Can Third- and Fourth-order Multipoles plus Radial Variation of Isodensity Ellipses Explain the Observed Flux Ratios in B1422+231? YES, and a Lesson Learned from a TNG100 Lensing Galaxy Sample

Flux ratio anomalies in multiply imaged quasar lenses are a long-standing issue. Using the classical system B1422+231 as a case study, we investigate how typical nonclumpy perturbations beyond elliptical shapes—multipoles m 3 , m 4 and radial variations in q , ϕ q —can account for the observed image positions and flux ratios under different observational precisions. We extract these perturbations from a preselected strong-lensing galaxy sample from the TNG100 simulation. Smooth macroscopic models ( SIE + γ , EPL + γ ) are then fitted to the observed image positions alone and to both positions and flux ratios, with and without including the extracted perturbations. With an astrometric uncertainty of σ p = 10 mas, both macromodels alone can already successfully fit image positions within 3 σ p . At σ p = 2 mas, however, “astrometric anomalies” appear if smooth macromodels alone are adopted. In this case, adding the extracted perturbations can explain the anomalous image positions. When both positions and flux ratios are adopted, the SIE + γ model family already shows “flux ratio anomalies” at photometric uncertainty σ f ≤ 10% (keeping σ p = 10 mas). When EPL + γ is used, the smooth model alone can simultaneously fit both positions and flux ratios with σ f = 10%, 5% but not with σ f = 2%, where flux ratio anomalies appear. Adding all four types of extracted perturbations can rescue the macromodels and explain the observed anomalous flux ratios. We present important lessons learned regarding model flexibility and degeneracy.