On the initial shear field of the cosmic web

Abstract

The initial shear field, characterized by a primordial perturbation potential, plays a crucial role in the formation of large scale structures. Hence, considerable analytic work has been based on the joint distribution of its eigenvalues, associated with Gaussian statistics. In addition, directly related morphological quantities such as ellipticity or prolateness are essential tools in understanding the formation and structural properties of halos, voids, sheets and filaments, their relation with the local environment, and the geometrical and dynamical classification of the cosmic web. To date, most analytic work has been focused on Doroshkevich's unconditional formulae for the eigenvalues of the linear tidal field, which neglect the fact that halos (voids) may correspond to maxima (minima) of the density field. I present here new formulae for the constrained eigenvalues of the initial shear field associated with Gaussian statistics, which include the fact that those eigenvalues are related to regions where the source of the displacement is positive (negative): this is achieved by requiring the Hessian matrix of the displacement field to be positive (negative) definite. The new conditional formulae naturally reduce to Doroshkevich's unconditional relations, in the limit of no correlation between the potential and the density fields. As a direct application, I derive the individual conditional distributions of eigenvalues and point out the connection with previous literature. Finally, I outline other possible theoretically- or observationally-oriented uses, ranging from studies of halo and void triaxial formation, development of structure-finding algorithms for the morphology and topology of the cosmic web, till an accurate mapping of the gravitational potential environment of galaxies from current and future generation galaxy redshift surveys.

12 pages, 3 figures. MNRAS in press

References in corpus (6)

• Multiscale Phenomenology of the Cosmic Web
• Environmental dependence in the ellipsoidal collapse model
• Alignments of Voids in the Cosmic Web
• On the Intrinsic Alignments of the Late-Type Spiral Galaxies from the Sloan Digital Sky Survey Data Release 7
• Modelling the shapes of the largest gravitationally bound objects
• Statistical properties of the linear tidal shear

Cited by in corpus (10)

• Evolution of the cosmic web
• Galaxy alignments: An overview
• A local bias approach to the clustering of discrete density peaks
• Almanac: Weak Lensing power spectra and map inference on the masked sphere
• Phase Space dynamics of triaxial collapse: Joint density-velocity evolution
• Analytical halo models of cosmic tidal fields
• Peaks and dips in Gaussian random fields: a new algorithm for the shear eigenvalues, and the excursion set theory
• On the anisotropic density distribution on large scales
• Ellipticity and prolaticity of the initial gravitational-shear field at the position of density maxima
• Accurate halo mass functions from the simplest excursion set theory