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

Early-type galaxies (ETGs) are observed to be more compact at z greater than or similar to 2 than in the local Universe. Remarkably, much of this size evolution appears to take place in a short similar to 1.8 Gyr time span between z similar to 2.2 and 1.3, which poses a serious challenge to hierarchical galaxy formation models where mergers occurring on a similar time-scale are the main mechanism for galaxy growth. We compute the merger-driven redshift evolution of stellar mass M-* proportional to (1+z)(aM), half-mass radius R-e proportional to (1 + z)(aR) and velocity dispersion sigma(0) proportional to (1 + z)(a sigma) predicted by concordance Lambda cold dark matter for a typical massive ETG in the redshift range z similar to 1.3-2.2. Neglecting dissipative processes, and thus maximizing evolution in surface density, we find -1.5 less than or similar to a(M) less than or similar to -0.6, -1.9 less than or similar to a(R) less than or similar to -0.7 and 0.06 less than or similar to a(sigma) less than or similar to 0.22, under the assumption that the accreted satellites are spheroids. It follows that the predicted z similar to 2.2 progenitors of z similar to 1.3 ETGs are significantly less compact (on average a factor of similar to 2 larger R-e at given M-*) than the quiescent galaxies observed at z greater than or similar to 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.