Efficient estimators for power spectrum and bispectrum multipole measurements
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915983983116288 |
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| author | Xie, Yunchen Zhao, Ruiyang Gu, Gan Wang, Xiaoma Mu, Xiaoyong Wang, Yuting Zhao, Gong-Bo Beutler, Florian Peacock, John A. |
| author_facet | Xie, Yunchen Zhao, Ruiyang Gu, Gan Wang, Xiaoma Mu, Xiaoyong Wang, Yuting Zhao, Gong-Bo Beutler, Florian Peacock, John A. |
| contents | Large galaxy surveys demand fast and scalable estimators for anisotropic clustering statistics beyond the monopole. We present a suite of efficient FFT-based estimators for power-spectrum and bispectrum multipoles, built upon exact conjugation and parity symmetries of spherical-harmonic--weighted Fourier transforms of real fields. These symmetries eliminate redundant magnetic sub-configurations, thereby reducing the computational cost by a factor of 2. For the Yamamoto power-spectrum multipoles, we further decrease the cost of high-order even multipoles by algebraically expressing ${L}_{2n}$ in terms of lower-order Legendre polynomials, thereby measuring modified high-order multipoles using only low-$\ell$ fields with a small and controlled deviation from the traditional definition. We introduce a new TripoSH bispectrum estimator obtained by compressing the Scoccimarro bispectrum along an alternative triangle side, which substantially reduces the FFT scaling for commonly used quadrupole configurations in the large-$k$-bin limit. We also derive an analytic treatment of bispectrum shot noise by integrating spherical-harmonic kernels over the triangle-constrained $k$-space volumes, avoiding additional FFTs or costly spherical-Bessel evaluations and enabling fast and accurate shot-noise subtraction. Based on these optimizations, we also introduce CosmoNPC, an open-source Python package for large-scale-structure clustering measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04864 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient estimators for power spectrum and bispectrum multipole measurements Xie, Yunchen Zhao, Ruiyang Gu, Gan Wang, Xiaoma Mu, Xiaoyong Wang, Yuting Zhao, Gong-Bo Beutler, Florian Peacock, John A. Cosmology and Nongalactic Astrophysics Large galaxy surveys demand fast and scalable estimators for anisotropic clustering statistics beyond the monopole. We present a suite of efficient FFT-based estimators for power-spectrum and bispectrum multipoles, built upon exact conjugation and parity symmetries of spherical-harmonic--weighted Fourier transforms of real fields. These symmetries eliminate redundant magnetic sub-configurations, thereby reducing the computational cost by a factor of 2. For the Yamamoto power-spectrum multipoles, we further decrease the cost of high-order even multipoles by algebraically expressing ${L}_{2n}$ in terms of lower-order Legendre polynomials, thereby measuring modified high-order multipoles using only low-$\ell$ fields with a small and controlled deviation from the traditional definition. We introduce a new TripoSH bispectrum estimator obtained by compressing the Scoccimarro bispectrum along an alternative triangle side, which substantially reduces the FFT scaling for commonly used quadrupole configurations in the large-$k$-bin limit. We also derive an analytic treatment of bispectrum shot noise by integrating spherical-harmonic kernels over the triangle-constrained $k$-space volumes, avoiding additional FFTs or costly spherical-Bessel evaluations and enabling fast and accurate shot-noise subtraction. Based on these optimizations, we also introduce CosmoNPC, an open-source Python package for large-scale-structure clustering measurements. |
| title | Efficient estimators for power spectrum and bispectrum multipole measurements |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2605.04864 |