Harmonic analysis of isotropic fields on the sphere with arbitrary masks

TL;DR

This paper introduces a novel harmonic analysis method for isotropic fields on the sphere with arbitrary masks, enabling diagonalization of the 2-point function and covariance matrix, thus improving the analysis of large-scale galaxy survey data.

Contribution

It develops a custom eigenbasis tailored to any survey geometry, preserving all information and simplifying the covariance structure for spherical Fourier-Bessel power spectrum estimation.

Findings

Eigenbasis diagonalizes the 2-point function for arbitrary masks.

The method simplifies covariance matrices to diagonal form.

Applicable to 3D spherical Fourier-Bessel power spectrum estimation.

Abstract

Obtaining constraints from the largest scales of a galaxy survey is challenging due to the survey mask allowing only partial measurement of large angular modes. This scatters information from the harmonic-space 2-point function away from the diagonal and introduces coupling between modes. In this paper, we derive a custom eigenbasis adapted to any particular survey geometry so that all information is retained on the diagonal. At the expense of a somewhat complex pixel- and selection-function-window, the result is a diagonal 2-point function with a simple shot noise, and a diagonal covariance matrix in the case of a Gaussian random field. We derive the basis on the surface of a sphere, and we use it to construct a 3D spherical Fourier-Bessel power spectrum estimator assuming a survey geometry that is separable in the angular and radial directions.