Measuring the surface mass density ellipticity of redMaPPer galaxy
  clusters using weak-lensing
  In this work we study the shape of the projected surface mass density
distribution of galaxy clusters using weak-lensing stacking techniques. In
particular, we constrain the average aligned component of the projected
ellipticity, $\epsilon$, for a sample of redMaPPer clusters ($0.1 \leq z <
0.4$). We consider six different proxies for the cluster orientation and
measure $\epsilon$ for three ranges of projected distances from the cluster
centres. The mass distribution in the inner region (up to $700\,$kpc) is better
traced by the cluster galaxies with a higher membership probability, while the
outer region (from $700\,$kpc up to $5\,$Mpc) is better traced by the inclusion
of less probable galaxy cluster members. The fitted ellipticity in the inner
region is $\epsilon = 0.21 \pm 0.04$, in agreement with previous estimates. We
also study the relation between $\epsilon$ and the cluster mean redshift and
richness. By splitting the sample in two redshift ranges according to the
median redshift, we obtain larger $\epsilon$ values for clusters at higher
redshifts, consistent with the expectation from simulations. In addition, we
obtain higher ellipticity values in the outer region of clusters at low
redshifts. We discuss several systematic effects that might affect the measured
lensing ellipticities and their relation to the derived ellipticity of the mass
distribution.
