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Massive elliptical galaxies can display structures that deviate from a pureelliptical shape, such as a twist of the principal axis or variations in theaxis ratio with galactocentric distance. Although satisfactory lens modeling isgenerally achieved without accounting for these azimuthal structures, thequestion about their impact on inferred lens parameters remains, in particular,on time delays as they are used in time-delay cosmography. This paper aims atcharacterizing these effects and quantifying their impact considering realisticamplitudes of the variations. We achieved this goal by creating mock lensinggalaxies with morphologies based on two data sets: observational data of localelliptical galaxies, and hydrodynamical simulations of elliptical galaxies at atypical lens redshift. We then simulated images of the lensing systems withspace-based data quality and modeled them in a standard way to assess theimpact of a lack of azimuthal freedom in the lens model. We find that twists inlensing galaxies are easily absorbed in homoeidal lens models by a change inorientation of the lens up to 10{\deg} with respect to the referenceorientation at the Einstein radius, and of the shear by up to 20{\deg} withrespect to the input shear orientation. The ellipticity gradients, on the otherhand, can introduce a substantial amount of shear that may impact the radialmass model and consequently bias $H_0$, up to 10 km/s/Mpc. However, we findthat light is a good tracer of azimuthal structures, meaning that directimaging should be capable of diagnosing their presence. This in turn impliesthat such a large bias is unlikely to be unaccounted for in standard modelingpractices. Furthermore, the overall impact of twists and ellipticity gradientsaverages out at a population level. For the galaxy populations we considered,the cosmological inference remains unbiased.

Consequences of the lack of azimuthal freedom in the modeling of lensing galaxies