Harmonic analysis of discrete tracers of large-scale structure

It is commonplace in cosmology to analyze fields projected onto the celestial sphere, and in particular density fields that are defined by a set of points e.g. galaxies. When performing an harmonic-space analysis of such data (e.g. an angular power spectrum) using a pixelized map one has to deal with aliasing of small-scale power and pixel window functions. We compare and contrast the approaches to this problem taken in the cosmic microwave background and large-scale structure communities, and advocate for a direct approach that avoids pixelization. We describe a method for performing a pseudo-spectrum analysis of a galaxy data set and show that it can be implemented efficiently using well-known algorithms for special functions that are suited to acceleration by graphics processing units (GPUs). The method returns the same spectra as the more traditional map-based approach if in the latter the number of pixels is taken to be sufficiently large and the mask is well sampled. The method is readily generalizable to cross-spectra and higher-order functions. It also provides a convenient route for distributing the information in a galaxy catalog directly in harmonic space, as a complement to releasing the configuration-space positions and weights, and a route to spectral apodization. Finally, we make public a code enabling the application of our method to existing and upcoming datasets.. Authors: Baleato Lizancos, Antón [Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)] (ORCID:0000000202326480); White, Martin [Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)] (ORCID:0000000199125070). DOE Contract: AC02-05CH11231. Subjects: 79 ASTRONOMY AND ASTROPHYSICS; galaxy surveys; power spectrum