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 earlier studies , we confirm that the scatter in the absolute magnitudes of the galaxies is small ( 0.3 magnitudes ) .
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 ( i.e. , BCGs were about 0.5 magnitudes fainter at z = 1 than today ) .
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 .
A likely explanation for the observed zero or negative evolution is that the stellar mass of the BCGs has been assembled over time through merging and accretion , as expected in hierarchical models of galaxy formation .
The colour evolution of the BCGs is consistent with that of an old stellar population ( z _ { form } > 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 the stellar mass in a typical BCG has grown by a factor \simeq 2 since z \simeq 1 if q _ { 0 } = 0.0 or by factor \simeq 4 if q _ { 0 } = 0.5 .
These results are in 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 .
The models predict a scatter in the luminosities of the BCGs that is somewhat larger than the observed one , but that depends on the criterion used to select the model clusters .