Enhancing Morphological Measurements of Cosmic Web with Delaunay Tessellation Field Estimation

TL;DR

This paper introduces a novel application of Delaunay tessellation field estimation (DTFE) to improve the measurement of Minkowski functionals for cosmic large-scale structure, significantly enhancing the extraction of cosmological information from sparse tracers.

Contribution

The study demonstrates that DTFE significantly outperforms traditional Gaussian smoothing in measuring Minkowski functionals, especially in discriminating redshift space distortions and constraining structure growth.

Findings

MF measurements with DTFE improve discriminative power by ~2 orders of magnitude for RSD effects.

MF measurements with DTFE enhance constraints on structure growth rate by a factor of 3-5.

DTFE provides substantial advantages over Gaussian smoothing in morphological analysis of cosmic web.

Abstract

The density fields constructed by traditional mass assignment methods are susceptible to irritating discreteness, which hinders morphological measurements of cosmic large-scale structure (LSS) through Minkowski functionals (MFs). For alleviating this issue, fixed-kernel smoothing methods are commonly used in literatures, at the expense of losing substantial structural information. In this work, we propose to measure MFs with Delaunay tessellation field estimation (DTFE) technique, with the goal to maximize extractions of morphological information from sparse tracers. We perform our analyses starting from matter fields and progressively extending to halo fields. At matter field level, we elucidate how discreteness affects the morphological measurements of LSS. Then, by comparing with traditional Gaussian smoothing scheme, we preliminarily showcase the advantages of DTFE for enhancing measurements of MFs from sparse tracers. At halo field level, we first numerically investigate various systematic effects on MFs of DTFE fields, which are induced by finite voxel sizes, halo number densities, halo weightings, and redshift space distortions (RSDs), respectively. Then, we explore the statistical power of MFs measured with DTFE for extracting cosmological information encoded in RSDs. We find that MFs measured with DTFE exhibit improvements by $\sim$ $2$ orders of magnitude in discriminative power for RSD effects and by a factor of $\sim$ $3$-$5$ in constraining power on structure growth rate over the MFs measured with Gaussian smoothing. These findings demonstrate the remarkable enhancements in statistical power of MFs achieved by DTFE, showing enormous application potentials of our method in extracting various key cosmological information from galaxy surveys.