Generalised model-independent characterisation of strong gravitational lenses VI: the origin of the formalism intrinsic degeneracies and their influence on $H_0$

Abstract

We give a physical interpretation of the formalism intrinsic degeneracies of the gravitational lensing formalism that we derived on a mathematical basis in part IV of this series. We find that all degeneracies occur due to the partition of the mass density along the line of sight. Usually, it is partitioned into a background (cosmic) density and a foreground deflecting object. The latter can be further partitioned into a main deflecting object and perturbers. Weak deflecting objects along the line of sight are also added, either to the deflecting object or as a correction of the angular diameter distances, perturbing the cosmological background density. A priori, this is an arbitrary choice of reference frame and partition. They can be redefined without changing the lensing observables which are sensitive to the integrated deflecting mass density along the entire line of sight. Reformulating the time delay equation such that this interpretation of the degeneracies becomes easily visible, we note that the source can be eliminated from this formulation, which simplifies reconstructions of the deflecting mass distribution or the inference of the Hubble constant, $H_0$. Subsequently, we list necessary conditions to break the formalism intrinsic degeneracies and discuss ways to break them by model choices or including non-lensing observables like velocity dispersions along the line of sight with their advantages and disadvantages. We conclude with a systematic summary of all formalism intrinsic degeneracies and possibilities to break them.

13 pages, 3 figures, accepted for publication in MNRAS, comments very welcome

References in corpus (11)

• Astrophysics Source Code Library
• A Bayesian approach to strong lensing modelling of galaxy clusters
• Hubble Space Telescope Combined Strong and Weak Lensing Analysis of the CLASH Sample: Mass and Magnification Models and Systematic Uncertainties
• H0LiCOW IV. Lens mass model of HE 0435-1223 and blind measurement of its time-delay distance for cosmology
• CLASH-VLT: Insights on the mass substructures in the Frontier Fields Cluster MACS J0416.1-2403 through accurate strong lens modeling
• H0LiCOW III. Quantifying the effect of mass along the line of sight to the gravitational lens HE 0435-1223 through weighted galaxy counts
• Weak lensing goes bananas: What flexion really measures
• On the Choice of Lens Density Profile in Time Delay Cosmography
• Non-parametric strong lens inversion of Cl~0024+1654: illustrating the monopole degeneracy
• Relativistic numerical cosmology with Silent Universes
• Towards a new proposal for the time delay in gravitational lensing