The energy shear of protohaloes

TL;DR

This paper introduces the 'energy shear' tensor as a positive definite alternative to the deformation tensor for modeling protohalo evolution, improving understanding of halo formation and cosmic web structure.

Contribution

It proposes the energy shear tensor as a better descriptor for protohalo deformation, especially for lower mass halos, simplifying models of halo abundance and cosmic web.

Findings

Energy shear tensor is positive definite.

Better description of protohalo deformation.

Simplifies models of halo formation.

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.