Constraining cosmological models using arc statistics in future SZ cluster surveys

Upcoming wide-area surveys in the submillimetre regime will allow the construction of complete galaxy cluster samples through their thermal Sunyaev-Zel'dovich effect. We propose an analytic method to predict the number of gravitationally lensed giant arcs produced by the cluster sample expected to be detectable for the Planck satellite. The statistics of lensed arcs can be used to constrain cosmological parameters. This computation implies the choice of an analytic cluster model which has to reproduce the lensing properties of realistic galaxy clusters. Comparing the results of analytic computations and numerical ray-tracing simulations, we show that spherical models with the Navarro-Frenk-White density profile fail by far to produce as many giant arcs as realistic galaxy clusters. This confirms the great importance of asymmetries and substructures in the lensing matter distribution. By elliptically distorting the lensing potential of spherical NFW density profiles, we show that the discrepancy between analytic and numerical computations can almost completely be removed.