We examine gravitational lensing constraints on the structure of galaxy clusters and compare them with the results of cosmological N-body simulations of cluster formation in cold dark matter ( CDM ) dominated universes .
We find that cluster core masses , as measured by the observed location of giant tangential arcs , generally exceed those of dark matter halos of similar velocity dispersion .
The magnitude of the discrepancy is a strong function of cluster mass .
Arc properties in the most massive clusters in the sample ( i.e .
those with velocity dispersion , \sigma \sim 1500 - 2000 km s ^ { -1 } ) are essentially consistent with the N-body predictions .
On the other hand , giant arcs in \sigma \sim 1000 km s ^ { -1 } clusters can only be reconciled with CDM cluster halos if their lensing power has been increased substantially by the presence of a massive ( \sim 3 \times 10 ^ { 12 } h ^ { -1 } M _ { \odot } ) central galaxy and of significant substructure .
Best agreement is found if the mass of the central galaxy and the effects of substructure are approximately independent of cluster mass .
Massive central galaxies with steep inner density profiles are also needed to explain a clear trend observed in our dataset between the radial thickness of giant tangential arcs and the velocity dispersion of the cluster lens .
The position and redshift of radial arcs may be used as independent tests of these results , but at present the dataset available is too limited to have a significant impact on these conclusions .
Our results depend only weakly on the cosmological model adopted , and suggest that structural parameters of clusters derived from strong lensing studies can not usefully constrain the values of cosmological parameters .