A complete FFT-based decomposition formalism for the redshift-space bispectrum
Abstract
To fully extract cosmological information from non-linear 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-Paczyński (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 to measure the bispectrum and (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 14σ detection of the anisotropic bispectrum in the L = 2 mode.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- March 2019
- DOI:
- 10.1093/mnras/sty3249
- arXiv:
- arXiv:1803.02132
- Bibcode:
- 2019MNRAS.484..364S
- Keywords:
-
- dark matter;
- large-scale structure of Universe;
- cosmology: observations;
- cosmology: theory;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- Astrophysics - Astrophysics of Galaxies
- E-Print:
- 23 pages, 13 figures