An adapted filter function for density split statistics in weak lensing

¹ Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
e-mail: pburger@astro.uni-bonn.de
² Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
³ Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK
⁴ Astronomisches Institut, Ruhr-Universität Bochum, German Centre for Cosmological Lensing, Universitätsstr. 150, 44801 Bochum, Germany

Received: 18 June 2020
Accepted: 25 August 2020

Abstract

Context. The density split statistics in weak gravitational lensing analyses probes the correlation between regions of different (foreground) galaxy number densities and their weak lensing signal, which is measured by the shape distortion of background galaxies.

Aims. In this paper, we reconsider density split statistics, by constructing a new angular filter function that is adapted to the expected relation between the galaxy number density and shear pattern, in a way that the filter weighting the galaxy number density is matched to the filter that is used to quantify the shear signal.

Methods. We used the results of numerical ray-tracing simulations, specifically through the Millennium Simulation supplemented by a galaxy distribution based on a semi-analytic model, to construct a matched pair of adapted filter functions for the galaxy density and the tangential shear signal. We compared the performance of our new filter to the previously used top-hat filter, applying both to a different and independent set of numerical simulations (SLICS, cosmo-SLICS).

Results. We show that the adapted filter yields a better correlation between the total matter and the galaxy distribution. Furthermore, the adapted filter provides a larger signal-to-noise ratio to constrain the bias between the total matter and the galaxy distribution, and we show that it is, in general, a more sensitive discriminator between different cosmologies, with the exception of cosmologies with very large σ₈ values. All analyses lead to the conclusion that our adapted filter should be favoured in future density split statistic works.