Effects of triaxiality on the statistics of large-separation gravitational lenses

We study the statistics of large-separation gravitational lens systems produced by nonspherical halos in the cold dark matter (CDM) model. Specifically, we examine how the triaxiality of CDM halos affects the overall lensing probabilities and the relative numbers of different image configurations (double, quadruple, and naked cusp lenses). We find that triaxiality significantly enhances lensing probabilities by a factor of ∼2-4, so it cannot be ignored. If CDM halos have central density slopes α. ≲ 1.5, we predict that a significant fraction (≳20%) of large-separation lenses should have naked cusp image configurations; this contrasts with lensing by isothermal (α ≈ 2) galaxies where naked cusp configurations are rare. The image multiplicities depend strongly on the inner density slope α: for α = 1, the naked cusp fraction is ≳60%, while for α = 1.5, quadruple lenses are actually the most probable. Thus, the image multiplicities in large-separation lenses offer a simple new probe of the inner density profiles of dark matter halos. We also compute the expected probabilities and image multiplicities for lensed quasars in the Sloan Digital Sky Survey and argue that the recent discovery of the large-separation quadruple lens SDSS J1004+4112 is consistent with expectations for CDM.