  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 catalogs. 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 $r_p\sim
1h^{-1}/Mpc$, 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 catalog. 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.
