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

TL;DR

The paper investigates how non-axisymmetric bar structures in spiral lens galaxies influence gravitational lensing flux ratio anomalies. Using 21 barred galaxies from the Auriga cosmological simulations, the authors generate smooth, bar-preserving mass models via Multi-Gaussian Expansion and perform strong-lensing simulations to quantify cusp-caustic anomalies through $R_{\mathrm{cusp}}$ as a function of opening angle $\Delta\phi$. A Fourier decomposition of the bar region reveals that higher-order even modes, particularly $m=4$ (boxy/peanut) and $m=6$ (hexapole), correlate exceptionally tightly with the flux anomaly ($r=0.85$ and $r=0.89$, $p\sim10^{-6}$ to $10^{-8}$), indicating that bar morphology can dominate or mimic subhalo signatures. The results highlight the need to account for complex bar structures in lens modeling and offer a potential avenue to diagnose bar morphology from lensing data, with implications for interpreting subhalo populations and galaxy evolution. All mathematical notation is presented with $...$ delimiters to ensure clarity in the accompanying data products and analyses.

Abstract

Gravitational lens flux ratio anomalies are a powerful probe of small-scale mass structures within lens galaxies. These anomalies are often attributed to dark matter subhalos, but the baryonic components of the lens can also play a significant role. This study investigates the impact of galactic bars, a common feature in spiral galaxies, on flux ratio anomalies. We conduct a systematic analysis using a sample of 21 barred galaxies from the high-resolution Auriga cosmological simulations. First, we model the projected mass distribution of these galaxies 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 the flux ratio anomalies by measuring their deviation from the theoretical cusp-caustic relation. To characterize the structural properties of the bars, we use a Fourier decomposition of the surface mass density in the bar region. Our primary finding is a strong, statistically significant correlation between the magnitude of the flux ratio anomaly 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 the flux anomaly, with Spearman correlation coefficients of r=0.85 and 0.89, and p-values on the order of 1e-6 and 1e-8, respectively. This demonstrates that flux ratio anomalies are highly sensitive to the complex, non-axisymmetric features of galactic bars. We conclude that the flux ratio anomaly can be a powerful indicator of a galactic bar's complex morphology. Failing to account for a bar's complex morphology can lead to a misinterpretation of the lensing signature, potentially causing an overestimation of the dark matter subhalo population.

Figures (6)

• Figure 1: This figure displays the dimensionless surface density maps ($\kappa = \Sigma/\Sigma_\mathrm{crit}$) for Au 10 from the Auriga simulation. The columns show two different galactic projections: a face on view (left) and an edge on view with the bar oriented side-on (right). The top panels present the density maps derived from the direct projection using an SPH kernel, while the bottom panels show the corresponding maps reconstructed using a Multi-Gaussian Expansion (MGE) fit. In all panels, the color bar indicates the density level, with warmer colors denoting higher density regions, and the white lines represent iso-density contours.
• Figure 2: The left panel shows a tangential caustic (where the source image is stretched along the tangential direction) in the source plane, and the red star indicates a source located near the cusp region. The right panel shows the critical curve in the image plane, where one can see four strong lensing images corresponding to the source. Note that the size of the star does not represent the strong lensing magnification. In the right panel, the angle $\Delta \phi$ is the opening angle defined in Section \ref{['subsec:R_cusp']}.
• Figure 3: This figure displays the source sampling and $R_{\mathrm{cusp}}$ result for Au 10 from the Auriga simulation. The top panels illustrate the tangential (diamond-shaped, where the source image is stretched along the tangential direction) and radial (elliptical-shaped, where the source image is stretched along the radial direction) caustics. The columns correspond to different galaxy projections: the left panel shows a face on view and the right panel shows an edge on view with a side on bar. The gray dots near the caustic cusps represent the sampled source positions, with $10^4$ points used for each position. The lower panels plot the cusp caustic relation, $R_{\mathrm{cusp}}$ (defined in Eq. \ref{['eq:R_cusp']}), as a function of the opening angle, $\Delta \phi$. In these plots, the red open circles denote the data from the sampled points, while the solid blue curves represent the best-fit linear polynomials. The yellow cross in each lower panel indicates the value of $R_{\mathrm{cusp}}$ at an opening angle of $60^\circ$, which is the value we used to characterize the lensing flux ratio anomaly.
• Figure 4: This figure shows the profiles of the relative Fourier amplitudes, $\mathrm{A_m/A_0}$, for Au 10 from the Auriga simulation. These profiles are measured in the bar's region, as determined in 2020MNRAS.491.1800B. The amplitudes are shown as a function of radius in kiloparsecs (kpc). The left and right columns correspond to different galaxy projections: a face on view and an edge on view with the bar is side on, respectively. The top row displays the odd Fourier components ($m=1, 3, 5$), while the bottom row displays the even components ($m=2, 4, 6$). Within each panel, different colored lines distinguish the Fourier modes as indicated by the legend.
• Figure 5: This figure shows the correlation between the peak Fourier amplitudes in the bar region, max($\mathrm{A_m/A_0}$), representing the strength of the bar's angular complexity, and the lensing caustic area. The top panel displays the results for the tangential caustic area. The tangential caustic has a diamond shape, as shown in Figure \ref{['fig:halo_10_Cusp_caustic_relation']}, and it stretches the source image along the tangential direction. The bottom panel displays the results for the radial caustic area. The radial caustic has an elliptical shape, as shown in Figure \ref{['fig:halo_10_Cusp_caustic_relation']}, and it stretches the source image along the radial direction. Each color represents a different Fourier component, from $m=1$ to $m=6$. The legend provides the Spearman correlation coefficient ($r$) and the associated p-value for each component, indicating the statistical significance of the correlation.