Substructure in the lens HE 0435-1223

TL;DR

This study analyzes dark matter substructure in the gravitational lens HE 0435-1223 by modeling the effects of clumps on image positions and flux ratios, using Bayesian evidence to compare models with different substructure configurations.

Contribution

It introduces a Bayesian framework to compare smooth and clumpy mass models, estimating substructure mass fractions and individual clump masses in a gravitational lens.

Findings

Models with a clump near image A are strongly favored.

Estimated mass of the primary clump is around 10^7.65 Msun.

Substructure mass fraction at Einstein radius is greater than 0.00077.

Abstract

We investigate the properties of dark matter substructure in the gravitational lens HE 0435-1223 (z_l=0.455) via its effects on the positions and flux ratios of the quadruply-imaged background quasar (z_s=1.689). We start with a smooth mass model, add individual, truncated isothermal clumps near the lensed images, and use the Bayesian evidence to compare the quality of different models. Compared with smooth models, models with at least one clump near image A are strongly favored. The mass of this clump within its Einstein radius is log(Mein/Msun) = 7.65 +0.87/-0.84. The Bayesian evidence provides weaker support for a second clump near image B, with log(Mein/Msun) = 6.55 +1.01/-1.51. We also examine models with a full population of substructure, and find the mass fraction in substructure at the Einstein radius to be f_sub > 0.00077, assuming the total clump masses follow a mass function dN/dM proportional to M^(-1.9) over the range M = 10^7-10^10 Msun. Few-clump and population models produce similar Bayesian evidence values, so neither type of model is objectively favored.