Abstract
ABSTRACT A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous ‘dark core’ – an overdense region with no optical counterpart – which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at $99{{\ \rm per\ cent}}$ confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.
Highlights
Gravitational lensing is an astrophysical phenomenon, that can be observed on galactic to cosmic spatial scales, through which distant images are distorted by the intervening mass density field
We propose a variety of estimators for σn based on the median absolute deviation (MAD) methodology, and subsequently extend these approaches to masked fields in a representative variety of cases
We have presented a sparse hierarchical Bayesian massmapping algorithm which provides a principled statistical framework through which, for the first time, we can conduct uncertainty quantification on recovered convergence maps without relying on any assumptions of Gaussianity
Summary
Gravitational lensing is an astrophysical phenomenon, that can be observed on galactic to cosmic spatial scales, through which distant images are distorted by the intervening mass density field. Many approaches to solving this lensing inverse problem have been developed (e.g. VanderPlas et al 2011; Kaiser & Squires 1993; Lanusse et al 2016; Wallis et al 2017; Jeffrey et al 2018; Chang et al 2018), with the industry standard being Kaiser-Squires (KS, Kaiser & Squires 1993). These approaches often produce reliable convergence estimators, they lack principled statistical approaches to uncertainty quantification and often assume or impose Gaussianty during the reconstruction process (Gaussian smoothing in the KS case – which is sub-optimal when one wishes to analyze small-scale non-Gaussian structure). For the reader solely interested in practical application of these techniques we recommend sections 5 onwards
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