Arc Statistics in Triaxial Dark Matter Halos: Testing the Collisionless Cold Dark Matter Paradigm

Statistics of lensed arcs in clusters of galaxies serve as a powerful probe of both the non-sphericity and the inner slope of dark matter halos. We develop a semi-analytic method to compute the number of arcs in triaxial dark matter halos. This combines the lensing cross section from the Monte Carlo ray-tracing simulations, and the probability distribution function (PDF) of the axis ratios evaluated from cosmological N-body simulations. This approach enables one to incorporate both asymmetries in the projected mass density and elongations along the line-of-sight analytically, for the first time in cosmological lensed arc statistics. As expected, triaxial dark matter halos significantly increase the number of arcs relative to spherical models; the difference amounts to more than one order of magnitude while the value of enhancement depends on the specific properties of density profiles. Then we compare our theoretical predictions with the observed number of arcs from 38 X-ray selected clusters. In contrast to the previous claims, our triaxial dark matter halos with inner density profile ρ ∝ r−1.5 in a Lambda-dominated cold dark matter (CDM) universe reproduces well the observation. Since both the central mass concentration and triaxial axis ratios (minor to major axis ratio ∼ 0.5) required to account for the observed data are consistent with cosmological N-body simulations, our result may be interpreted to lend strong support for the collisionless CDM paradigm at the mass scale of clusters.