Source-position transformation -- an approximate invariance in strong gravitational lensing

TL;DR

This paper introduces a new approximate invariance transformation in strong gravitational lensing that explains why different mass models can fit the same lensing data, potentially impacting mass and Hubble constant measurements.

Contribution

It identifies a new global transformation of lensing mass distributions that nearly preserves observable lensing features, extending the known mass-sheet transformation.

Findings

The transformation reproduces image positions and flux ratios approximately.

It explains the degeneracy of lens models fitting the same data.

Provides an example demonstrating the transformation's effectiveness.

Abstract

The main obstacle for gravitational lensing to determine accurate masses of deflectors, or to determine precise estimates for the Hubble constant, is the degeneracy of lensing observables with respect to the mass-sheet transformation (MST). The MST is a global modification of the mass distribution which leaves all image positions, shapes and flux ratios invariant, but which changes the time delay. Here we show that another global transformation of lensing mass distributions exists which almost leaves image positions and flux ratios invariant, and of which the MST is a special case. Whereas for axi-symmetric lenses this source position transformation exactly reproduces all strong lensing observables, it does so only approximately for more general lens situations. We provide crude estimates for the accuracy with which the transformed mass distribution can reproduce the same image positions as the original lens model, and present an illustrative example of its performance. This new invariance transformation most likely is the reason why the same strong lensing information can be accounted for with rather different mass models.