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The environmental dark matter mass around clusters is investigated by taking into account dark halo-cluster correlations. We find that while the surrounding dark matter significantly increases the lensing amplification factor as compared to that caused by foreground clusters only, the total enhancement factor for background QSOs still remains quite insufficient to explain the observed strong QSO-cluster associations. Effects of the environmental matter on the cluster mass estimates through the inversion of weak-lensing distortions of background galaxies are also studied. For relatively small clusters, the existence of the environmental dark matter would lead to an overestimate of the cluster mass, whereas for large clusters, their mass would be underestimated.
Fan et al. (Thu,) studied this question.