Line-of-sight effects in strong gravitational lensing

Abstract

While most strong-gravitational-lensing systems may be roughly modelled by a single massive object between the source and the observer, in the details all the structures near the light path contribute to the observed images. These additional contributions, known as line-of-sight effects, are non-negligible in practice. This article proposes a new theoretical framework to model the line-of-sight effects, together with very promising applications at the interface of weak and strong lensing. Our approach relies on the dominant-lens approximation, where one deflector is treated as the main lens while the others are treated as perturbations. The resulting framework is technically simpler to handle than the multi-plane lensing formalism, while allowing one to consistently model any sub-critical perturbation. In particular, it is not limited to the usual external-convergence and external-shear parameterisation. As a first application, we identify a specific notion of line-of-sight shear that is not degenerate with the ellipticity of the main lens, and which could thus be extracted from strong-lensing images. This result supports and improves the recent proposal that Einstein rings might be powerful probes of cosmic shear. As a second application, we investigate the distortions of strong-lensing critical curves under line-of-sight effects, and more particularly their correlations across the sky. We find that such correlations may be used to probe, not only the large-scale structure of the Universe, but also the dark-matter halo profiles of strong lenses. This last possibility would be a key asset to improve the accuracy of the measurement of the Hubble-Lemaître constant via time-delay cosmography.

Strong gravitational lensing's `external shear' is not shear

“…Indeed, the best-fit value of external shear matched a model of the line of sight for three of six galaxy lenses studied by Wong et al (2011). Subsequent papers have even proposed using external shear as relatively high signal-to-noise measurements of the 'cosmic' shear along individual lines of sight (Birrer et al 2017;Desprez et al 2018;Kuhn et al 2020;Fleury et al 2021;Hogg et al 2022). However, the best-fit values of external shear did not match the lines of sight to the three other galaxies studied by Wong et al (2011) -and, in general, best-fit values are much larger than expected for both galaxy lenses (Keeton et al 1997;Witt & Mao 1997;Hilbert et al 2007;Suyu et al 2010;Barrera et al 2021) and cluster lenses (Robertson et al 2020;Limousin et al 2022).…”

Strong lensing time-delay cosmography in the 2020s

“…A potential way to further improve the external convergence determination is to reconstruct the entire light cone of structure around the strong lens, by assigning mass to the galaxies that are observed. First theoretical frameworks have been put forth (e.g., Collett et al 2013;McCully et al 2017;Fleury et al 2021). Subtleties remain in decoupling the cosmological dependence of the external convergence to measure the D Dt and D d distances without dependence on cosmological model assumptions.…”

Comments on the mass sheet degeneracy in cosmography analyses

“…Constraining such a small effect observationally or theoretically would be challenging. This point is important because certain combinations of weak lensing shear terms can, in principle, be measured directly from imaging data [59,67]. For convergence, Eq.…”

“…These modifications must be taken into account in lensing analyses [56]. In the tidal approximation, the lens equation becomes [41,44,45,47,[57][58][59] (see also App. A)…”

“…In this appendix we review the derivation of the weak lensing effects in the lens equation. These results are known [40,41,44,45,47,[57][58][59], and we include them here for completeness of the main text. Let us suppose that we have a strong deflector located at a comoving distance η l .…”