We study the statistics of large-separation gravitational lens systems produced by non-spherical 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 \sim 2–4 , so it can not be ignored .
If CDM halos have central density slopes \alpha \lesssim 1.5 , we predict that a significant fraction ( \gtrsim 20 % ) of large-separation lenses should have naked cusp image configurations ; this contrasts with lensing by isothermal ( \alpha \approx 2 ) galaxies where naked cusp configurations are rare .
The image multiplicities depend strongly on the inner density slope \alpha : for \alpha = 1 , the naked cusp fraction is \gtrsim 60 % ; while for \alpha = 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 .