宇宙中最大的爱因斯坦半径是多少？
What is the largest Einstein radius in the universe?
摘要：
爱因斯坦半径在透镜研究中起着核心作用，因为它表征了引力透镜的强度。爱因斯坦半径在上截止点附近的分布应该可以探测到宇宙中最大的质量浓度。采用三轴晕模型，我们计算了大爱因斯坦半径的预期分布。为了评估宇宙方差，我们生成了一些全天空的蒙特卡罗实现。我们发现宇宙中最大的爱因斯坦半径对宇宙学模型是敏感的：对于源红移z=1，它们分别是42^{+9}_{-7}，35^{+8}_{-6}和54^{+12}_{-7}角秒，假设WMAP 5，WMAP 3和WMAP 1数据的最佳拟合参数。这些数值与目前的观测结果大体一致，因为它们并不完整。对于相同的源红移，我们预计在全天35（WMAP 5），15（WMAP 3）和150（WMAP 1）团具有爱因斯坦半径大于20”。虽然最大爱因斯坦半径的值几乎不受当前感兴趣的原始非高斯性的影响，但大透镜团的丰度应该与CMB竞争探测非高斯性，但只有在其他宇宙学参数得到很好测量的情况下。我们还发现，这些“超透镜”集群构成了一个高度偏见的人口。例如，这些超透镜簇的大部分具有优先与视线对准的主轴。因此，与具有相似红移和质量的典型星系团相比，这些星系团的投影质量分布更圆，椭圆率为0.2，并且具有40%-60%的浓度。我们认为，在A1689中测量到的大浓度与我们在1.2σ水平上的模型预测一致。（节录）
英文摘要：
The Einstein radius plays a central role in lens studies as it characterises the strength of gravitational lensing. The distribution of Einstein radii near the upper cutoff should probe the largest mass concentrations in the universe. Adopting a triaxial halo model, we compute expected distributions of large Einstein radii. To assess the cosmic variance, we generate a number of all-sky Monte-Carlo realisations. We find that the expected largest Einstein radius in the universe is sensitive to the cosmological model: for a source redshift z=1, they are 42^{+9}_{-7}, 35^{+8}_{-6}, and 54^{+12}_{-7} arcseconds, assuming best-fit parameters of the WMAP5, WMAP3 and WMAP1 data, respectively. These values are broadly consistent with current observations given their incompleteness. For the same source redshift, we expect in all-sky 35 (WMAP5), 15 (WMAP3), and 150 (WMAP1) clusters that have Einstein radii larger than 20". Whilst the values of the largest Einstein radii are almost unaffected by the primordial non-Gaussianity currently of interest, the abundance of large lens clusters should probe non-Gaussianity competitively with CMB, but only if other cosmological parameters are well-measured. We also find that these "superlens" clusters constitute a highly biased population. For instance, a substantial fraction of these superlens clusters have major axes preferentially aligned with the line-of-sight. As a consequence, the projected mass distributions of the clusters are rounder by an ellipticity of 0.2 and have 40%-60% larger concentrations compared with typical clusters with similar redshifts and masses. We argue that the large concentration measured in A1689 is consistent with our model prediction at the 1.2σlevel. (Abridged)
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