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. 
C. Nipoti, T. Treu, A. Leauthaud, K. Bundy, A. B. Newman, M. W. Auger
astro-ph.GA astro-ph.CO