1997A&A...319..764H

We have constructed a scheme to predict the number of arcs that should be observed in clusters, that fully takes into account both the detection conditions in the arc survey and the evolution of the source galaxies. The scheme has been applied to Le Fevre et al.'s arc survey data in order to constrain the models of cluster mass distribution. The canonical model of the source galaxy evolution proposed by Yoshii (1993ApJ...403..552Y) is adopted. We have found that any spherical cluster mass distribution models even with very small core radius, cannot reproduce a number of arcs as large as the number observed in Le Fevre et al.'s arc survey. Recently, Bartelmann, Steinmetz & Weiss (1995A&A...297....1B; hereafter BSW) showed that their inhomogeneous model constructed numerically can produce a much larger number of giant luminous arcs than the non-singular isothermal sphere model with the same core radius and the same velocity dispersion as those in their model. However, we have found that their cluster mass distribution model cannot reproduce a number of arcs as large as observed. We suggest that one of the possible solutions to reproduce the observed arc number is that the clusters have inhomogeneities similar to these in BSW's model as a whole and that the core radius of the clusters may be much smaller than that in BSW's model. A speculation on the evolution of the cooling flow and the hot gas in the cluster central region is made based on this suggestion. A possible variation of the lens model with the non-thermal pressure is also briefly discussed in order to examine how it enhances the expected number of giant luminous arcs.