用于天球非高斯研究的弱透镜质量图的重建
Reconstruction of weak lensing mass maps for non-Gaussian studies in the celestial sphere
摘要：
本文提出了一种新的方法来重建弱透镜质量或会聚映射，作为研究宇宙密度场非高斯性的一种探索。虽然以前的调查依赖于平天近似，但即将到来的第四阶段调查将覆盖具有大视场（FOV）的大面积区域，以激励球体上的大规模重建。在这里，我们提出了一种改进的凯撒-斯奎尔斯（KS+）质量反演方法，使用HEALPix像素化的领域，同时控制系统的影响。与KS+方法一样，在没有噪声正则化的情况下重建收敛图，以保留信息内容并允许非高斯研究。这种新方法的结果进行了比较与凯撒-斯奎尔斯（KS）的估计器上实现的弯曲的天空，使用高分辨率的现实N体模拟。通过估计两点关联函数、三阶和四阶矩以及重建收敛图的峰值计数来评价该方法的质量。掩蔽，采样和噪声的影响进行了测试。我们还研究了由平天近似引入的系统误差。我们表明，改进的凯撒-斯奎尔斯球（SKS+）方法系统地提高了10倍的推断相关误差，并提供平均20- 30%更好的最大信噪比峰值估计相比，凯撒-斯奎尔斯球（SKS）。我们还表明，SKS+方法几乎是无偏的，并减少了约2和4的第三和第四阶矩，分别由一个因素的错误。最后，我们展示了如何重建的收敛场直接在天球上消除了投影的影响，并允许排除或考虑一个特定的领域在处理。
英文摘要：
We present a novel method for reconstructing weak lensing mass or convergence maps as a probe to study non-Gaussianities in the cosmic density field. While previous surveys have relied on a flat-sky approximation, the forthcoming stage IV survey will cover such large areas with a large field of view (FOV) to motivate mass reconstruction on the sphere. Here, we present an improved Kaiser-Squires (KS+) mass inversion method using a HEALPix pixelisation of the sphere while controlling systematic effects. As in the KS+ methodology, the convergence maps were reconstructed without noise regularisation to preserve the Information content and allow for non-Gaussain studies. The results of this new method were compared with those of the Kaiser-Squires (KS) estimator implemented on the curved sky using high-resolution realistic N-body simulations. The quality of the method was evaluated by estimating the two-point correlation functions, third- and fourth-order moments, and peak counts of the reconstructed convergence maps. The effects of masking, sampling, and noise were tested. We also examined the systematic errors introduced by the flat-sky approximation. We show that the improved Kaiser-Squires on the sphere (SKS+) method systematically improves inferred correlation errors by 10 times and provide on average a 20-30 % better maximum signal-to-noise peak estimation compared to Kaiser-Squires on the sphere (SKS). We also show that the SKS+ method is nearly unbiased and reduces errors by a factor of about 2 and 4 in the third and fourth-order moments, respectively. Finally, we show how the reconstruction of the convergence field directly on the celestial sphere eliminates the projection effects and allows the exclusion or consideration of a specific region of the sphere in the processing.
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