Lensed Image Angles: New Statistical Evidence for Substructure

TL;DR

This paper presents a new statistical method analyzing the angular distribution of lensed quads to infer the prevalence of substructure in galaxy lenses, revealing that substructure is likely common.

Contribution

It introduces a novel angular-based statistical approach to study galaxy lens substructure using only image angles, independent of image distances.

Findings

Lenses with convex isodensity contours are identical in the bisector plane.

Lumpy substructure affects the angular distribution of quads.

Substructure is likely a common feature in galaxy lenses.

Abstract

We introduce a novel statistical way of analyzing the projected mass distribution in galaxy lenses based solely on the angular distribution of images in quads around the lens center. The method requires the knowledge of the lens center location, but the images' distances from the lens center are not used at all. If the images of a quad are numbered in order of arrival time, \theta_1 through \theta_4, and \theta_{ij} is the angle between images i and j, then we define the 'bisector' plane whose axes are linear combinations of \theta_{23} and \theta_{14}. The bisector plane of a given lens contains all the quads produced by the lens. We show empirically that all two-fold symmetric lenses with convex, i.e. non-wavy or petal-like isodensity contours are identical in the bisector plane of their quads. We also study lenses with twisting isodensity contours, lumpy substructure, etc. Our results suggest that to reproduce the general characteristics of the observed quad population, kpc-scale substructure must be a common feature of galaxy lenses.