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arXiv · 2109.13352

Harmonic analysis of isotropic fields on the sphere with arbitrary masks

Henry S. Grasshorn Gebhardt·Olivier Doré
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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.

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Henry S. Grasshorn Gebhardt, Olivier Doré. 2021-09-27. Harmonic analysis of isotropic fields on the sphere with arbitrary masks. https://doi.org/10.1088/1475-7516/2022/01/038

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