The energy shear of protohaloes

Abstract

As it collapses to form a halo, the shape of a protohalo patch is deformed by the initial shear field. This deformation is often modeled using the "deformation" tensor, constructed from second derivatives of the gravitational potential, whose trace gives the initial overdensity. However, especially for lower mass protohalos, this matrix is not always positive definite: one of its eigenvalues has a different sign from the others. We show that the evolution of a patch is better described by the "energy shear" tensor, which is positive definite and plays a direct role in the evolution. This positive-definiteness simplifies models of halo abundances, assembly and of the cosmic web.

9 pages, 10 figures

References in corpus (5)

• Properties of Dark Matter Haloes in Clusters, Filaments, Sheets and Voids
• Non-local Lagrangian bias
• Ellipsoidal halo finders and implications for models of triaxial halo formation
• The causal effect of environment on halo mass and concentration
• Getting in shape with minimal energy. A variational principle for protohaloes

Cited by in corpus (3)

• Cosmological perturbation theory for large scale structure in phase space
• A universal and physically motivated threshold for Hessian-based cosmic web identification: V-Web case
• Excursion Sets with a "Perfect" Collapse Model