Galaxy clusters, being the most massive objects in the Universe, exhibit the strongest alignment with the large-scale structure. However, mis-identification of members due to projection effects from the large-scale structure can occur. We studied the impact of projection effects on the measurement of the intrinsic alignment of galaxy clusters, using galaxy cluster mock catalogues. Our findings showed that projection effects result in a decrease of the large-scale intrinsic alignment signal of the cluster and produce a bump at r(p) similar to 1 h(-1) Mpc, most likely due to interlopers and missed member galaxies. This decrease in signal explains the observed similar alignment strength between bright central galaxies and clusters in the SDSS redMaPPer cluster catalogue. The projection effect and cluster intrinsic alignment signal are coupled, with clusters having lower fractions of missing members or having higher fraction of interlopers exhibiting higher alignment signals in their projected shapes. We aim to use these findings to determine the impact of projection effects on galaxy cluster cosmology in future studies.
