Bayesian strong gravitational-lens modelling on adaptive grids: objective detection of mass substructure in Galaxies

Abstract

We introduce a new adaptive and fully Bayesian grid‐based method to model strong gravitational lenses with extended images. The primary goal of this method is to quantify the level of luminous and dark mass substructure in massive galaxies, through their effect on highly magnified arcs and Einstein rings. The method is adaptive on the source plane, where a Delaunay tessellation is defined according to the lens mapping of a regular grid on to the source plane. The Bayesian penalty function allows us to recover the best non‐linear potential‐model parameters and/or a grid‐based potential correction and to objectively quantify the level of regularization for both the source and potential. In addition, we implement a Nested‐Sampling technique to quantify the errors on all non‐linear mass model parameters – marginalized over all source and regularization parameters – and allow an objective ranking of different potential models in terms of the marginalized evidence. In particular, we are interested in comparing very smooth lens mass models with ones that contain mass substructures. The algorithm has been tested on a range of simulated data sets, created from a model of a realistic lens system. One of the lens systems is characterized by a smooth potential with a power‐law density profile, 12 include a Navarro, Frenk and White (NFW) dark matter substructure of different masses and at different positions and one contains two NFW dark substructures with the same mass but with different positions. Reconstruction of the source and lens potential for all of these systems shows the method is able, in a realistic scenario, to identify perturbations with masses ≳107 M⊙ when located on the Einstein ring. For positions both inside and outside of the ring, masses of at least 109 M⊙ are required (i.e. roughly the Einstein ring of the perturber needs to overlap with that of the main lens). Our method provides a fully novel and objective test of mass substructure in massive galaxies.

Gravitational detection of a low-mass dark satellite galaxy at cosmological distance

“…This allowed the location and the number of possible substructures in a specific lens potential to be quantified. Previous simulations have shown that we can detect more than one substructure in the same system when located at a position where they can affect the lensed images 10 . All three independent data sets and considered models showed a positive potential correction located at the same position, see for example Fig.…”

“…We used an analytic model to determine the mass and the statistical significance of the substructure in the context of a physical model 9,10 . In this analytic approach, a truncated pseudo-Jaffe model was used to parameterize the substructure mass and position, giving three extra free parameters.…”

Properties of nested sampling

“…They naturally occur as marginals in Bayesian testing and model choice (Jeffreys, 1939;Robert, 2001, Chapters 5 and 7). Nested sampling has been well received in astronomy and has been applied successfully to several cosmological problems, see, for instance, Mukherjee et al (2006), Shaw et al (2007), and Vegetti & Koopmans (2009), among others. In addition, Murray et al (2006) develop a nested sampling algorithm for computing the normalising constant of Potts models.…”

Constraints on the identity of the dark matter from strong gravitational lenses

“…It can also distort the images of extended giant arcs or Einstein rings (e.g. Koopmans 2005;Vegetti & Koopmans 2009a;Vegetti et al 2012;Hezaveh et al 2016).…”