A theoretical view of the T-web statistical description of the cosmic web
arxiv(2023)
Abstract
The classification of the cosmic web into different environments is both a
tool to study in more detail the formation of halos and galaxies via the link
between their properties and the large-scale environment and as a class of
objects whose statistics contain cosmological information. In this paper, we
present an analytical framework to compute the probability of the different
environments in the cosmic web based on the T-web formalism that classifies
structures in four different classes (voids, walls, filaments, knots) by
studying the eigenvalues of the tidal tensor (Hessian of the gravitational
potential). This method relies on studying the eigenvalues of the tidal tensor
with respect to a given threshold and thus requires the knowledge of the JPDF
of those eigenvalues. We perform a change of variables in terms of minimally
correlated rotational invariants and we study their distribution in the linear
regime of structure formation, and in the quasi-linear regime with the help of
a Gram-Charlier expansion and tree-order Eulerian perturbation theory. This
expansion allows us to predict the probability of the different environments in
the density field at a given smoothing scale as a function of the chosen
threshold and redshift. We check the validity of our predictions by comparing
those predictions to measurements made in the N-body Quijote simulations. We
notably find that scaling the threshold value with the non-linear amplitude of
fluctuations allows us to capture almost entirely the redshift evolution of the
probability of the environments, even if we assume that the density field is
Gaussian (corresponding to the linear regime of structure formation). We also
show that adding mild non-Gaussian corrections in the form of third-order
cumulants of the field provides even more precise predictions for cosmic web
abundances up to scales as small as 5 Mpc/h and redshifts down to z 0.
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