Trans-Dimensional Bayesian Inference for Gravitational Lens Substructures

TL;DR

This paper presents a Bayesian approach using trans-dimensional inference to detect and characterize dark substructures in gravitational lensing systems, accommodating an unknown number of substructures with a hierarchical prior.

Contribution

It introduces a novel Bayesian method employing reversible jump MCMC and Diffusive Nested Sampling to infer the number and properties of substructures in gravitational lenses.

Findings

Successfully applied to simulated data with known substructures.

Detected potential substructures in the Cosmic Horseshoe system.

Identified limitations due to model misspecifications.

Abstract

We introduce a Bayesian solution to the problem of inferring the density profile of strong gravitational lenses when the lens galaxy may contain multiple dark or faint substructures. The source and lens models are based on a superposition of an unknown number of non-negative basis functions (or "blobs") whose form was chosen with speed as a primary criterion. The prior distribution for the blobs' properties is specified hierarchically, so the mass function of substructures is a natural output of the method. We use reversible jump Markov Chain Monte Carlo (MCMC) within Diffusive Nested Sampling (DNS) to sample the posterior distribution and evaluate the marginal likelihood of the model, including the summation over the unknown number of blobs in the source and the lens. We demonstrate the method on two simulated data sets: one with a single substructure, and one with ten. We also apply the method to the g-band image of the "Cosmic Horseshoe" system, and find evidence for more than zero substructures. However, these have large spatial extent and probably only point to misspecifications in the model (such as the shape of the smooth lens component or the point spread function), which are difficult to guard against in full generality.