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.

中文翻译：

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使用弱透镜测量 redMapPer 星系团的表面质量密度椭圆度

在这项工作中，我们使用弱透镜堆叠技术研究了星系团投影表面质量密度分布的形状。特别是，我们限制了投影椭圆度的平均对齐分量 $\epsilon$，用于 redMapPPer 集群样本 ($0.1 \leq z < 0.4$)。我们考虑了集群方向的六个不同代理，并针对距集群中心的三个投影距离范围测量 $\epsilon$。内部区域（最高$700\,$kpc）的质量分布由隶属概率较高的星团星系更好地追踪，而外部区域（从$700\,$kpc 到$5\,$Mpc）更好通过包含不太可能的星系团成员进行追踪。内部区域的拟合椭圆度为 $\epsilon = 0.21 \pm 0.04$，与之前的估计一致。我们还研究了 $\epsilon$ 与集群均值红移和丰富度之间的关系。通过根据红移中值将样本分成两个红移范围，我们在较高红移处获得更大的 $\epsilon$ 值，这与模拟的预期一致。此外，我们在低红移的星团外部区域获得了更高的椭圆度值。我们讨论了几种可能影响测量的透镜椭圆度的系统效应及其与质量分布的派生椭圆度的关系。我们在低红移的簇的外部区域获得了更高的椭圆度值。我们讨论了几种可能影响测量的透镜椭圆度的系统效应及其与质量分布的派生椭圆度的关系。我们在低红移的簇的外部区域获得了更高的椭圆度值。我们讨论了几种可能影响测量的透镜椭圆度的系统效应及其与质量分布的派生椭圆度的关系。