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.
