The frequency of giant arcs— highly distorted and strongly gravitationally lensed background galaxies— is a powerful test for cosmological models .
Previous comparisons of arc statistics for the currently favored concordance cosmological model ( a flat lambda-dominated universe ) with observations have shown an apparently large discrepancy .
We present here new ray-shooting results , based on a high resolution ( 1024 ^ { 3 } particles in a 320 h ^ { -1 } Mpc box ) large-scale structure simulation normalized to the WMAP observations .
We follow light rays through a pseudo-3D matter distribution approximated by up to 38 lens planes , and evaluate the occurrence of arcs for various source redshifts .
We find that the frequency of strongly lensed background sources is a steep function of source redshift : the optical depth for giant arcs increases by a factor of five when the background sources are moved from redshift z _ { s } = 1.0 
to z _ { s } = 1.5 .
This is a consequence of a moderate decrease of the critical surface mass density for lensing , combined with the very steep cluster mass function at the high mass end .
Our results are consistent with those of Bartelmann et al .
( 1998 ) if we— as they did— restrict all sources to be exactly at z _ { s } = 1 .
But if we allow for a more realistic distribution of source redshifts extending to or beyond z _ { s } \geq 1.5 , the apparent discrepancy vanishes : the frequency of arcs is increased by about a factor of ten as compared to previous estimates , and results in roughly one arc per 20 square degrees over the sky .
This prediction for an LCDM model is then in good agreement with the observed frequency of arcs .
Hence we consider the “ missing arc ” problem for a concordance LCDM cosmology to be solved .