The positions of multiple images in galaxy lenses are related to the galaxy mass distribution. Smooth elliptical mass profiles were previously shown to be inadequate in reproducing the quad population. In this paper, we explore the deviations from such smooth elliptical mass distributions. Unlike most other work, we use a model-free approach based on the relative polar image angles of quads, and their position in 3D space with respect to the Fundamental Surface of Quads. The FSQ is defined by quads produced by elliptical lenses. We have generated thousands of quads from synthetic populations of lenses with substructure consistent with ΛCDM simulations, and found that such perturbations are not sufficient to match the observed distribution of quads relative to the FSQ. The result is unchanged even when subhalo masses are increased by a factor of ten, and the most optimistic lensing selection bias is applied. We then produce quads from galaxies created using two components, representing baryons and dark matter. The transition from the mass being dominated by baryons in inner radii to being dominated by dark matter in outer radii can carry with it asymmetries, which would affect relative image angles. We run preliminary experiments using lenses with two elliptical mass components with nonidentical axis ratios and position angles, perturbations from ellipticity in the form of nonzero Fourier coefficients a 4 and a 6 , and artificially offset ellipse centers as a proxy for asymmetry at image radii. We show that combination of these effects is a promising way of accounting for quad population properties. We conclude that the quad population provides a unique and sensitive tool for constraining detailed mass distribution in the centers of galaxies.

In the context of gravitational lensing, the density profile of lensing galaxies is often considered to be perfectly elliptical. Potential angular structures are generally ignored, except to explain flux ratios of point-like sources (i.e. flux ratio anomalies). Surprisingly, the impact of azimuthal structures on extended images of the source has not been characterised, nor has its impact on the H0 inference. We address this task by creating mock images of a point source embedded in an extended source and lensed by an elliptical galaxy on which multipolar components are added to emulate boxy or discy isodensity contours. Modelling such images with a density profile free of angular structure allows us to explore the detectability of image deformation induced by the multipoles in the residual frame. Multipole deformations are almost always detectable for our highest signal-to-noise ratio (S/N) mock data. However, the detectability depends on the lens ellipticity and Einstein radius, on the S/N of the data, and on the specific lens modelling strategy. Multipoles also introduce small changes to the time-delays. We therefore quantify how undetected multipoles would impact H0 inference. When no multipoles are detected in the residuals, the impact on H0 for a given lens is in general less than a few km s−1 Mpc−1, but in the worst-case scenario, combining low S/N in the ring and large intrinsic boxyness or discyness, the bias on H0 can reach 10−12 km s−1 Mpc−1. If we now look at the inference on H0 from a population of lensing galaxies with a distribution of multipoles representative of what is found in the light profile of elliptical galaxies, we find a systematic bias on H0 of less than 1%. A comparison of our mock systems to the state-of-the-art time-delay lens sample studied by the H0LiCOW and TDCOSMO collaborations indicates that multipoles are currently unlikely to be a source of substantial systematic bias on the inferred value of H0 from time-delay lenses.

Massive elliptical galaxies can display structures that deviate from a pure elliptical shape, such as a twist of the principal axis or variations in the axis ratio with galactocentric distance. Although satisfactory lens modeling is generally achieved without accounting for these azimuthal structures, the question about their impact on inferred lens parameters remains, in particular, on time delays as they are used in time-delay cosmography. This paper aims at characterizing these effects and quantifying their impact considering realistic amplitudes of the variations. We achieved this goal by creating mock lensing galaxies with morphologies based on two data sets: observational data of local elliptical galaxies, and hydrodynamical simulations of elliptical galaxies at a typical lens redshift. We then simulated images of the lensing systems with space-based data quality and modeled them in a standard way to assess the impact of a lack of azimuthal freedom in the lens model. We find that twists in lensing galaxies are easily absorbed in homoeidal lens models by a change in orientation of the lens up to 10° with respect to the reference orientation at the Einstein radius, and of the shear by up to 20° with respect to the input shear orientation. The ellipticity gradients, on the other hand, can introduce a substantial amount of shear that may impact the radial mass model and consequently bias H0, up to 10 km s−1 Mpc−1. However, we find that light is a good tracer of azimuthal structures, meaning that direct imaging should be capable of diagnosing their presence. This in turn implies that such a large bias is unlikely to be unaccounted for in standard modeling practices. Furthermore, the overall impact of twists and ellipticity gradients averages out at a population level. For the galaxy populations we considered, the cosmological inference remains unbiased.

Galaxy lenses are frequently modeled as an elliptical mass distribution with external shear and isothermal spheres to account for secondary and line-of-sight galaxies. There is statistical evidence that some fraction of observed quads are inconsistent with these assumptions, and require a dipole-like contribution to the mass with respect to the light. Simplifying assumptions about the shape of mass distributions can lead to the incorrect recovery of parameters such as H0. We create several tests of synthetic quad populations with different deviations from an elliptical shape, then fit them with an ellipse+shear model, and measure the recovered values of H0. Kinematic constraints are not included. We perform two types of fittings- one with a single point source and one with an array of sources emulating an extended source. We carry out two model-free comparisons between our mock quads and the observed population. One result of these comparisons is a statistical inconsistency not yet mentioned in the literature: the image distance ratios with respect to the lens center of observed quads appear to span a much wider range than those of synthetic or simulated quads. Bearing this discrepancy in mind, our mock populations can result in biases on H0  $\sim 10{{\ \rm per\ cent}}$.

Gravitational lensing offers a competitive method to measure H0 with the goal of 1% precision. A major obstacle comes in the form of lensing degeneracies, such as the mass sheet degeneracy (MSD), which make it possible for a family of density profiles to reproduce the same lensing observables but return different values of H0. The modeling process artificially selects one choice from this family, potentially biasing H0. The effect is more pronounced when the profile of a given lens is not perfectly described by the lens model, which will always be the case to some extent. To explore this, we quantify the bias and spread in H0 by creating quads from two-component mass models and fitting them with a power-law ellipse+shear model. We find that the bias does not correspond to the estimate one would calculate by transforming the profile into a power law near the image radius. We also emulate the effect of including stellar kinematics by performing fits where the slope is constrained to the true value. Informing the fit using the true value near the image radius can introduce substantial bias (0–23% depending on the model). We confirm using Jeans arguments that kinematic constraints can result in a biased value of H0, though the degree of bias depends on the region kinematic modeling probes in specific lenses. We conclude that lensing degeneracies manifest through commonplace modeling approaches in a more complicated way than is assumed in the literature. If stellar kinematics incorrectly break the MSD, their inclusion may introduce more bias than their omission.