Fast estimation of aperture-mass statistics - II. Detectability of higher order statistics in current and future surveys

We explore an alternative method to the usual shear correlation function approach for the estimation of aperture mass statistics in weak-lensing survey data. Our approach builds on the direct estimator method. In this paper, we extend our analysis to statistics of arbitrary order and to the multiscale aperture mass statistics. We show that there always exists a linear order algorithm to retrieve any of these generalized aperture mass statistics from shape catalogues when the direct estimator approach is adopted. We validate our approach through application to a large number of Gaussian mock-lensing surveys where the true answer is known and we do this up to 10th-order statistics. We then apply our estimators to an ensemble of real-world mock catalogues obtained from N-body simulations - the SLICS mocks, and show that one can expect to retrieve detections of higher order clustering up to fourth order in a KiDS-1000 like survey. We expect that these methods will be of most utility for future wide-field surveys like Euclid and the Rubin Telescope.

Automated summary

We present an alternative method for estimating aperture mass statistics in weak-lensing survey data, extending the analysis to arbitrary order statistics and multiscale aperture mass statistics. Our approach demonstrates a linear order algorithm for retrieving generalized aperture mass statistics and is validated through Gaussian mock-lensing surveys and real-world mock catalogues, showing potential for detecting higher-order clustering in surveys like KiDS-1000. These methods are expected to be useful for upcoming wide-field surveys such as Euclid and the Rubin Telescope.