Enhancing Morphological Measurements of the Cosmic Web with Delaunay Tessellation Field Estimation

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). To alleviate this issue, fixed-kernel smoothing methods are commonly used in the literature, at the expense of losing substantial structural information. In this work, we propose to measure MFs with the Delaunay tessellation field estimation (DTFE) technique, with the goal of maximizing the extraction of morphological information from sparse tracers. We perform our analyses starting from matter fields and progressively extending to halo fields. At the matter-field level, we elucidate how discreteness affects morphological measurements of LSS. Then, by comparing with the traditional Gaussian smoothing scheme, we preliminarily showcase the advantages of DTFE for enhancing measurements of MFs from sparse tracers. At the 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 the cosmological information encoded in RSDs. We find that MFs measured with DTFE exhibit improvements by ∼2 orders of magnitude in discriminative power for RSD effects and by a factor of ∼3–5 in constraining power on the 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 for our method in extracting various key cosmological information from galaxy surveys.