Topological Defects in Gravitational Lensing Shear Fields

TL;DR

This paper analyzes topological defects in gravitational lensing shear fields, linking their patterns to the curvature of the lensing potential surface and providing methods to quantify their statistical properties.

Contribution

It introduces a novel interpretation of shear field defects through potential surface curvature and relates defect statistics to lensing potential correlations.

Findings

Characteristic defect configurations identified in simulated shear maps

Defect abundance related to lensing potential correlation functions

Topological defect analysis offers insights into lensing field structures

Abstract

Shear fields due to weak gravitational lensing have characteristic coherent patterns. We describe the topological defects in shear fields in terms of the curvature of the surface described by the lensing potential. A simple interpretation of the characteristic defects is given in terms of the the umbilical points of the potential surface produced by ellipsoidal halos. We show simulated lensing shear maps and point out the typical defect configurations. Finally, we show how statistical properties such as the abundance of defects can be expressed in terms of the correlation function of the lensing potential.