The Effects of Halo-to-Halo Variation on Substructure Lensing

We explore the halo-to-halo variation of dark matter substructure in galaxy-sized dark matter 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 fsub ~ 0. 25%, but that the variance is large with a 95-percentile range of 0 <= fsub <= 1%. We quantify possible effects of substructure on quadruply-imaged lens systems using the cusp relation and the simple statistic, Rcusp. We estimate that the probability of obtaining the large values of the Rcusp 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 dark matter halos have more large substructures and give rise to large values of Rcusp 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 Rcusp.