A Bayesian analysis of regularized source inversions in gravitational lensing

By Sherry H. Suyu, Philip J. Marshall, M. P. Hobson, R. Blandford. 2006

163 citations recorded by the source corpus.

Strong gravitational lens systems with extended sources are of special interest because they provide additional constraints on the models of the lens systems. To use a gravitational lens system for measuring the Hubble constant, one would need to determine the lens potential and the source intensity distribution simultaneously. A linear inversion method to reconstruct a pixellated source brightness distribution of a given lens potential model was introduced by Warren & Dye. In the inversion process, regularization on the source intensity is often needed to ensure a successful inversion with a faithful resulting source. In this paper, we use Bayesian analysis to determine the optimal regularization constant (strength of regularization) of a given form of regularization and to objectively choose the optimal form of regularization given a selection of regularizations. We consider and compare quantitatively three different forms of regularization previously described in the literature for source inversions in gravitational lensing: zeroth-order, gradient and curvature. We use simulated data with the exact lens potential to demonstrate the method. We find that the preferred form of regularization depends on the nature of the source distribution.

Subfields: Artificial Intelligence, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/7204d4470f1ea472ffebde4eaa363199625e20f7

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Citations in the corpus

THE SLOAN LENS ACS SURVEY. X. STELLAR, DYNAMICAL, AND TOTAL MASS CORRELATIONS OF MASSIVE EARLY-TYPE GALAXIES (2010, background): “…additional external information on the mass density slope, such as that inferred from multiply-imaged extended sources (Warren & Dye 2003; Suyu et al. 2006) and from stellar kinematics (Treu & Koopmans 2002; Koopmans et al. 2003), can help to break these degeneracies and provide robust…”
A Bayesian approach to strong lensing modelling of galaxy clusters (2007, methodology): “Recent work on regularisation techniques Bradač et al. (2005); Suyu et al. (2006) has improved the situation in this regard somewhat.”
Strong Lensing by Galaxies (2010, methodology): “Although the high redshift samples with measured velocity dispersions are small, they seem to suggest a somewhat larger intrinsic scatter around γ′ = 2 (Treu & Koopmans 2004).”
Galaxy Masses: A Review (2013, background): “To minimize contamination by field galaxies, with their much more extended halos, early work has been confined to early type galaxies (Natarajan et al. 1998; Limousin et al. 2007), but recently Natarajan et al.”
TWO ACCURATE TIME-DELAY DISTANCES FROM STRONG LENSING: IMPLICATIONS FOR COSMOLOGY (2012, unknown): “The extended source on a grid is modeled following Suyu et al. (2006), with curvature regularization.”
The Sloan Lens ACS Survey. VI. Discovery and Analysis of a Double Einstein Ring (2008, methodology): “The second approach is the linear source inversion and parametric potential fitting method described by Warren & Dye (2003), Treu & Koopmans (2004), Koopmans (2005) and Suyu et al. (2006).”
DISSECTING THE GRAVITATIONAL LENS B1608+656. II. PRECISION MEASUREMENTS OF THE HUBBLE CONSTANT, SPATIAL CURVATURE, AND THE DARK ENERGY EQUATION OF STATE (2009, methodology): “Specifically, we try zeroth-order, gradient and curvature forms for P (s|λ, g), and the curvature form for P (δψ), as described in Suyu et al. (2006) and Suyu et al. (2009).”
Inference of the cold dark matter substructure mass function at z = 0.2 using strong gravitational lenses (2014, background): “Similarly, Suyu et al. (2006) showed that different source surface brightness distributions may require different forms of 1 The noise in each pixel includes background noise from the sky and the electronics as well as shot noise.”
Time delay cosmography (2016, background): “…the parametrization of some of the components is simple and others are complex (Warren and Dye 2003; Treu and Koopmans 2004; Brewer and Lewis 2006; Suyu et al. 2006; Suyu and Halkola 2010), or where flexibly parametrized “corrections” are added to simply parametrized models (Koopmans 2005;…”
Two-dimensional kinematics of SLACS lenses – III. Mass structure and dynamics of early-type lens galaxies beyond z ≃ 0.1 (2011, methodology): “By employinga pixelated source reconstruction method (see e.g. Warren & Dye 2003, Koopmans 2005, Suyu et al. 2006) for the lensing and some flavour of the Schwarzschild orbit superposition method (Schwarzschild 1979; see Thomas 2010 for a review of the developments of this technique) for the…”
Detection of a dark substructure through gravitational imaging (2009, background): “…of Bayesian statistics which allowsus to determine the best set of non-linear parameters for a given potential and the linear parameters of the source, to objectively set the level of regularization and to compare different model families (MacKay 1992, 2003; Suyu et al. 2006; Brewer & Lewis 2006).”