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arXiv 2501.08718astro-ph.CO
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宇宙剪切角功率谱中的像素化效应

Pixelization effects in cosmic shear angular power spectra

Alex Hall, Nicolas Tessore

AI总结:

本文系统研究宇宙剪切角功率谱中的像素化偏差,提出改进估计量、空像素校正、交错方案及定制像素窗函数等方法,将小尺度残余偏差降至百分之一水平。

摘要:

我们对像素化对宇宙剪切的影响进行了全面研究,揭示了基于离散星表的标准伪-$C_\ell$估计量中的若干偏差来源。我们推导出能够在小尺度上将残余偏差降至百分之一水平的模型。我们阐明了混叠效应以及HEALPix像素形状变化对功率谱的影响,并展示了在离散自旋-2设定下如何作出HEALPix像素窗函数近似。基于源位置和权重应被视为固定的原则,我们对标准估计量及其建模提出了若干改进。我们展示了如何通过修改混合矩阵或应用我们推导出的校正因子来处理空像素。我们为HEALPix网格引入了一种近似交错方案,并证明该方案能够减轻混叠效应的影响。我们引入了针对巡天足迹定制的专用像素窗函数,并证明对于带限频谱,使用各向同性窗函数所产生的偏差可以有效降至零。本工作部分旨在为角功率谱中与像素相关的效应提供有用的参考,这些效应对正在进行和即将开展的透镜效应与聚类巡天具有重要意义。

英文摘要:

We conduct a comprehensive study into the impact of pixelization on cosmic shear, uncovering several sources of bias in standard pseudo-$C_\ell$ estimators based on discrete catalogues. We derive models that can bring residual biases to the percent level on small scales. We elucidate the impact of aliasing and the varying shape of HEALPix pixels on power spectra and show how the HEALPix pixel window function approximation is made in the discrete spin-2 setting. We propose several improvements to the standard estimator and its modelling, based on the principle that source positions and weights are to be considered fixed. We show how empty pixels can be accounted for either by modifying the mixing matrices or applying correction factors that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and show that it can mitigate the effects of aliasing. We introduce bespoke pixel window functions adapted to the survey footprint and show that, for band-limited spectra, biases from using an isotropic window function can be effectively reduced to zero. This work partly intends to serve as a useful reference for pixel-related effects in angular power spectra, which are of relevance for ongoing and forthcoming lensing and clustering surveys.

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