Disentangle model flexibility from observational data insufficiency in singularity-map deviations

Determine quantitatively whether deviations between reconstructed and true $A_3$-lines in singularity maps arise from insufficient model flexibility, inadequate observational constraints, or both, particularly for complex cluster mass distributions such as Hera.

Background

The paper introduces singularity maps as diagnostics of third- and higher-order derivatives of the lensing potential, which are not well constrained by standard strong-lensing observables such as image positions, time delays, and flux ratios. Comparisons for the simulated clusters Ares and Hera show that the reconstructed $A_3$-lines can deviate substantially from the true structures, especially in regions with sparse observational constraints or complex mass distributions.

For Hera, the deviations may reflect radial variation in the position-angle twist that is not captured by the assumed multipole parameterization, while more generally the discrepancies could result from either limitations in the lens-model parameterization or insufficient data. The paper explicitly leaves the quantitative disentanglement of these effects unresolved.