Harmonic analysis of isotropic fields on the sphere with arbitrary masks

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.

31+4 pages, 13 figures

References in corpus (6)

• Cosmological constraints from BOSS with analytic covariance matrices
• Generating Log-normal Mock Catalog of Galaxies in Redshift Space
• SuperFaB: a fabulous code for Spherical Fourier-Bessel decomposition
• Nonlinear Redshift-Space Distortions in the Harmonic-space Galaxy Power Spectrum
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