Gravitational Lens Statistics for Generalized NFW Profiles: Parameter Degeneracy and Implications for Self-Interacting Cold Dark Matter
Strong lensing is a powerful probe of the distribution of matter in the cores of clusters of galaxies. Recent studies suggest that the cold dark matter model predicts cores that are denser than those observed in galaxies, groups and clusters. One possible resolution of the discrepancy is that the dark matter has strong interactions (SIDM), which leads to lower central densities. A generalized form of the Navarro, Frenk and White profile (Zhao profile) may be used to describe these halos. In this paper we examine gravitational lensing statistics for this class of model. The optical depth to multiple imaging is a very sensitive function of the profile parameters in the range of interest for SIDM halos around clusters of galaxies. Less concentrated profiles, which result from larger self-interaction cross-sections, can produce many fewer lensed pairs. Lensing statistics provide a powerful test for SIDM. More realistic and observationally oriented calculations remain to be done, however larger self-interaction cross-sections may well be ruled out by the very existence of strong lenses on galaxy cluster scales. The inclusion of centrally dominant cluster galaxies should boost the cross-section to multiple imaging. However our preliminary calculations suggest that the additional multiple imaging rate is small with respect to the differences in multiple imaging rate for different halo profiles. In future statistical studies, it will be important to properly account for the scatter among halo profiles since the optical depth to multiple imaging is dominated by the most concentrated members of a cluster population.