ARC STATISTICS WITH REALISTIC CLUSTER POTENTIALS .1. METHOD AND 1ST RESULTS

We study the capability of a numerically modeled galaxy cluster to pro duce giant arcs. The cluster is formed from CDM-like density perturbat ions via gravitational collapse, which is numerically treated with an N-body tree code. We also compute the X-ray emissivity of the baryonic intracluster medium under the assumption that this gas is filled into the gravitational potential of the dark cluster material. From the le nsing properties of the cluster, from the statistical properties of th e giant arcs produced by the cluster, and from comparing the cluster p roperties derived both from lensing and from the X-ray properties of t he intracluster gas, we conclude (1) that clusters may be significantl y more efficient for lensing than estimated from their velocity disper sion on the basis of isothermal-sphere models, (2) that the discrepanc y between cluster core radii derived from lensing and from their X-ray surface brightness may be understood assuming that the intracluster g as was expelled from the cluster galaxies when the dark 'body' of the cluster had already formed, and (3) that clusters may be efficient in producing giant arcs even if they have extended cores and a fairly sha llow surface-density profile. This may mean that arcs may be much easi er to produce, and therefore more abundant, than previously estimated.