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.

arXiv comment13 pages, 3 figures, accepted for publication in MNRAS, comments very welcome

References in corpus (57)

• Planck 2015 results. XIII. Cosmological parameters
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• Astrophysics Source Code Library
• A Bayesian approach to strong lensing modelling of galaxy clusters
• The Sloan Lens ACS Survey. III - The Structure and Formation of Early-type Galaxies and their Evolution since z~1
• Dissecting the Gravitational Lens B1608+656. II. Precision Measurements of the Hubble Constant, Spatial Curvature, and the Dark Energy Equation of State
• H0LiCOW - IX. Cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 and a new measurement of the Hubble constant
• Two accurate time-delay distances from strong lensing: Implications for cosmology
• H0LiCOW I. $H_0$ Lenses in COSMOGRAIL's Wellspring: Program Overview
• Hubble Space Telescope Combined Strong and Weak Lensing Analysis of the CLASH Sample: Mass and Magnification Models and Systematic Uncertainties
• Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing
• Cosmology from gravitational lens time delays and Planck data
• The Frontier Fields Lens Modeling Comparison Project
• Fluctuations of the luminosity distance
• 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
• Inhomogeneous cosmological models: exact solutions and their applications
• Evidence for dark matter contraction and a Salpeter IMF in a massive early-type galaxy
• The Hubble Constant from the Gravitational Lens B1608+656
• Source-position transformation -- an approximate invariance in strong gravitational lensing
• Cosmological Constraints from the double source plane lens SDSSJ0946+1006
• New test of the FLRW metric using the distance sum rule
• Modelling the line-of-sight contribution in substructure lensing
• Lensing Degeneracies Revisited
• The mass-sheet degeneracy and time-delay cosmography: Analysis of the strong lens RXJ1131-1231
• H0LiCOW III. Quantifying the effect of mass along the line of sight to the gravitational lens HE 0435-1223 through weighted galaxy counts
• Analytic Cross Sections for Substructure Lensing
• The properties of field elliptical galaxies at intermediate redshift. II: photometry and spectroscopy of an HST selected sample
• A New Hybrid Framework to Efficiently Model Lines of Sight to Gravitational Lenses
• Measuring the value of the Hubble constant "à la Refsdal"
• Pixelated Lenses and H_0 from Time-delay QSOs
• Analytic Time Delays and H_0 Estimates for Gravitational Lenses
• Lens galaxies in the Illustris simulation: power-law models and the bias of the Hubble constant from time-delays
• Survey of Gravitationally-lensed Objects in HSC Imaging (SuGOHI). II. Environments and Line-of-Sight Structure of Strong Gravitational Lens Galaxies to z ~ 0.8
• Weak lensing goes bananas: What flexion really measures
• H0LiCOW II. Spectroscopic survey and galaxy-group identification of the strong gravitational lens system HE0435-1223
• A Unifying Framework for Self-consistent Gravitational Lensing and Stellar Dynamics Analyses of Early-Type Galaxies
• H0LiCOW VIII. A weak lensing measurement of the external convergence in the field of the lensed quasar HE0435$-$1223
• Lensing degeneracies and mass substructure
• On the Choice of Lens Density Profile in Time Delay Cosmography
• The Hubble constant from SN Refsdal
• Line-of-sight effects in strong lensing: Putting theory into practice
• Non-parametric strong lens inversion of Cl~0024+1654: illustrating the monopole degeneracy
• Generalised model-independent characterisation of strong gravitational lenses IV: formalism-intrinsic degeneracies
• Relativistic numerical cosmology with Silent Universes
• Weak lensing and the Dyer-Roeder approximation
• The role of multiple images and model priors in measuring $H_0$ from supernova Refsdal in galaxy cluster MACS J1149.5+2223
• Generalised model-independent characterisation of strong gravitational lenses II: Transformation matrix between multiple images
• Generalised model-independent characterisation of strong gravitational lenses I: Theoretical foundations
• Strong lensing modeling in galaxy clusters as a promising method to test cosmography I. Parametric dark energy models
• Mesh-free free-form lensing I: Methodology and application to mass reconstruction
• Two-dimensional kinematics of SLACS lenses - IV. The complete VLT-VIMOS data set
• Model-independent and model-based local lensing properties of CL0024+1654 from multiply-imaged galaxies
• Generalised model-independent characterisation of strong gravitational lenses III: perturbed axisymmetric lenses
• The projected gravitational potential of the galaxy cluster MACS~J1206 derived from galaxy kinematics
• Multiply-imaged time-varying sources behind galaxy clusters - Comparing FRBs to QSOs, SNe, and GRBs
• Towards a new proposal for the time delay in gravitational lensing

Cited by in corpus (14)

• Is the Observable Universe Consistent with the Cosmological Principle?
• $\Lambda$CDM Tensions: Localising Missing Physics through Consistency Checks
• A model-independent characterisation of strong gravitational lensing by observables
• The Unsettled Number: Hubble's Tension
• Extended lens reconstructions with Grale: exploiting time domain, substructural and weak-lensing information
• Much ado about no offset -- Characterising the anomalous multiple-image configuration and the model-driven displacement between light and mass in the multi-plane strong lens Abell 3827
• Generalised model-independent characterisation of strong gravitational lenses VII: impact of source properties and higher-order lens properties on the local lens reconstruction
• Generalised model-independent characterisation of strong gravitational lenses VIII. automated multi-band feature detection to constrain local lens properties
• Model-independent and model-based local lensing properties of B0128+437 from resolved quasar images
• Solving the Hubble tension à la Ellis & Stoeger 1987
• Hamilton's Object Revisited: A challenging source redshift of a strong lensing configuration
• Testing General Relativity on Galactic Scales via DESI-BAO and Strong Lensing: Circumventing Assumptions on the Hubble Constant, Sound Horizon, and Dark Energy
• Across the Universe: GW231123 as a magnified and diffracted black hole merger
• A short review on joint weak and strong cluster lens-mass reconstruction