The K-band Hubble diagram for the brightest cluster galaxies: a test for galaxy formation and evolution models

The K-band Hubble diagram for a sample of brightest cluster galaxies (BCGs) in the redshift range 0 < z <1 shows a very small scatter (0.3 magnitudes r.m.s). The BCGs exhibit very little luminosity evolution in this redshift range: if q(0) = 0.0 we detect no luminosity evolution; for q(0) = 0.5 we measure a small negative evolution. If the mass in stars of these galaxies had remained constant over this period of time, substantial positive luminosity evolution would be expected: BCGs should have been brighter in the past since their stars were younger. This suggests that the stellar mass of the BCGs has been assembled over time through merging and accretion. We estimate that the 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 similar or equal to 4 if q(0) = 0.5. These results are in remarkably good agreement with the predictions of semi-analytic models of galaxy formation and evolution set in the context of a hierarchical scenario for structure formation.