Lensing Optical Depth for Substructure and Isolated Dark Matter Halos

Multiple-image quasar lenses can be used to constrain the substructure mass fraction in galaxy-sized dark matter halos via anomalous flux ratios of lensed images. The flux ratios, however, can be affected by both the substructure in the lens halo and by isolated small-mass halos along the entire line-ofsight to the lensed source. While lensing by dark matter clumps near the lens galaxy is more efficient than elsewhere, the cumulative effect of all objects along the line-of-sight could be significant. Here we estimate the potential contribution of isolated clumps to the substructure lensing signal using a simple model motivated by cosmological simulations. We find that the contribution of isolated clumps to the total lensing optical depth ranges from a few to tens percent, depending on assumptions and the particular configuration of the lens. Therefore, although the contribution of isolated clumps to the lensing signal is not dominant, it should not be neglected in detailed analyses of substructure lensing. The total optical depth for lensing is high, τ ∼ 0.2− 20 in the currently favored ΛCDM model. Lensing by small-mass dark matter halos within and outside the lens could therefore naturally explain the high frequency of anomalous flux ratios in observed lenses. Nevertheless, constraints on properties of the substructure population or accurate cosmological constraints, such as the mass of the warm dark matter particle, are difficult if not impossible to derive at this point. The difficulty is due to the high sensitivity of the prediction to the spatial distribution of substructure halos in the innermost regions of the lens halo, which is still very uncertain. Subject headings: gravitational lensing – cosmology: theory – dark matter