A complete FFT-based decomposition formalism for the redshift-space bispectrum
A complete FFT-based decomposition formalism for the redshift-space bispectrum
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DOI：
10.1093/mnras/sty3249
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发表时间：
2018-03
影响因子：
4.8
通讯作者：
Naonori S. Sugiyama;S. Saito;F. Beutler;H. Seo
中科院分区：
文献类型：
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作者：
Naonori S. Sugiyama;S. Saito;F. Beutler;H. Seo
为了从红移空间的非线性星系分布中充分提取宇宙学信息，必须包含两点相关函数之外的高阶统计量。在本文中，我们提出了一个新的分解形式计算的各向异性双谱的红移空间和测量它从星系样本。我们的形式主义使用三极球谐分解与零总角动量压缩红移空间双谱中的3D模式分布。这种方法保留了宇宙的三个基本属性：统计均匀性，各向同性和宇称对称性，使我们能够有效地分离由红移空间失真（RSD）和Alcock-Paczy '{n}ski（AP）效应引起的各向异性信号。各向异性信号的相关展开系数被简化为一个多极指数$L$，并且$L> 0$模仅由RSD或AP效应引起。我们的形式主义有两个优点：（1）我们可以利用快速傅立叶变换（FFT）来测量双谱;（2）它给出了一个简单的表达式来校正测量几何，即，视窗功能。作为演示，我们测量的分解的双谱从重子振荡光谱巡天（BOSS）数据Release 12，并首次提出了一个14\sigma $检测的各向异性双谱在$L=2$模式。
To fully extract cosmological information from nonlinear galaxy distribution in redshift space, it is essential to include higher-order statistics beyond the two-point correlation function. In this paper, we propose a new decomposition formalism for computing the anisotropic bispectrum in redshift space and for measuring it from galaxy samples. Our formalism uses tri-polar spherical harmonic decomposition with zero total angular momentum to compress the 3D modes distribution in the redshift-space bispectrum. This approach preserves three fundamental properties of the Universe: statistical homogeneity, isotropy, and parity-symmetry, allowing us to efficiently separate the anisotropic signal induced by redshift-space distortions (RSDs) and the Alcock-Paczy\'{n}ski (AP) effect from the isotropic bispectrum. The relevant expansion coefficients in terms of the anisotropic signal are reduced to one multipole index $L$, and the $L> 0$ modes are induced only by the RSD or AP effects. Our formalism has two advantages: (1) we can make use of Fast Fourier Transforms (FFTs) to measure the bispectrum; (2) it gives a simple expression to correct for the survey geometry, i.e., the survey window function. As a demonstration, we measure the decomposed bispectrum from the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, and, for the first time, present a $14\sigma$ detection of the anisotropic bispectrum in the $L=2$ mode.