SuperFaB: a fabulous code for Spherical Fourier-Bessel decomposition. (arXiv:2102.10079v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Gebhardt_H/0/1/0/all/0/1">Henry S. Grasshorn Gebhardt</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Dore_O/0/1/0/all/0/1">Olivier Doré</a>
The spherical Fourier-Bessel (SFB) decomposition is a natural choice for the
radial/angular separation that allows optimal extraction of cosmological
information from large volume galaxy surveys. 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 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 in the past. The estimator
is demonstrated on simplified 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.
The spherical Fourier-Bessel (SFB) decomposition is a natural choice for the
radial/angular separation that allows optimal extraction of cosmological
information from large volume galaxy surveys. 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 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 in the past. The estimator
is demonstrated on simplified 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.
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