[论文解读] The three-point correlation function of cosmic shear. II: Relation to the bispectrum of the projected mass density and generalized third-order aperture measures

Petra Schneider, M. Kilbinger+1 more|ArXiv.org|Aug 19, 2003

Galaxies: Formation, Evolution, Phenomena参考文献 29被引用 27

一句话总结

本文推导了宇宙弱引力透镜的三阶相关函数（3PCF）与投影质量密度的三阶谱之间的显式关系，引入广义的三阶孔径测量方法，以从3PCF中提取全部信息。研究表明，3PCF的自然分量可简化E/B模分解，且三阶孔径统计量能以高灵敏度探测系统误差，同时利用宇称对称性识别具有宇宙学意义的非高斯特征。

ABSTRACT

We study the relation of the three-point cosmic shear statistics to the third-order statistical properties of the underlying convergence, expressed in terms of its bispectrum. Explicit relations for the natural components of the shear three-point correlation function in terms of the bispectrum are derived. The behavior of the correlation function under parity transformation is obtained and found to agree with previous results. We find that in contrast to the two-point shear correlation function, the three-point function at a given angular scale θis not affected by power in the bispectrum on much larger scales. These relations are then inverted to obtain the bispectrum in terms of the three-point shear correlator; two different expressions, corresponding to different natural components of the shear correlator, are obtained and can be used to separate E and B-mode shear contributions. These relations allow us to explicitly show that correlations containing an odd power of B-mode shear vanish for parity-symmetric fields. Generalizing a recent result by Jarvis et al., we derive expressions for the third-order aperture measures, employing multiple angular scales, in terms of the (natural components of the) three-point shear correlator and show that they contain essentially all the information about the underlying bispectrum. We discuss the many useful features these (generalized) aperture measures have that makes them convenient for future analyses of the skewness of the cosmic shear field (and any other polar field, such as the polarization of the Cosmic Microwave Background). (Abridged)

研究动机与目标

• 建立弱引力透镜三阶相关函数与投影质量密度三阶谱之间的直接数学联系。
• 将二阶孔径统计量推广至三阶，实现对宇宙弱引力透镜中非高斯特征的稳健表征。
• 开发对E模和B模剪切贡献敏感的孔径测量方法，并利用宇称不变性检测系统误差。
• 为未来高精度宇宙弱引力透镜巡天提取宇宙学信息提供实用框架。

提出的方法

• 利用旋转和宇称变换性质推导弱引力透镜3PCF的自然分量，将8分量张量简化为具有物理意义的组合。
• 反演3PCF-三阶谱关系，以3PCF表达三阶谱，得到对应于E模和B模分离的两个独立表达式。
• 通过基于弱引力透镜3PCF的多角度尺度定义，将孔径质量概念推广至三阶。
• 采用CNPT中的滤波函数，尽管不具有紧支集，但实现了代数简洁性并直接关联至三阶谱。
• 将形式化方法应用于证明：在宇称不变场中，B模剪切的奇次幂为零，与理论预期一致。
• 证明广义三阶孔径测量量包含三阶谱的全部信息，因此在宇宙学推断中为最优方法。

实验结果

研究问题

• RQ1 如何将宇宙弱引力透镜的三阶相关函数与投影质量密度的三阶谱联系起来？
• RQ2 弱引力透镜3PCF的自然分量是什么？它们如何简化对E模和B模贡献的分析？
• RQ3 能否从弱引力透镜3PCF推导出广义三阶孔径测量量？它们是否包含关于底层三阶谱的全部信息？
• RQ4 宇称对称性如何约束三阶剪切统计量的行为？这一约束如何用于系统误差检测？

主要发现

• 弱引力透镜3PCF的自然分量在旋转和宇称变换下变换简单，可实现E模与B模贡献的清晰分解。
• 在给定角尺度θ处，3PCF对三阶谱中的大尺度功率不敏感，这与两点统计量不同。
• 通过两个对应于E模和B模分量的独立表达式，可从弱引力透镜3PCF重构三阶谱。
• 基于多滤波半径定义的广义三阶孔径测量量，包含关于底层三阶谱的全部信息，且对观测几何和数据缺口不敏感。
• 具有B模剪切奇次幂的孔径测量量在宇称对称场中为零，提供了一种稳健的系统误差检测方法。
• 该形式化方法可直接从测量的剪切相关函数计算三阶统计量，便于应用于真实巡天和光线追踪模拟。