The Growth in Size and Mass of Cluster Galaxies since z=2
We study the formation and evolution of Brightest Cluster Galaxies starting from a $z=2$ population of quiescent ellipticals and following them to $z=0$. To this end, we use a suite of nine high-resolution dark matter-only simulations of galaxy clusters in a $Λ$CDM universe. We develop a scheme in which simulation particles are weighted to generate realistic and dynamically stable stellar density profiles at $z=2$. Our initial conditions assign a stellar mass to every identified dark halo as expected from abundance matching; assuming there exists a one-to-one relation between the visible properties of galaxies and their host haloes. We set the sizes of the luminous components according to the observed relations for $z∼2$ massive quiescent galaxies. We study the evolution of the mass-size relation, the fate of satellite galaxies and the mass aggregation of the cluster central. From $z=2$, these galaxies grow on average in size by a factor 5 to 10 of and in mass by 2 to 3. The stellar mass growth rate of the simulated BCGs in our sample is of 1.9 in the range $0.3<z<1.0$ consistent with observations, and of 1.5 in the range $0.0<z<0.3$. Furthermore the satellite galaxies evolve to the present day mass-size relation by $z=0$. Assuming passively evolving stellar populations, we present surface brightness profiles for our cluster centrals which resemble those observed for the cDs in similar mass clusters both at $z=0$ and at $z=1$. This demonstrates that the $Λ$CDM cosmology does indeed predict minor and major mergers to occur in galaxy clusters with the frequency and mass ratio distribution required to explain the observed growth in size of passive galaxies since $z=2$. Our experiment shows that Brightest Cluster Galaxies can form through dissipationless mergers of quiescent massive $z=2$ galaxies, without substantial additional star formation.