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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2507.03749 |
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| _version_ | 1866912645442961408 |
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| author | Tessore, Nicolas Hall, Alex |
| author_facet | Tessore, Nicolas Hall, Alex |
| contents | We show that the `shot noise' bias in angular clustering power spectra observed from discrete samples of points is not noise, but rather a known additive contribution that naturally arises due to degenerate pairs of points. In particular, we show that the true shot noise contribution cannot have a `non-Poissonian' value, even though all point processes with non-trivial two-point statistics are non-Poissonian. Apparent deviations from the `Poissonian' value can arise when significant correlations or anti-correlations are localised on small spatial scales. However, such deviations always correspond to a physical difference in two-point statistics, not a difference in noise. In the context of simulations, if clustering is treated as the tracer of a discretised underlying density field, any sub- or super-Poissonian sampling of the tracer induces such small-scale modifications and vice versa; we show this explicitly using recent innovations in angular power spectrum estimation from discrete catalogues. Finally, we show that the full covariance of clustering power spectra can also be computed explicitly: it depends only on the two-, three- and four-point statistics of the point process. The usual Gaussian covariance approximation appears as one term in the shot noise contribution, which is non-diagonal even for Gaussian random fields and Poisson sampling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shot noise in clustering power spectra Tessore, Nicolas Hall, Alex Cosmology and Nongalactic Astrophysics We show that the `shot noise' bias in angular clustering power spectra observed from discrete samples of points is not noise, but rather a known additive contribution that naturally arises due to degenerate pairs of points. In particular, we show that the true shot noise contribution cannot have a `non-Poissonian' value, even though all point processes with non-trivial two-point statistics are non-Poissonian. Apparent deviations from the `Poissonian' value can arise when significant correlations or anti-correlations are localised on small spatial scales. However, such deviations always correspond to a physical difference in two-point statistics, not a difference in noise. In the context of simulations, if clustering is treated as the tracer of a discretised underlying density field, any sub- or super-Poissonian sampling of the tracer induces such small-scale modifications and vice versa; we show this explicitly using recent innovations in angular power spectrum estimation from discrete catalogues. Finally, we show that the full covariance of clustering power spectra can also be computed explicitly: it depends only on the two-, three- and four-point statistics of the point process. The usual Gaussian covariance approximation appears as one term in the shot noise contribution, which is non-diagonal even for Gaussian random fields and Poisson sampling. |
| title | Shot noise in clustering power spectra |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2507.03749 |