SIMBAD references

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 favoured. The mass of this clump within its Einstein radius is log₁₀(M^A_Ein) = 7.65^+0.87_- 0.84_(in units of h^–1₇₀M_☉). The Bayesian evidence provides weaker support for a second clump near image B, with log₁₀(M^B_Ein) = 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>rsim 0.000 77, assuming the total clump masses follow a mass function dN/dM∝M^–1.9 over the range M= 10^7–1010^ M_☉. Few-clump and population models produce similar Bayesian evidence values, so neither type of model is objectively favoured.