Substructure in the lens HE 0435-1223
  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.
