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.

arXiv comment20+10 pages, 16 figures

References in corpus (52)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• Acoustic Signatures in the Primary Microwave Background Bispectrum
• Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report
• Cosmology and Fundamental Physics with the Euclid Satellite
• Power Spectrum Analysis of Three-Dimensional Redshift Surveys
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Large-Scale Galaxy Bias
• Reconstructing the linear power spectrum of cosmological mass fluctuations
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)
• Extended Limber Approximation
• A unified pseudo-$C_{\ell }$ framework
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Testing gravity with redshift-space distortions using the power spectrum multipoles
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in Fourier-space
• The 2dF Galaxy Redshift Survey: Spherical Harmonics analysis of fluctuations in the final catalogue
• Fast Estimators for Redshift-Space Clustering
• A Measurement of the Quadrupole Power Spectrum in the Clustering of the 2dF QSO Survey
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the emission line galaxy sample from the anisotropic power spectrum between redshift 0.6 and 1.1
• A Spherical Harmonic Analysis of Redshift Space
• The Pseudo-$C_l$ method: Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
• Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
• Measuring line-of-sight dependent Fourier-space clustering using FFTs
• Wiener Reconstruction of Density, Velocity, and Potential Fields from All-Sky Galaxy Redshift Surveys
• Cosmology with the Wide-Field Infrared Survey Telescope -- Multi-Probe Strategies
• Galaxy Power Spectrum Multipoles Covariance in Perturbation Theory
• CMBFAST for spatially closed universes
• Cosmological constraints from BOSS with analytic covariance matrices
• Beyond the plane-parallel approximation for redshift surveys
• Spherical Harmonic Analysis of the PSCz Galaxy Catalogue: Redshift distortions and the real-space power spectrum
• Interpreting measurements of the anisotropic galaxy power spectrum
• Estimating the large-scale angular power spectrum in the presence of systematics: a case study of Sloan Digital Sky Survey quasars
• Cosmological constraints from COMBO-17 using 3D weak lensing
• Integral constraints in spectroscopic surveys
• Thinking Outside the Box: Effects of Modes Larger than the Survey on Matter Power Spectrum Covariance
• Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space
• Redshift-space distortions with wide angular separations
• All-Sky Analysis of the General Relativistic Galaxy Power Spectrum
• Generating Log-normal Mock Catalog of Galaxies in Redshift Space
• Galaxy-CMB and galaxy-galaxy lensing on large scales: sensitivity to primordial non-Gaussianity
• Galaxy power-spectrum responses and redshift-space super-sample effect
• 3DEX: a code for fast spherical Fourier-Bessel decomposition of 3D surveys
• Optimised angular power spectra for spectroscopic galaxy surveys
• Fast and easy super-sample covariance of large scale structure observables
• 3-dimensional spherical analyses of cosmological spectroscopic surveys
• 3D galaxy clustering with future wide-field surveys: Advantages of a spherical Fourier-Bessel analysis
• Covariance of the matter power spectrum including the survey window function effect: N-body simulations vs. fifth-order perturbation theory on grid
• Effects of Linear Redshift Space Distortions and Perturbation Theory on BAOs: A 3D Spherical Analysis
• Nonlinear Redshift-Space Distortions in the Harmonic-space Galaxy Power Spectrum
• Hybrid-basis inference for large-scale galaxy clustering: combining spherical and Cartesian Fourier analyses
• Galaxy Clustering in 3D and Modified Gravity Theories
• Mitigating the impact of fiber assignment on clustering measurements from deep galaxy redshift surveys

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