are observed to be more compact at z>2 than in the local Universe. Remarkably, much of this size evolution appears to take place in a short (1.8 Gyr) time span between z=2.2 and z=1.3, which poses a serious challenge to hierarchical galaxy formation models where mergers occurring on a similar timescale are the main mechanism for galaxy growth. We compute the merger-driven redshift evolution of stellar mass Mstar\propto(1+z)^aM, half-mass radius Re\propto(1+z)^aR and velocity-dispersion sigma0\propto(1+z)^asigma predicted by concordance Lambda cold dark matter for a typical massive ETG in the redshift range z=1.3-2.2. Neglecting dissipative processes, and thus maximizing evolution in surface density, we find -1.5<aM<-0.6, -1.9<aR<-0.7 and 0.06<asigma<0.22, under the assumption that the accreted satellites are spheroids. It follows that the predicted z=2.2 progenitors of z=1.3 ETGs are significantly less compact (on average a factor of 2 larger Re at given Mstar) than the quiescent galaxies observed at z>2. Furthermore, we find that the scatter introduced in the size-mass correlation by the predicted merger-driven growth is difficult to reconcile with the tightness of the observed scaling law. We conclude that - barring unknown systematics or selection biases in the current measurements - minor and major mergers with spheroids are not sufficient to explain the observed size growth of ETGs within the standard model.