面向最优剪切场重建的PDF-Folding方法
Towards Optimal Reconstruction of Shear Field with PDF-Folding
AI总结：
本文提出PDF-Folding方法，一种统计最优的剪切场重建技术，无需平滑核，减少小尺度信息损失，在一般观测条件下达到最优信噪比，并验证于真实星系团数据。
摘要：
弱引力透镜提供了一种直接描绘宇宙中物质密度分布的方法。为了从剪切目录重建密度场，一个重要的步骤是从剪切目录构建剪切场，由于背景星系分布的不均匀性以及形状噪声的存在，这一步骤可能相当不平凡。我们提出了PDF-Folding方法，作为一种统计上最优的剪切场重建方法。它是PDF-SYM方法的扩展，后者先前是为优化Fourier_Quad剪切估计器的叠加剪切信号以及剪切-剪切相关性而设计的。PDF-Folding不需要像传统方法那样使用平滑核，因此在小尺度上减少了信息损失，并避免了由于剪切在核尺度上的空间变化而可能产生的偏差。我们通过解析推理和数值示例表明，新方法在一般观测条件下（即存在不均匀的背景密度或掩膜）可以达到重建剪切图上的最优信噪比。我们还展示了新方法在前景星系团周围真实数据上的表现。
英文摘要：
Weak lensing provides a direct way of mapping the density distribution in the universe. To reconstruct the density field from the shear catalog, an important step is to build the shear field from the shear catalog, which can be quite nontrivial due to the inhomogeneity of the background galaxy distribution and the shape noise. We propose the PDF-Folding method as a statistically optimal way of reconstructing the shear field. It is an extention of the PDF-SYM method, which is previously designed for optimizing the stacked shear signal as well as the shear-shear correlation for the Fourier\_Quad shear estimators. PDF-Folding does not require smoothing kernels as in traditional methods, therefore it suffers less information loss on small scales, and avoids possible biases due to the spatial variation of shear on the scale of the kernel. We show with analytic reasoning as well as numerical examples that the new method can reach the optimal signal-to-noise ratio on the reconstructed shear map under general observing conditions, i.e., with inhomogeneous background densities or masks. We also show the performance of the new method on real data around foreground galaxy clusters.
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