A maximum-entropy method for reconstructing the projected mass distribution of gravitational lenses

Bridle, S. L.; Hobson, M. P.; Lasenby, A. N.; Saunders, Richard

doi:10.1046/j.1365-8711.1998.01877.x

Cited by 85 publications

(90 citation statements)

References 18 publications

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“…Therefore, in this paper we utilize the Hessian matrix to estimate the rms values of the mass pixels. Bridle et al (1998) demonstrated that the errors derived from their Hessian matrix are consistent with the values obtained from Monte Carlo simulations. We also confirmed their claim by performing independent simulations using a low-resolution (20 × 20) mass grid.…”

Section: Mass Luminosity and Significance Estimationsupporting

confidence: 72%

A STUDY OF THE DARK CORE IN A520 WITH THEHUBBLE SPACE TELESCOPE: THE MYSTERY DEEPENS

Jee

Mahdavi

Hoekstra

et al. 2012

ApJ

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We present a Hubble Space Telescope/Wide Field Planetary Camera 2 weak-lensing study of A520, where a previous analysis of ground-based data suggested the presence of a dark mass concentration. We map the complex mass structure in much greater detail, leveraging more than a factor of three increase in the number density of source galaxies available for lensing analysis. The "dark core" that is coincident with the X-ray gas peak, but not with any stellar luminosity peak, is now detected with more than 10σ significance. The ∼1.5 Mpc filamentary structure elongated in the NE-SW direction is also clearly visible. Taken at face value, the comparison among the centroids of dark matter, intracluster medium, and galaxy luminosity is at odds with what has been observed in other merging clusters with a similar geometric configuration. To date, the most remarkable counterexample might be the Bullet Cluster, which shows a distinct bow-shock feature as in A520, but no significant weak-lensing mass concentration around the X-ray gas. With the most up-to-date data, we consider several possible explanations that might lead to the detection of this peculiar feature in A520. However, we conclude that none of these scenarios can be singled out yet as the definite explanation for this puzzle.

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Section: Mass Luminosity and Significance Estimationsupporting

confidence: 72%

A STUDY OF THE DARK CORE IN A520 WITH THEHUBBLE SPACE TELESCOPE: THE MYSTERY DEEPENS

Jee

Mahdavi

Hoekstra

et al. 2012

ApJ

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“…We determine by iteration the Bayesian value of ¼ˆ(p; m) by the following equation (Bridle et al 1998):…”

Section: Maximum Entropy Mass Reconstruction Methodsmentioning

confidence: 99%

Combining Lens Distortion and Depletion to Map the Mass Distribution of A1689

Umetsu

Broadhurst

2008

Astrophysical Journal

139

199

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We derive a projected 2D mass map of the well-studied galaxy cluster A1689 based on an entropy-regularized maximum likelihood combination of the lens magnification and distortion of red background galaxies registered in deep Subaru images. The method is not restricted to the weak regime but applies to the whole area outside the tangential critical curve, where nonlinearity between the surface mass density and the observables extends to a radius of a few arcminutes. The known strong-lensing information is also readily incorporated in this approach, represented as a central pixel with a mean surface density close to the critical value. We also utilize the distortion measurements to locally downweight the intrinsic clustering noise, which otherwise perturbs the depletion signal. The projected mass profile continuously steepens with radius and is well fitted by the Navarro-Frenk-White model, but with a surprisingly large concentration c vir ¼ 13:4 þ5:3 À3:3 , lying far from the predicted value of c vir $ 5, corresponding to the measured virial mass, M vir ¼ (2:1 AE 0:2) ; 10 15 M , posing a challenge to the standard assumptions defining the ÃCDM model. We examine the consistency of our results with estimates derived with the standard weak-lensing estimators and by comparison with the inner mass profile obtained from strong lensing. All the reconstructions tested here imply a virial mass in the range M vir ¼ (1:5Y2:1) ; 10 15 M , and the combined ACS and Subaru 2D mass reconstruction yields a tight constraint on the concentration parameter, c vir ¼ 12:7 AE 1 AE 2:8 (c 200 $ 10), improving upon the statistical accuracy of our earlier 1D analysis. Importantly, our best-fitting profile properly reproduces the observed Einstein radius of 45 00 (z s ¼ 1), in contrast to other weak-lensing work, reporting lower concentration profiles, which underestimate the observed Einstein radius.

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“…(1) and (2). (Magnification information can also be used to improve the reconstruction (see Bridle et al 1998), but is typically more noisy than the shear measurements and has not been considered in this paper). For this purpose, we take the Fourier transform of these equations and obtain…”

Section: Mass Inversionmentioning

confidence: 99%

Weak lensing mass reconstruction using wavelets

Starck

Pires

Réfrégier

2006

A&A

102

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This paper presents a new method for the reconstruction of weak lensing mass maps. It uses the multiscale entropy concept, which is based on wavelets, and the False Discovery Rate (FDR) which allows us to derive robust detection levels in wavelet space. We show that this new restoration approach outperforms several standard techniques currently used for weak shear mass reconstruction. This method can also be used to separate E and B modes in the shear field, and thus test for the presence of residual systematic effects. We concentrate on large blind cosmic shear surveys, and illustrate our results using simulated shear maps derived from N-Body ΛCDM simulations (Vale & White 2003) with added noise corresponding to both ground-based and space-based observations.

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A maximum-entropy method for reconstructing the projected mass distribution of gravitational lenses

Cited by 85 publications

References 18 publications

A STUDY OF THE DARK CORE IN A520 WITH THEHUBBLE SPACE TELESCOPE: THE MYSTERY DEEPENS

A STUDY OF THE DARK CORE IN A520 WITH THEHUBBLE SPACE TELESCOPE: THE MYSTERY DEEPENS

Combining Lens Distortion and Depletion to Map the Mass Distribution of A1689

Weak lensing mass reconstruction using wavelets

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