# Bayesian Strong Gravitational-Lens Modeling on Adaptive Grids: Objective Detection of Mass Substructure in Galaxies

**Authors:** S. Vegetti, L. V. E. Koopmans  
**arXiv:** [0805.0201](https://arxiv.org/abs/0805.0201)  
**Date:** 2008-05-02  
**Summary page:** https://www.summarizepaper.com/en/paper/0805.0201v2/

## Key points

- Introduces adaptive and fully Bayesian grid-based method for modeling strong gravitational lenses
- Objective is to quantify presence of luminous and dark-mass substructure in galaxies
- Utilizes adaptive approach on source plane with Delaunay tessellation based on lens mapping
- Employs Bayesian penalty function to recover optimal non-linear potential-model parameters and/or grid-based potential correction
- Enables objective assessment of regularization levels for both source and potential
- Implements Nested-Sampling technique to quantify uncertainties associated with non-linear mass model parameters
- Validates algorithm on simulated data sets derived from realistic lens system model
- Successfully identifies perturbations with masses ≥ 10^7 solar masses on Einstein ring under realistic conditions
- Requires perturbations with masses ≥ 10^9 solar masses for detection inside or outside the ring
- Provides valuable insights into nature of massive galaxies by quantifying presence of substructure

## Summary

The paper titled "Bayesian Strong Gravitational-Lens Modeling on Adaptive Grids: Objective Detection of Mass Substructure in Galaxies" introduces a novel adaptive and fully Bayesian grid-based method for modeling strong gravitational lenses with extended images. The main objective of this method is to quantify the presence of luminous and dark-mass substructure in massive galaxies by analyzing their impact on highly-magnified arcs and Einstein rings. The proposed method utilizes an adaptive approach on the source plane, where a Delaunay tessellation is defined based on the lens mapping of a regular grid onto the source plane. By employing a Bayesian penalty function, the method can effectively recover the optimal non-linear potential-model parameters and/or a grid-based potential correction. Additionally, it enables an objective assessment of regularization levels for both the source and potential. To quantify uncertainties associated with non-linear mass model parameters, the authors implement a Nested-Sampling technique. This technique allows for accurate estimation of errors and facilitates ranking different potential models based on marginalized evidence. Of particular interest is comparing smooth lens mass models with those containing mass-substructures. To validate the effectiveness of their algorithm, the authors test it on various simulated data sets derived from a realistic lens system model. These data sets include lens systems characterized by smooth potentials with power-law density profiles, as well as systems featuring NFW dark-matter substructures at different masses and positions. One specific case involves two NFW dark substructures with identical masses but differing positions. The results demonstrate that the proposed method can successfully identify perturbations with masses greater than or equal to 10^7 solar masses when located on the Einstein ring under realistic conditions. For positions both inside and outside of the ring, perturbations with masses of at least 10^9 solar masses are required for detection. In conclusion, this paper presents an innovative approach to modeling strong gravitational lenses using adaptive grids and Bayesian techniques which proves effective in quantifying the presence of luminous and dark-mass substructure in massive galaxies, providing valuable insights into the nature of these systems.