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Register a new userNon-parametric strong lens inversion of Cl~0024+1654: illustrating the monopole degeneracy
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The cluster lens Cl 0024+1654 is undoubtedly one of the most beautiful examples of strong gravitational lensing, providing five large images of a single source with well-resolved substructure. Using the information contained in the positions and the shapes of the images, combined with the null space information, a non-parametric technique is used to infer the strong lensing mass map of the central region of this cluster. This yields a strong lensing mass of 1.60x10^14 M_O within a 0.5 radius around the cluster center. This mass distribution is then used as a case study of the monopole degeneracy, which may be one of the most important degeneracies in gravitational lensing studies and which is extremely hard to break. We illustrate the monopole degeneracy by adding circularly symmetric density distributions with zero total mass to the original mass map of Cl 0024+1654. These redistribute mass in certain areas of the mass map without affecting the observed images in any way. We show that the monopole degeneracy and the mass-sheet degeneracy together lie at the heart of the discrepancies between different gravitational lens reconstructions that can be found in the literature for a given object, and that many images/sources, with an overall high image density in the lens plane, are required to construct an accurate, high-resolution mass map based on strong-lensing data.
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In this article we study the well-known strong lensing system SDSS J1004+4112. Not only does it host a large-separation lensed quasar with measured time-delay information, but several other lensed galaxies have been identified as well. A previously developed strong lens inversion procedure that is designed to handle a wide variety of constraints, is applied to this lensing system and compared to results reported in other works. Without the inclusion of a tentative central image of one of the galaxies as a constraint, we find that the model recovered by the other constraints indeed predicts an image at that location. An inversion which includes the central image provides tighter constraints on the shape of the central part of the mass map. The resulting model also predicts a central image of a second galaxy where indeed an object is visible in the available ACS images. We find masses of 2.5x10^13 M_O and 6.1x10^13 M_O within a radius of 60 kpc and 110 kpc respectively, confirming the results from other authors. The resulting mass map is compatible with an elliptical generalization of a projected NFW profile, with r_s = 58_{-13}^{+21} arcsec and c_vir = 3.91 +/- 0.74. The orientation of the elliptical NFW profile follows closely the orientation of the central cluster galaxy and the overall distribution of cluster members.
We present a comprehensive mass reconstruction of the rich galaxy cluster Cl 0024+17 at z~0.4 from ACS data, unifying both strong- and weak-lensing constraints. The weak-lensing signal from a dense distribution of background galaxies (~120 per square arcmin) across the cluster enables the derivation of a high-resolution parameter-free mass map. The strongly-lensed objects tightly constrain the mass structure of the cluster inner region on an absolute scale, breaking the mass-sheet degeneracy. The mass reconstruction of Cl 0024+17 obtained in such a way is remarkable. It reveals a ringlike dark matter substructure at r~75 surrounding a soft, dense core at r~50. We interpret this peculiar sub-structure as the result of a high-speed line-of-sight collision of two massive clusters 1-2 Gyr ago. Such an event is also indicated by the cluster velocity distribution. Our numerical simulation with purely collisionless particles demonstrates that such density ripples can arise by radially expanding, decelerating particles that originally comprised the pre-collision cores. Cl 0024+17 can be likened to the bullet cluster 1E0657-56, but viewed $along$ the collision axis at a much later epoch. In addition, we show that the long-standing mass discrepancy for Cl 0024+17 between X-ray and lensing can be resolved by treating the cluster X-ray emission as coming from a superposition of two X-ray systems. The clusters unusual X-ray surface brightness profile that requires a two isothermal sphere description supports this hypothesis.
Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate how sparse optimisation can address the problem. As a first step towards a full free-form lens modelling technique, we consider linear inversion of the lensed source under sparse regularisation and joint deblending from the lens light profile. The method is based on morphological component analysis, assuming a known mass model. We show with numerical experiments that representing the lens and source light using an undecimated wavelet basis allows us to reconstruct the source and to separate it from the foreground lens at the same time. Both the source and lens light have a non-analytic form, allowing for the flexibility needed in the inversion to represent arbitrarily small and complex luminous structures in the lens and source. in addition, sparse regularisation avoids over-fitting the data and does not require the use of any adaptive mesh or pixel grid. As a consequence, our reconstructed sources can be represented on a grid of very small pixels. Sparse regularisation in the wavelet domain also allows for automated computation of the regularisation parameter, thus minimising the impact of arbitrary choice of initial parameters. Our inversion technique for a fixed mass distribution can be incorporated in future lens modelling technique iterating over the lens mass parameters. The python package corresponding to the algorithms described in this article can be downloaded via the github platform at https://github.com/herjy/SLIT.
We describe a new method for analyzing gravitational lens images, for the case where the source light distribution is pixelized. The method is suitable for high resolution, high S/N data of a multiply-imaged extended source. For a given mass distribution, we show that the step of inverting the image to obtain the deconvolved pixelized source light distribution, and the uncertainties, is a linear one. This means that the only parameters of the non-linear problem are those required to model the mass distribution. This greatly simplifies the search for a min.-chi^2 fit to the data and speeds up the inversion. The method is extended in a straightforward way to include linear regularization. We apply the method to simulated Einstein ring images and demonstrate the effectiveness of the inversion for both the unregularized and regularized cases.
The vast quantity of strong galaxy-galaxy gravitational lenses expected by future large-scale surveys necessitates the development of automated methods to efficiently model their mass profiles. For this purpose, we train an approximate Bayesian convolutional neural network (CNN) to predict mass profile parameters and associated uncertainties, and compare its accuracy to that of conventional parametric modelling for a range of increasingly complex lensing systems. These include standard smooth parametric density profiles, hydrodynamical EAGLE galaxies and the inclusion of foreground mass structures, combined with parametric sources and sources extracted from the Hubble Ultra Deep Field. In addition, we also present a method for combining the CNN with traditional parametric density profile fitting in an automated fashion, where the CNN provides initial priors on the latters parameters. On average, the CNN achieved errors 19 $pm$ 22 per cent lower than the traditional methods blind modelling. The combination method instead achieved 27 $pm$ 11 per cent lower errors over the blind modelling, reduced further to 37 $pm$ 11 per cent when the priors also incorporated the CNN-predicted uncertainties, with errors also 17 $pm$ 21 per cent lower than the CNN by itself. While the CNN is undoubtedly the fastest modelling method, the combination of the two increases the speed of conventional fitting alone by factors of 1.73 and 1.19 with and without CNN-predicted uncertainties, respectively. This, combined with greatly improved accuracy, highlights the benefits one can obtain through combining neural networks with conventional techniques in order to achieve an efficient automated modelling approach.
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