Non-parametric strong lens inversion of Cl~0024+1654: illustrating the monopole degeneracy

TL;DR

This paper employs a non-parametric method to reconstruct the mass distribution of galaxy cluster Cl 0024+1654 using strong lensing data, highlighting the monopole degeneracy's role in lensing mass uncertainties.

Contribution

It demonstrates the impact of the monopole degeneracy on gravitational lensing mass reconstructions and emphasizes the need for numerous images for accurate mass mapping.

Findings

Mass within 0.5' radius is 1.60x10^14 M_O.

Adding zero-mass circular distributions shows the monopole degeneracy.

High image density is crucial for precise mass maps.

Abstract

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.