The details of the stellar mass assembly of brightest cluster galaxies ( BCGs ) remain an unresolved problem in galaxy formation .
We have developed a novel approach that allows us to construct a sample of clusters that form an evolutionary sequence , and have applied it to the Spitzer IRAC Shallow Cluster Survey ( ISCS ) to examine the evolution of BCGs in progenitors of present-day clusters with mass of ( 2.5 - 4.5 ) \times 10 ^ { 14 } M _ { \odot } .
We follow the cluster mass growth history extracted from a high resolution cosmological simulation , and then use an empirical method that infers the cluster mass based on the ranking of cluster luminosity to select high- z clusters of appropriate mass from ISCS to be progenitors of the given set of z = 0 clusters .
We find that , between z = 1.5 and 0.5 , the BCGs have grown in stellar mass by a factor of 2.3 , which is well-matched by the predictions from a state-of-the-art semi-analytic model .
Below z = 0.5 we see hints of differences in behavior between the model and observation .