THE K-BAND HUBBLE DIAGRAM FOR THE BRIGHTEST CLUSTER GALAXIES - A TESTOF HIERARCHICAL GALAXY FORMATION MODELS

We analyse the K-band Hubble diagram for a sample of brightest cluster galaxies (BCGs) in the redshift range 0<z<1. In good agreement with e arlier studies, we confirm that the scatter in the absolute magnitudes of the galaxies is small (0.3 mag). The BCGs exhibit very little lumi nosity evolution in this redshift range: if q(0) = 0.0, we detect no l uminosity evolution; for q(0), = 0.5, we measure a small negative evol ution (i.e., BCGs were about 0.5 mag fainter at z=1 than today). If th e mass in stars of these galaxies had remained constant over this peri od of time, substantial positive luminosity evolution would be expecte d: BCGs should have been brighter in the past, since their stars were younger. A likely explanation for the observed zero or negative evolut ion is that the stellar mass of the BCGs has been assembled over time through merging and accretion, as expected in hierarchical models of g alaxy formation. The colour evolution of the BCGs is consistent with t hat of an old stellar population (z(for)>2) that is evolving passively . We can thus use evolutionary population synthesis models to estimate the rate of growth in stellar mass for these systems. We find that th e stellar mass in a typical BCG has grown by a factor similar or equal to 2 since z similar or equal to 1 if q(0) = 0.0, or by factor simila r or equal to 4 if q(0) = 0.5. These results are in good agreement wit h the predictions of semi-analytic models of galaxy formation and evol ution set in the context of a hierarchical scenario for structure form ation. The models predict a scatter in the luminosities of the BCGs th at is somewhat larger than the observed one, but that depends on the c riterion used to select the model clusters.