具有分量加权的自旋-s场的伪$C_\ell$s方法
Pseudo-$C_\ell$s for spin-$s$ fields with component-wise weighting
AI总结：
本文将标准伪$C_\ell$功率谱估计方法推广至由正定权重矩阵加权的自旋-s场，推导并验证了各向异性权重分量的模耦合系数，并在公开代码NaMaster中实现了该高效算法。
摘要：
我们将标准的伪$C_\ell$功率谱估计方法推广至自旋-s场，该场由一个一般的正定权重矩阵加权，该矩阵耦合了场的不同自旋分量（例如CMB极化分析中的$Q$和$U$图，或弱引力透镜中的$γ_1$和$γ_2$剪切分量）。相关的应用场景包括具有显著各向异性噪声特征的数据，或必须对不同场分量应用不同掩膜的情况。权重矩阵图被分为自旋-0部分（对应标准伪$C_\ell$方法中的“掩膜”）和自旋-$2s$部分（仅由矩阵的各向异性元素产生，导致角尺度与$E/B$模式间的额外耦合）。我们推导并验证了涉及这些各向异性权重分量功率谱的模耦合系数的一般表达式。该推广算法在计算效率上与标准方法相当。我们已在公开代码NaMaster中实现了该方法。
英文摘要：
We present a generalisation of the standard pseudo-$C_\ell$ approach for power spectrum estimation to the case of spin-$s$ fields weighted by a general positive-definite weight matrix that couples the different spin components of the field (e.g. $Q$ and $U$ maps in CMB polarisation analyses, or $γ_1$ and $γ_2$ shear components in weak lensing). Relevant use cases are, for example, data with significantly anisotropic noise properties, or situations in which different masks must be applied to the different field components. The weight matrix map is separated into a spin-0 part, which corresponds to the "mask" in the standard pseudo-$C_\ell$ approach, and a spin-$2s$ part sourced solely by the anisotropic elements of the matrix, leading to additional coupling between angular scales and $E/B$ modes. The general expressions for the mode-coupling coefficients involving the power spectra of these anisotropic weight components are derived and validated. The generalised algorithm is as computationally efficient as the standard approach. We implement the method in the public code NaMaster.
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