Caustics of Compensated Spherical Lens Models

TL;DR

This paper investigates the caustic structures of compensated spherical lens models, revealing significant differences between area and angular diameter distances and demonstrating size shrinking effects in gravitational lensing.

Contribution

It provides explicit models of caustic surfaces in compensated spherical lenses, confirming that area distances can substantially differ from angular diameter distances.

Findings

Area distances can differ significantly from angular diameter distances.

Apparent sizes shrink by a factor of about 3 near cusps.

Residual effects persist even when summing over multiple lenses.

Abstract

We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect.