The integrated angular bispectrum of weak lensing

Abstract

We investigate three-point statistics in weak lensing convergence, through the integrated bispectrum. This statistic involves measuring power spectra in patches, and is thus easy to measure, and avoids the complexity of estimating the very large number of possible bispectrum configurations. The integrated bispectrum principally probes the squeezed limit of the bispectrum. To be useful as a set of summary statistics, accurate theoretical predictions of the signal are required, and, assuming Gaussian sampling distributions, the covariance matrix. In this paper, we investigate through simulations how accurate are theoretical formulae for both the integrated bispectrum and its covariance, finding that there a small inaccuracies in the theoretical signal, and more serious deviations in the covariance matrix, which may need to be estimated using simulations.

Position-Dependent Correlation Function of Weak Lensing Convergence

“…Note that the patches can be localised in real space or in the Fourier domain. To take into account the survey mask an elaborate procedure involving Monte Carlo (MC) realisations exists in the literature [41,44]. One of the advantages of working in the real space, however, is that this can be circumvented.…”

“…In previous works such estimators have been used in 3D for quantifying galaxy clustering [12], 21cm studies [40], the Cosmic Microwave Background (CMB) in 2D [41], as well as in 1D to probe Lyman-α absorption features [42,43]. The IB estimator has also been applied to weak lensing [44]. Our aim here is to develop these estimators for probing future 2D projected weak lensing surveys, and in particular Euclid [8].…”

“…Our aim here is to develop these estimators for probing future 2D projected weak lensing surveys, and in particular Euclid [8]. Instead of focussing on the harmonic domain [44] we concentrate on the angu- lar domain. Working in configuration space has the advantage that the observational mask can be dealt with more easily than in harmonic space.…”

Dark Energy Survey Year 3 Results: Three-Point Shear Correlations and Mass Aperture Moments

“…The community has followed several approaches to extracting the information contained in higher order shear statistics. For example, non-Gaussian information can be obtained with position-dependent or integrated 2pt lensing signatures (Halder et al 2021, Jung et al 2021, peak statistics (Kacprzak et al 2016, Zürcher et al 2021, density splits of the shear field (Friedrich et al 2018, Gruen et al 2018) as well as with techniques borrowed from artificial intelligence and neural networks (Cheng et al 2020, Fluri et al 2019, Jeffrey et al 2021, Lu et al 2021). Another approach is to directly measure 3rd or higher order statistics of the shear field in the form of ellipticity correlations (Van Waerbeke et al (2002), Benabed & Scoccimarro (2006)), mass aperture moments (Fu et al 2014, Jarvis et al 2004, Semboloni et al 2011 or lensing mass maps (Gatti et al 2021a).…”

Response approach to the integrated shear 3-point correlation function: the impact of baryonic effects on small scales

“…Here, we focus our attention on a particularly promising way of accessing 3PCF information in the cosmic shear field using a statistic called the integrated shear 3-point correlation function 𝜁 ± (𝛼), which has been described recently 1 in Halder et al 2021 (see also Munshi et al (2021), and for studies of its harmonic counterpart we refer to Munshi et al (2020) and Jung et al (2021)). Concretely, 𝜁 ± (𝛼) describes the correlation between (i) the shear 2PCF measured locally inside well-defined patches on the sky, and (ii) the 1-point aperture shear mass of the patches.…”