Degeneracies of parametric lens model families near folds and cusps

TL;DR

This paper introduces a method to evaluate and select gravitational lens models based on model-independent ratios of lensing potential derivatives, enabling efficient exclusion of incompatible models and better understanding of lensing phenomena.

Contribution

The authors develop a novel approach to compare model-independent lensing ratios with model predictions, allowing for effective model selection and exclusion in gravitational lensing analysis.

Findings

Method accurately reproduces previous model fit results.

Can exclude entire lens model families based on derivative ratios.

Applicable to galaxy and galaxy cluster lensing cases.

Abstract

We develop an approach to select families of lens models that can describe doubly and triply gravitationally lensed images near folds and cusps using the model-independent ratios of lensing-potential derivatives derived in Wagner & Bartelmann (2015). Models are selected by comparing these model-independent ratios of potential derivatives to (numerically determined) ratios of potential derivatives along critical curves for entire lens model families in a given range of parameter values. This comparison returns parameter ranges which lens model families can reproduce observation within, as well as sections of the critical curve where image sets of the observed type can appear. If the model-independent potential-derivative ratios inferred from the observation fall outside the range of these ratios derived for the lens model family, the entire family can be excluded as a feasible model in the given volume in parameter space. We employ this approach for the family of singular isothermal spheres with external shear to examples of lensing by a galaxy and two galaxy clusters (JVAS B1422+231, SDSS J2222+2745, and MACS J1149.5+2223) and show that the results obtained by our general method are in good agreement with results of previous model fits.