Orientation Bias of Optically Selected Galaxy Clusters and Its Impact on
  Stacked Weak Lensing Analyses
  Weak-lensing measurements of the averaged shear profiles of galaxy clusters
binned by some proxy for cluster mass are commonly converted to cluster mass
estimates under the assumption that these cluster stacks have spherical
symmetry. In this paper we test whether this assumption holds for optically
selected clusters binned by estimated optical richness. Using mock catalogues
created from N-body simulations populated realistically with galaxies, we ran a
suite of optical cluster finders and estimated their optical richness. We
binned galaxy clusters by true cluster mass and estimated optical richness and
measure the ellipticity of these stacks. We find that the processes of optical
cluster selection and richness estimation are biased, leading to stacked
structures that are elongated along the line-of-sight. We show that
weak-lensing alone cannot measure the size of this orientation bias. Weak
lensing masses of stacked optically selected clusters are overestimated by up
to 3-6 per cent when clusters can be uniquely associated with haloes. This
effect is large enough to lead to significant biases in the cosmological
parameters derived from large surveys like the Dark Energy Survey, if not
calibrated via simulations or fitted simultaneously. This bias probably also
contributes to the observed discrepancy between the observed and predicted
Sunyaev-Zel'dovich signal of optically-selected clusters.
