2011ApJ...741..117C

We explore the halo-to-halo variation of dark matter (DM) substructure in galaxy-sized DM halos, focusing on its implications for strongly gravitational lensed systems. We find that the median value for projected substructure mass fractions within projected radii of 3% of the host halo virial radius is approximately f_sub~ 0.25%, but that the variance is large with a 95 percentile range of 0 ≤ f_sub ≤ 1%. We quantify possible effects of substructure on quadruply imaged lens systems using the cusp relation and the simple statistic, R_cusp. We estimate that the probability of obtaining the large values of the R_cusp which have been observed from substructure effects is roughly ∼10^–3 to ∼10^–2. We consider a variety of possible correlations between host halo properties and substructure properties in order to probe possible sample biases. In particular, low-concentration host DM halos have more large substructures and give rise to large values of R _cusp more often. However, there is no known observational bias that would drive observed quadruply imaged quasars to be produced by low-concentration lens halos. Finally, we show that the substructure mass fraction is a relatively reliable predictor of the value of R_cusp.