Using N-body simulations, we have modeled the production and evolution of diffuse, low surface brightness intracluster light (ICL) in three simulated galaxy clusters. Using an observational definition of ICL to be luminosity at a surface brightness mu_V>26.5 mag/sq.arcsec, we have found that the fraction of cluster luminosity contained in ICL generally increases as clusters evolve, although there are large deviations from this trend over short timescales, including sustained periods of decreasing ICL luminosity. Most ICL luminosity increases come in short, discrete events which are highly correlated with group accretion events within the cluster. In evolved clusters we find that ~10-15% of the clusters luminosity is at ICL surface brightness. The morphological structure of the ICL changes with time, evolving from a complex of filaments and small-scale, relatively high surface brightness features early in a clusters history, to a more diffuse and amorphous cluster-scale ICL envelope at later times. Finally, we also see a correlation between the evolution of ICL at different surface brightnesses, including a time delay between the evolution of faint and extremely faint surface brightness features which is traced to the differing dynamical timescales in the group and cluster environment.
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