The growth of brightest cluster galaxies and intracluster light over the past 10 billion years

We constrain the evolution of the brightest cluster galaxy plus intracluster light (BCG + ICL) using an ensemble of 42 galaxy groups and clusters that span redshifts of z = 0.05-1.75 and masses of M-500,M-c = 2 x 10(13)-10(15) M-circle dot. Specifically, we measure the relationship between the BCG + ICL stellar mass M-star and M-500,M-c at projected radii 10 < r < 100 kpc for three different epochs. At intermediate redshift ((z) over bar = 0.40), where we have the best data, we find M-star M-500,c(0.48 +/- 0.06). Fixing the exponent of this power law for all redshifts, we constrain the normalization of this relation to be 2.08 +/- 0.21 times higher at (z) over bar = 0.40 than at high redshift ((z) over bar = 1.55). We find no change in the relation from intermediate to low redshift ((z) over bar = 0.10). In other words, for fixed M-500,M-c, M-star at 10 < r < 100 kpc increases from (z) over bar = 1.55 to (z) over bar = 0.40 and not significantly thereafter. Theoretical models predict that the physical mass growth of the cluster from z = 1.5 to z = 0 within r(500,c) is 1.4x, excluding evolution due to definition of r(500,c). We find that M-star within the central 100 kpc increases by similar to 3.8x over the same period. Thus, the growth of M-star in this central region is more than a factor of 2 greater than the physical mass growth of the cluster as a whole. Furthermore, the concentration of the BCG + ICL stellar mass, defined by the ratio of stellar mass within 10 kpc to the total stellar mass within 100 kpc, decreases with increasing M-500,M-c at all z. We interpret this result as evidence for inside-out growth of the BCG + ICL over the past 10 Gyr, with stellar mass assembly occurring at larger radii at later times.