  Using the full six years of imaging data from the Dark Energy Survey, we
study the surface brightness profiles of galaxy cluster central galaxies and
intra-cluster light. We apply a ``stacking'' method to over four thousand
galaxy clusters identified by the redMaPPer cluster finding algorithm in the
redshift range of 0.2 to 0.5. This yields high signal-to-noise radial profile
measurements of the central galaxy and intra-cluster light out to 1 Mpc from
the cluster center. Using redMaPPer richness as a cluster mass indicator, we
find that the intra-cluster light brightness has a strong mass dependence
throughout the 0.2 to 0.5 redshift range, and the dependence grows stronger at
a larger radius. In terms of redshift evolution, we find some evidence that the
central galaxy, as well as the diffuse light within the transition region
between the cluster central galaxy and intra-cluster light within 80 kpc from
the center, may be growing over time. At larger radii, more than 80 kpc away
from the cluster center, we do not find evidence of additional redshift
evolution beyond the cluster mass dependence, which is consistent with the
findings from the IllustrisTNG hydrodynamic simulation. We speculate that the
major driver of intra-cluster light growth, especially at large radii, is
associated with cluster mass growth. Finally, we find that the color of the
cluster central galaxy and intra-cluster light displays a radial gradient that
becomes bluer at a larger radius, which is consistent with a stellar stripping
and disruption origin of intra-cluster light as suggested by simulation
studies.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics