In the near future, ultra deep observations of galaxy clusters with HST or JWST will uncover 300 − 1000 lensed multiple images, increasing the current count per cluster by up to an order of magnitude. This will further refine our view of clusters, leading to a more accurate and precise mapping of the total and dark matter distribution in clusters, and enabling a better understanding of background galaxy population and their luminosity functions. However, to effectively use that many images as input to lens inversion will require a re-evaluation of, and possibly upgrades to the existing methods. In this paper we scrutinize the performance of the free-form lens inversion method Grale in the regime of 150 − 1000 input images, using synthetic massive galaxy clusters. Our results show that with an increasing number of input images, Grale produces improved reconstructed mass distributions, with the fraction of the lens plane recovered at better than 10% accuracy increasing from 40 − 50% for ∼150 images to 65% for ∼ 1000 images. The reconstructed time delays imply a more precise measurement of H 0 , with 1% bias. While the fidelity of the reconstruction improves with the increasing number of multiple images used as model constraints, ∼ 150 to ∼1000, the lens plane rms deteriorates from ∼ 0.11 to ∼ 0.28 . Since lens plane rms is not necessarily the best indicator of the quality of the mass reconstructions, looking for an alternative indicator is warranted.
Abell 1689 is a well studied cluster of galaxies and one of the largest gravitational lens systems ever observed. We have obtained a reconstruction of the cluster Abell 1689 using G , a free-form lens inversion method that relies exclusively on the multiple image data. Non-inclusion of any data related to cluster member galaxies ensures an unbiased measure of the mass distribution, which is the most notable feature of this method. We used two different sets of multiply lensed systems from the available strong lensing data -one containing only the secure systems (107 images), and the other containing all available systems, only excluding some very non-secure systems (151 images). Both the reconstructions produced similar mass distributions whose circularly symmetric radial profiles are well fit with the Navarro-Frenk-White (NFW) profile with concentration parameter values, 𝑐 ∼ 6.8. For the very well-constrained central ∼100 kpc region of the cluster we made detailed comparison of the G reconstructed lensing mass and stellar mass retrieved by the Spectral Energy Distribution (SED) fitting software ++. We found an offset in the light peak of the Brightest Cluster Galaxy (BCG) and its associated lensing mass peak, of about 10 kpc. We also found a light-unaccompanied mass peak in this region, whose location agrees with features retrieved by some of the earlier reconstructions using different methodologies. Both the light-unaccompanied mass peak and the BCG offset are consistent with dark matter self-interaction cross-section 𝜎 1cm 2 /g, while the mass peak is in tension with larger cross-sections.
Due to the finite amount of observational data, the best-fit parameters corresponding to the reconstructed cluster mass have uncertainties. In turn, these uncertainties affect the inferences made from these mass models. Following our earlier work, we have studied the effect of such uncertainties on the singularity maps in simulated and actual galaxy clusters. The mass models for both simulated and real clusters have been constructed using grale. The final best-fit mass models created using grale give the simplest singularity maps and a lower limit on the number of point singularities that a lens has to offer. The simple nature of these singularity maps also puts a lower limit on the number of three image (tangential and radial) arcs that a cluster lens has. Hence, we estimate the number of galaxy sources giving rise to the three image arcs, which can be observed with the James Webb Space Telescope (JWST). We find that we expect to observe at least 20-30 tangential and 5-10 radial three-image arcs in the Hubble Frontier Fields cluster lenses with the JWST.
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