Gravitational lensing by a spiral galaxy I: the influence from bar's structure to the flux ratio anomaly

Gravitational lens flux ratio anomalies are a powerful probe of small-scale mass structures, often attributed to dark matter subhalos. However, baryonic components can also play a significant role. This study investigates, for the first time, the impact of bars on flux ratio anomalies. We conduct a systematic analysis using barred galaxies from the Auriga simulations. First, we model the projected mass distribution with the Multi-Gaussian Expansion formalism. This method yields smooth lens potentials that preserve the primary bar structure while mitigating numerical noise. We then perform strong lensing simulations and quantify flux ratio anomalies by measuring their deviation from the theoretical cusp-caustic relation, denoted as $R_{\text{cusp}}$. Our primary finding is a strong, statistically significant correlation between the flux ratio anomaly magnitude and the strength of higher-order even Fourier modes. Specifically, the strengths of the boxy/peanut and hexapole components show an exceptionally tight correlation with $R_{\text{cusp}}$, with Spearman correlation coefficients of $r=0.85$ and $0.89$, and p-values on the order of ${10}^{-6}$ and ${10}^{-8}$, respectively. This demonstrates that flux ratio anomalies are highly sensitive to complex, non-axisymmetric bar features. We conclude that flux ratio anomalies can be powerful indicators of bar morphology. Failing to account for such morphology can lead to misinterpreting lensing signatures and potentially overestimating the dark matter subhalo population.