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A large variance exists in the amplitude of the Stellar Mass - Halo Mass(SMHM) relation for group and cluster-size halos. Using a sample of 254clusters, we show that the magnitude gap between the brightest central galaxy(BCG) and its second or fourth brightest neighbor accounts for a significantportion of this variance. We find that at fixed halo mass, galaxy clusters witha higher magnitude gap have a higher BCG stellar mass. This relationship isalso observed in semi-analytic representations of low-redshift galaxy clustersin simulations. This SMHM-magnitude gap stratification likely results from BCGgrowth via hierarchical mergers and may link assembly of the halo with thegrowth of the BCG. Using a Bayesian model, we quantify the importance of themagnitude gap in the SMHM relation using a multiplicative stretch factor, whichwe find to be significantly non-zero. The inclusion of the magnitude gap in theSMHM relation results in a large reduction in the inferred intrinsic scatter inthe BCG stellar mass at fixed halo mass. We discuss the ramifications of thisresult in the context of galaxy formation models of centrals in group andcluster-sized halos.

The Impact of Environment on the Stellar Mass - Halo Mass Relation