Harmonic analysis of discrete tracers of large-scale structure
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913293443006464 |
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| author | Lizancos, Antón Baleato White, Martin |
| author_facet | Lizancos, Antón Baleato White, Martin |
| contents | 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. We make public a code enabling the application of our method to existing and upcoming datasets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_12285 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Harmonic analysis of discrete tracers of large-scale structure Lizancos, Antón Baleato White, Martin Cosmology and Nongalactic Astrophysics 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. We make public a code enabling the application of our method to existing and upcoming datasets. |
| title | Harmonic analysis of discrete tracers of large-scale structure |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2312.12285 |