2004ApJ...604L...5M

We review the evidence for substructures from the anomalous flux ratios in gravitational lenses. Using high-resolution numerical simulations, we show that at typical image positions, the fraction of surface mass density in substructures is ≲0.5% with mass above 10^–4 virial masses in the ``concordance'' ΛCDM cosmology. Substructures outside the virial radius (but projected at typical lens image positions) only increase the fraction moderately. Several effects, in particular baryonic settling and the requirement of compactness, may further decrease the predictions by a factor of few. The predicted fraction with appropriate properties thus appears to be lower than that required by lensing, although both are still uncertain. More speculative substructures such as massive black holes (M∼10⁵-10⁶ M_☉) in the halo may offer viable alternatives.