Towards an application of fourth-order shear statistics II: Efficient estimation of fourth-order shear correlation functions and an application to the DES Y3 data
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| Format: | Preprint |
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2025
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| _version_ | 1866914030437793792 |
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| author | Porth, Lucas Silvestre-Rosello, Elena Schneider, Peter Larma, Martina |
| author_facet | Porth, Lucas Silvestre-Rosello, Elena Schneider, Peter Larma, Martina |
| contents | Higher-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. Stage-III lensing surveys have sufficient statistical power to significantly detect cumulant-based statistics up to fourth order. We derive and validate an efficient estimation procedure for the four-point correlation function (4PCF) of polar fields such as weak lensing shear. We then use our approach to measure the shear 4PCF and the fourth-order aperture mass statistics in the DES Y3 survey. We construct an efficient estimator for fourth-order shear statistics which builds on the multipole decomposition of the shear 4PCF. We then validate our estimator on mock ellipticity catalogues obtained from Gaussian random fields and on realistic $N$-body simulations. Finally, we apply our estimator to the DES Y3 data and present a measurement of the fourth-order aperture statistics in a non-tomographic setup. Due to its quadratic scaling, our estimator provides a significant speed-up over hypothetical brute force or tree-based estimation methods of the shear 4PCF. We report a significant detection of the connected part of the fourth-order aperture mass in the DES Y3 data. We find the sampling distribution of the fourth-order aperture mass to be significantly skewed. We make our estimator code available on GitHub as part of the orpheus package. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards an application of fourth-order shear statistics II: Efficient estimation of fourth-order shear correlation functions and an application to the DES Y3 data Porth, Lucas Silvestre-Rosello, Elena Schneider, Peter Larma, Martina Cosmology and Nongalactic Astrophysics Higher-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. Stage-III lensing surveys have sufficient statistical power to significantly detect cumulant-based statistics up to fourth order. We derive and validate an efficient estimation procedure for the four-point correlation function (4PCF) of polar fields such as weak lensing shear. We then use our approach to measure the shear 4PCF and the fourth-order aperture mass statistics in the DES Y3 survey. We construct an efficient estimator for fourth-order shear statistics which builds on the multipole decomposition of the shear 4PCF. We then validate our estimator on mock ellipticity catalogues obtained from Gaussian random fields and on realistic $N$-body simulations. Finally, we apply our estimator to the DES Y3 data and present a measurement of the fourth-order aperture statistics in a non-tomographic setup. Due to its quadratic scaling, our estimator provides a significant speed-up over hypothetical brute force or tree-based estimation methods of the shear 4PCF. We report a significant detection of the connected part of the fourth-order aperture mass in the DES Y3 data. We find the sampling distribution of the fourth-order aperture mass to be significantly skewed. We make our estimator code available on GitHub as part of the orpheus package. |
| title | Towards an application of fourth-order shear statistics II: Efficient estimation of fourth-order shear correlation functions and an application to the DES Y3 data |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2509.07974 |