Euclid preparation. LIX. Angular power spectra from discrete observations

Abstract

We present the framework for measuring angular power spectra in the Euclid mission. The observables in galaxy surveys, such as galaxy clustering and cosmic shear, are not continuous fields, but discrete sets of data, obtained only at the positions of galaxies. We show how to compute the angular power spectra of such discrete data sets, without treating observations as maps of an underlying continuous field that is overlaid with a noise component. This formalism allows us to compute exact theoretical expectations for our measured spectra, under a number of assumptions that we track explicitly. In particular, we obtain exact expressions for the additive biases ("shot noise") in angular galaxy clustering and cosmic shear. For efficient practical computations, we introduce a spin-weighted spherical convolution with a well-defined convolution theorem, which allows us to apply exact theoretical predictions to finite-resolution maps, including HEALPix. When validating our methodology, we find that our measurements are biased by less than 1% of their statistical uncertainty in simulations of Euclid's first data release.

27 pages, 12 figures. Code available at https://github.com/heracles-ec/heracles. v2: Author Accepted Manuscript

References in corpus (39)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Euclid. I. Overview of the Euclid mission
• Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data
• The linear power spectrum of observed source number counts
• A unified pseudo-$C_{\ell }$ framework
• HMcode-2020: Improved modelling of non-linear cosmological power spectra with baryonic feedback
• Galaxy alignments: An overview
• The Intrinsic Alignment of Galaxies and its Impact on Weak Gravitational Lensing in an Era of Precision Cosmology
• Analysis of two-point statistics of cosmic shear: I. Estimators and covariances
• The 2dF Galaxy Redshift Survey: Spherical Harmonics analysis of fluctuations in the final catalogue
• Galaxy alignments: Observations and impact on cosmology
• A novel sampling theorem on the sphere
• Galaxy alignments: Theory, modelling and simulations
• KiDS-1000 Methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis
• Galaxy-galaxy lensing estimators and their covariance properties
• COSEBIs: Extracting the full E-/B-mode information from cosmic shear correlation functions
• CMB temperature and polarisation pseudo-Cl estimators and covariances
• Cosmic shear covariance: The log-normal approximation
• Hierarchical Cosmic Shear Power Spectrum Inference
• Dark Energy Survey Year 3 Results: Galaxy clustering and systematics treatment for lens galaxy samples
• Shear Power Spectrum Reconstruction using Pseudo-Spectrum Method
• Cosmic shear power spectra in practice
• Euclid preparation: XIX. Impact of magnification on photometric galaxy clustering
• Scanning strategy for mapping the Cosmic Microwave Background anisotropies with Planck
• Euclid. V. The Flagship galaxy mock catalogue: a comprehensive simulation for the Euclid mission
• Fast and Exact Spin-s Spherical Harmonic Transforms
• Improved cosmic microwave background (de-)lensing using general spherical harmonic transforms
• How should spin-weighted spherical functions be defined?
• Euclid: The reduced shear approximation and magnification bias for Stage IV cosmic shear experiments
• GLASS: Generator for Large Scale Structure
• Organised Randoms: Learning and correcting for systematic galaxy clustering patterns in KiDS using self-organising maps
• Almanac: Weak Lensing power spectra and map inference on the masked sphere
• Catalog-based pseudo-$C_{\ell }$s
• Almanac: MCMC-based signal extraction of power spectra and maps on the sphere
• Testing Quadratic Maximum Likelihood estimators for forthcoming Stage-IV weak lensing surveys
• Mapping Spatially Varying Additive Biases in Cosmic Shear Data

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