Centroid positions of peaks identified in weak lensing mass maps often show offsets with respect to other means of identifying halo centres, like position of the brightest cluster galaxy or X-ray emission centroid. Here we study the effect of projected large-scale structure (LSS), smoothing of mass maps, and shape noise on the weak lensing peak positions. Additionally we compare the offsets in mass maps to those found in parametric model fits. Using ray-tracing simulations through the Millennium Run $N$-body simulation, we find that projected LSS does not alter the weak-lensing peak position within the limits of our simulations spatial resolution, which exceeds the typical resolution of weak lensing maps. We conclude that projected LSS, although a major contaminant for weak-lensing mass estimates, is not a source of confusion for identifying halo centres. The typically reported offsets in the literature are caused by a combination of shape noise and smoothing alone. This is true for centroid positions derived both from mass maps and model fits.
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