The Magnification Invariant of Circularly-symmetric Lens Models

TL;DR

This paper investigates the magnification invariants in various circularly-symmetric gravitational lens models, demonstrating their existence and dependence on the characteristic surface mass density, which enhances understanding of lensing phenomena.

Contribution

It extends the concept of magnification invariants to disk and 3D symmetric lens models, showing their existence and how they vary with model parameters.

Findings

Magnification invariants exist for all studied lens models.

Invariants are significantly affected by the characteristic surface mass density.

Results provide deeper insight into gravitational lensing behavior.

Abstract

In the context of strong gravitational lensing, the magnification of image is of crucial importance to constrain various lens models. For several commonly used quadruple lens models, the magnification invariants, defined as the sum of the signed magnifications of images, have been analytically derived when the image multiplicity is a maximum. In this paper, we further study the magnification of several disk lens models, including (a) exponential disk lens, (b) Gaussian disk lens, (c) modified Hubble profile lens, and another two of the popular three-dimensional symmetrical lens model, (d) NFW lens and (e) Einasto lens. We find that magnification invariant does also exist for each lens model. Moreover, our results show that magnification invariants can be significantly changed by the characteristic surface mass density $\kappa_{\rm c}$.