1999A&A...351..413M

We present ROSAT HRI X-ray observations of all the galaxy clusters in the Le Fevre et al. arc survey sample in order to study the spatial distribution of the intra-cluster medium (ICM), and examine the expected number of giant luminous arcs for the sample using two spherically symmetric lens models constrained by our X-ray data. Isothermal β model assumes that the ICM is isothermal and is in the hydrostatic equilibrium. ENF98-NFW model assumes that the `universal' dark matter halo profile proposed by Navarro, Frenk & White (INFW) is a valid description of the underlying dark matter distribution. Adopting the result of N-body/gas-dynamical simulations by Eke et al. dark matter distribution in the ENF98-NFW model can be constrained by the X-ray surface brightness distribution of the ICM. The expected number of giant luminous arcs in the sample is then calculated taking into account both detection conditions in the arc survey and the evolution of source galaxies. We find that the isothermal β model cannot reproduce the observed number of giant luminous arcs even allowing uncertainties in the source galaxy model. The ENF98-NFW model displays good agreement in number of giant luminous arcs. However, some clusters have their virial temperature 3-4 times higher than their X-ray temperature obtained from spectral data or from the L<sub>X</sub>-T relation. Thus, we conclude that both spherical models which are consistent with all the available X-ray data cannot reproduce the observed number of giant luminous arcs in the sample. To solve this discrepancy we believe that the giant luminous arc statistics will need to take properly into account `irregularity' in the mass distribution in each cluster.