A universal, physically motivated threshold for Hessian-based cosmic web identification: The V-Web case

¹ Departamento de Física Teórica, Módulo 15, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain
² Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, Warsaw, Poland
³ Centro de Investigación Avanzada en Física Fundamental (CIAFF), Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain
⁴ International Centre for Radio Astronomy Research, University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia

^⋆ Corresponding author; edward.olex@uam.es

Received: 10 December 2024
Accepted: 24 February 2025

Abstract

Context. The study of large-scale structure benefits from an accurate and robust identification of the cosmic web. Having access to such classifications can facilitate a more complete extraction of cosmological information encoded therein. This information can then help us to improve the mapping and our understanding of galaxy-environment interactions. Classification methods such as T-web and V-web, based on the Hessian matrix, are widely used to single out voids, sheets, filaments, and knots. However, these techniques depend on a threshold parameter whose value is chosen without physical justification and usually rely on a user’s visual impression. Thus, the universality of these results will be limited.

Aims. In this paper, we focus on the V-web method. Our aim is to find a physical motivation for deriving a universal threshold that can be applied across different cosmic scales and epochs.

Methods. V-web classifies the large-scale structure using the eigenvalues of the velocity shear tensor. Using a set of gravity-only simulations, we have introduced a normalization that incorporates the standard deviation of the velocity divergence field, isolating the beyond-Gaussian evolution of cosmic web elements.

Results. In the Zeldovich approximation, the probability of presence of each cosmic web element remains constant at a threshold equal to 0. For the first time, we reveal that this behaviour also holds in the non-linear regime for a normalized positive ‘constant volume threshold’ that depends on both the redshift and the applied smoothing scale. The conservation of volume fractions is valid for the studied redshifts between 0 and 2, regardless of cosmic variance, and it is most precise for intermediate smoothing scales around 3 Mpc/h. The properties of the cosmic web derived using this approach in the V-web align with expectations from other methods, including visual impressions. We provide a general fit formula to compute the constant volume threshold for any standard cosmological simulation, regardless of its specific properties.