Degeneracies in parameter estimates for models of gravitational lens systems

Gorenstein, M. V.; Falco, E.; Shapiro, I. I.

doi:10.1086/166226

Cited by 185 publications

(170 citation statements)

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“…a given distribution of observed images can be reproduced by many different mass distributions. The most recognized degeneracy is mass sheet degeneracy, MSD (Gorenstein et al 1988;Saha 2000). It rescales the mass surface density by s: κ(θ) → sκ(θ), and adds a constant thickness mass sheet of surface mass density (1 − s), in units of critical density Table 2 shows the widths of these distributions (also displayed in each panel), quantified by the Normalized Median Absolute Deviation (see Section 3).…”

Section: Why Models' Magnifications Differ: Lensing Degeneraciesmentioning

confidence: 99%

Lens models under the microscope: comparison ofHubble Frontier Fieldcluster magnification maps

Priewe

Williams

Liesenborgs

et al. 2016

Mon. Not. R. Astron. Soc.

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Using the power of gravitational lensing magnification by massive galaxy clusters, the Hubble Frontier Fields provide deep views of six patches of the high redshift Universe. The combination of deep Hubble imaging and exceptional lensing strength has revealed the greatest numbers of multiply-imaged galaxies available to constrain models of cluster mass distributions. However, even with O(100) images per cluster, the uncertainties associated with the reconstructions are not negligible. The goal of this paper is to show the diversity of model magnification predictions. We examine 7 and 9 mass models of Abell 2744 and MACS J0416, respectively, submitted to the Mikulski Archive for Space Telescopes for public distribution in September 2015. The dispersion between model predictions increases from 30% at common low magnifications (µ ∼ 2) to 70% at rare high magnifications (µ ∼ 40). MACS J0416 exhibits smaller dispersions than Abell 2744 for 2 < µ < 10. We show that magnification maps based on different lens inversion techniques typically differ from each other by more than their quoted statistical errors. This suggests that some models underestimate the true uncertainties, which are primarily due to various lensing degeneracies. Though the exact mass sheet degeneracy is broken, its generalized counterpart is not broken at least in Abell 2744. Other, local degeneracies are also present in both clusters. Our comparison of models is complementary to the comparison of reconstructions of known synthetic mass distributions. By focusing on observed clusters, we can identify those that are best constrained, and therefore provide the clearest view of the distant Universe.

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Section: Why Models' Magnifications Differ: Lensing Degeneraciesmentioning

confidence: 99%

Lens models under the microscope: comparison ofHubble Frontier Fieldcluster magnification maps

Priewe

Williams

Liesenborgs

et al. 2016

Mon. Not. R. Astron. Soc.

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“…For example, mass sheet degeneracy, and some other degeneracies where different lenses reproduce exactly the same image observables have been well studied (Falco et al 1985;Gorenstein et al 1988;Saha 2000;Liesenborgs & De Rijcke 2012), especially in relation to mass modeling, where degeneracies affect E-mail:…”

Section: Introductionmentioning

confidence: 99%

Model-free analysis of quadruply imaged gravitationally lensed systems and substructured galaxies

Woldesenbet

Williams

2015

Mon. Not. R. Astron. Soc.

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Multiple image gravitational lens systems, and especially quads are invaluable in determining the amount and distribution of mass in galaxies. This is usually done by mass modeling using parametric or free-form methods. An alternative way of extracting information about lens mass distribution is to use lensing degeneracies and invariants. Where applicable, they allow one to make conclusions about whole classes of lenses without model fitting. Here, we use approximate, but observationally useful invariants formed by the three relative polar angles of quad images around the lens center to show that many smooth elliptical+shear lenses can reproduce the same set of quad image angles within observational error. This result allows us to show in a model-free way what the general class of smooth elliptical+shear lenses looks like in the three dimensional (3D) space of image relative angles, and that this distribution does not match that of the observed quads. We conclude that, even though smooth elliptical+shear lenses can reproduce individual quads, they cannot reproduce the quad population. What is likely needed is substructure, with clump masses larger than those responsible for flux ratio anomalies in quads, or luminous or dark nearby perturber galaxies.

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“…For a general magnitude of flexion (Goldberg & Leonard 2007;Okura et al 2008), F ∼ 0.03 arcsec −1 , and for a typical scale of background source size ∼ 2 arcsec, the variation of magnification over the image can be significant, |∆µ/µ| ∼ 10%. In weak lensing, the shape of images is unchanged if the surface mass density κ is transformed as κ → κ ′ = λκ + (1 − λ), which is known as the mass-sheet degeneracy (Gorenstein et al 1988). The real observable quantity in weak lensing is the reduced shear g = γ/(1 − κ).…”

Section: Basic Formalismmentioning

confidence: 99%

Measurement of differential magnification

2014

Monthly Notices of the Royal Astronomical Society

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In gravitational lensing, the magnification effect changes the luminosity and size of a background galaxy. If the image sizes are not small compared to the scale over which the magnification and shear vary, higher-order distortions occur which are termed differential magnification. We give an approximation of the magnification gradient for several halo models. Assuming a symmetric distribution of source brightness, estimates for the differential magnification are obtained and then tested with simulations. One of the main uncertainties of our estimators comes from the finite resolution of the image. We study the strength of our method with the resolution of current and future telescopes. We point out that out method is a potential approach to estimate the first flexion, and can be used to study galaxy and cluster mass profiles.

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Degeneracies in parameter estimates for models of gravitational lens systems

Cited by 185 publications

References 0 publications

Lens models under the microscope: comparison ofHubble Frontier Fieldcluster magnification maps

Lens models under the microscope: comparison ofHubble Frontier Fieldcluster magnification maps

Model-free analysis of quadruply imaged gravitationally lensed systems and substructured galaxies

Measurement of differential magnification

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