Weak lensing of strong lensing: beyond the tidal regime

TL;DR

This paper extends strong lensing analysis by incorporating line-of-sight flexion effects, which are usually neglected, showing their potential bias on parameter recovery and proposing a minimal model to include them.

Contribution

It introduces a minimal model for line-of-sight flexion in strong lensing, adding four parameters and analyzing its impact on lens modeling accuracy.

Findings

Line-of-sight flexion is predicted to be around 10^{-3} arcsec^{-1} for galactic scales.

Neglecting flexion biases shear estimates by up to 2σ.

Including flexion improves modeling accuracy but reduces precision.

Abstract

The analysis of strong lensing images usually involves an external convergence and shear, which are meant to model the effect of perturbations along the line of sight, on top of the main lens. Such a description of line-of-sight perturbations supposes that the corresponding gravitational fields can be treated in the tidal regime. Going one step further introduces additional effects, known as flexion, which have been hitherto neglected in strong lensing. In this work, we build a minimal model for the line-of-sight flexion, which adds four new complex parameters to the lens model. Contrary to convergence and shear, the line-of-sight flexion cannot be projected onto the main lens plane. For a $\Lambda$CDM cosmology, we predict the typical line-of-sight flexion to be on the order of $10^{-3} \mathrm{arcsec}^{-1}$ on galactic scales. Neglecting its effect in lens modelling is found to bias the recovery of other parameters; in particular, the line-of-sight shear can be biased up to $2\sigma$. Accounting for the line-of-sight flexion in our minimal framework restores accuracy, at the the cost of degrading precision. With current imaging capabilities, the line-of-sight flexion is unlikely to be measurable on individual strong lensing images; it must therefore be considered a nuisance parameter rather than an observable in its own right.