SuperFaB: a fabulous code for Spherical Fourier-Bessel decomposition

Abstract

The spherical Fourier-Bessel (SFB) decomposition is a natural choice for the radial/angular separation that allows extraction of cosmological information from large volume galaxy surveys, taking into account all wide-angle effects. In this paper we develop a SFB power spectrum estimator that allows the measurement of the largest angular and radial modes with the next generation of galaxy surveys. The code measures the pseudo-SFB power spectrum, and takes into account mask, selection function, pixel window, and shot noise. We show that the local average effect (or integral constraint) is significant only in the largest-scale mode, and we provide an analytical covariance matrix. By imposing boundary conditions at the minimum and maximum radius encompassing the survey volume, the estimator does not suffer from the numerical instabilities that have proven challenging for SFB analyses in the past. The estimator is demonstrated on simplified but realistic Roman-like, SPHEREx-like, and Euclid-like mask and selection functions. For intuition and validation, we also explore the SFB power spectrum in the Limber approximation. We release the associated public code written in Julia.

20+10 pages, 16 figures

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Cited by in corpus (16)

• The observed galaxy power spectrum in General Relativity
• The Impact of Anisotropic Redshift Distributions on Angular Clustering
• Constraining Cosmic Inflation with Observations: Prospects for 2030
• Constraining low redshift [CII] Emission by Cross-Correlating FIRAS and BOSS Data
• The full-sky Spherical Fourier-Bessel power spectrum in general relativity
• Harmonic analysis of isotropic fields on the sphere with arbitrary masks
• Exact Modeling of Power Spectrum Multipole through Spherical Fourier-Bessel Basis
• Flat-sky Angular Power Spectra Revisited
• Relativistic and wide-angle corrections to galaxy power spectra
• A Differentiable, End-to-End Forward Model for 21 cm Cosmology: Estimating the Foreground, Instrument, and Signal Joint Posterior
• Triple-Spherical Bessel Function Integrals with Exponential and Gaussian Damping: Towards an Analytic N-Point Correlation Function Covariance Model
• Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
• Separating Angular and Radial Modes with Spherical-Fourier Bessel Power Spectrum on All Scales and Implications for Systematics Mitigation
• Fisher matrix for the angular power spectrum of multi-tracer galaxy surveys
• Large-scale Modeling of the Observed Power Spectrum Multipoles
• The Covariance of Photometric and Spectroscopic Two-Point Statistics: Implications for Cosmological Parameter Inference