Bridging the Gap Between Simply Parametrized and Free-Form Pixelated Models of Galaxy Lenses: The Case of WFI 2033-4723 Quad

Abstract

We study the radial and azimuthal mass distribution of the lensing galaxy in WFI 2033-4723. Mindful of the fact that modeling results depend on modeling assumptions, we examine two very different recent models: simply parametrized (SP) models from the H0LiCOW collaboration, and pixelated free-form (FF) glass models. In addition, we fit our own models which are a compromise between the astrophysical grounding of SP, and the flexibility of FF approaches. Our models consist of two offset parametric mass components, and generate many solutions, all fitting the quasar point image data. Among other results, we show that to reproduce point image properties the lensing mass must be lopsided, but the origin of this asymmetry can reside in the main lens plane or along the line of sight. We also show that there is a degeneracy between the slope of the density profile and the magnitude of external shear, and that the models from various modeling approaches are connected not by the mass sheet degeneracy, but by a more generalized transformation. Finally, we discuss interpretation degeneracy which afflicts all mass modeling: inability to correctly assign mass to the main lensing galaxy vs. nearby galaxies or line of sight structures. While this may not be a problem for the determination of H 0 , interpretation degeneracy may become a major issue for the detailed study of galaxy structure.

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

“…Moreover, Van De Vyvere et al (2022b did not investigate the effect of b4 'twisting' perturbations (Section 6.1.4) or mis-centering (Section 6.2.2), both of which we observe in the critical curves of real galaxies, and whose effects may not average away. For example, the centre of mass in the H0LiCOW model of lens WFI 2033-4723 is offset from the centre of light by ∼10× astrometric uncertainty (Suyu et al 2010;Barrera et al 2021), and a similar offset in iPTF16geu increases asymmetry (Diego et al 2022). Such offsets are unphysical (Schaller et al 2015), so it is not clear that complexities in the mass distributions of real lenses can be safely ignored by averaging over a population.…”

“…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). Using mock observations, Cao et al (2022, hereafter C22) demonstrated that the best-fit shear can be incorrect if the model of the mass distribution is missing complexity.…”

Strong Lensing by Galaxies

“…Free-form modeling is not, however, the only way to generate lens model ensembles; parametric models, with the number of parameters somewhat exceeding the number of data constraints, have also been used recently (Williams and Zegeye, 2020;Barrera et al, 2021).…”