Efficient estimators for power spectrum and bispectrum multipole measurements

TL;DR

This paper introduces efficient FFT-based estimators for galaxy clustering statistics, reducing computational costs and enabling fast, accurate measurements of power spectrum and bispectrum multipoles in large surveys.

Contribution

It presents novel symmetry-based optimizations, algebraic expressions for high-order multipoles, a new bispectrum estimator, and an analytic shot noise treatment, all implemented in the CosmoNPC Python package.

Findings

Reduced computational cost by a factor of 2 using symmetry considerations.

Expressed high-order multipoles in terms of lower-order ones for efficiency.

Developed a bispectrum estimator that scales better for large k-bins.

Abstract

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.