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.
