Image Properties of Embedded Lenses

TL;DR

This paper derives analytic expressions for image properties of embedded point mass lenses in a flat $\Lambda$CDM universe, highlighting how embedding modifies lensing effects and incorporates the cosmological constant.

Contribution

It provides new analytic formulas for lensing quantities considering embedding effects, improving realism over traditional superposition models.

Findings

Embedding reduces gravitational force range, affecting deflection and amplification.

Embedding causes small but significant changes in weak lensing distortions, over 10%.

Introduces negative surface mass density in lensing models.

Abstract

We give analytic expressions for image properties of objects seen around point mass lenses embedded in a flat $\Lambda$CDM universe. An embedded lens in an otherwise homogeneous universe offers a more realistic representation of the lens's gravity field and its associated deflection properties than does the conventional linear superposition theory. Embedding reduces the range of the gravitational force acting on passing light beams thus altering all quantities such as deflection angles, amplifications, shears and Einstein ring sizes. Embedding also exhibits the explicit effect of the cosmological constant on these same lensing quantities. In this paper we present these new results and demonstrate how they can be used. The effects of embedding on image properties, although small i.e., usually less than a fraction of a percent, have a more pronounced effect on image distortions in weak lensing where the effects can be larger than 10%. Embedding also introduces a negative surface mass density for both weak and strong lensing, a quantity altogether absent in conventional Schwarzschild lensing. In strong lensing we find only one additional quantity, the potential part of the time delay, which differs from conventional lensing by as much as 4%, in agreement with our previous numerical estimates.