Spherical bispectrum expansion and quadratic estimators
arxiv(2024)
摘要
We describe a general expansion of spherical (full-sky) bispectra into a set
of orthogonal modes. For squeezed shapes, the basis separates
physically-distinct signals and is dominated by the lowest moments. In terms of
reduced bispectra, we identify a set of discrete polynomials that are pairwise
orthogonal with respect to the relevant Wigner 3j symbol, and reduce to
Chebyshev polynomials in the flat-sky (high-momentum) limit for both
parity-even and parity-odd cases. For squeezed shapes, the flat-sky limit is
equivalent to previous moment expansions used for CMB bispectra and quadratic
estimators, but in general reduces to a distinct expansion in the angular
dependence of triangles at fixed total side length (momentum). We use the
full-sky expansion to construct a tower of orthogonal CMB lensing quadratic
estimators and construct estimators that are immune to foregrounds like point
sources or noise inhomogeneities. In parity-even combinations (such as the
lensing gradient mode from TT, or the lensing curl mode from EB) the
leading two modes can be identified with information from the magnification and
shear respectively, whereas the parity-odd combinations are shear-only.
Although not directly separable, we show that these estimators can nonetheless
be evaluated numerically sufficiently easily.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要