Fourth-order galaxy–galaxy lensing: Theoretical framework and direct estimation

Context. Traditional galaxy–galaxy lensing is a well-established method of probing the statistical properties of the Universe’s matter and galaxy distribution. However, this approach does not provide all the statistical information that can be obtained if the matter and galaxy distribution have non-Gaussian features. To study these non-Gaussianities, it is necessary to consider higher-order statistical measures. Aims. The aim of this work was to extend the analytical basis describing the statistical correlations between galaxies and shear to the fourth order, with a special emphasis on the associated aperture statistics. To include fourth-order statistics in future analysis of the relation between mass and galaxies, we further investigated whether we can expect to detect these statistics from observations of stage IV surveys. Methods. We defined the four-point correlation function (4PCF) between the shear and the positions of triplets of foreground galaxies and derived its relation to the respective trispectrum. We converted the 4PCF to aperture statistics and derived the analytical form of the respective filter function, which we then implemented in a numerical integration pipeline. Furthermore, we developed a direct estimator that allowed us to measure galaxy–mass aperture moments of arbitrary order on pixelized data using a fast Fourier transform (FFT) algorithm. Results. We show that the aperture measure ⟨𝒩3Map⟩ can be calculated with subpercent accuracy on relevant aperture scales, θ, by means of numerical integration. Furthermore, we applied the FFT-based direct estimator to a mock catalog with a realistic stage IV survey setup on a sky area of 2000 deg2 and detected the connected part of ⟨𝒩3Map⟩(θ) with a signal-to-noise ratio of roughly nine on small aperture scales.