Annu. Rev. Astron. Astrophys. 1999. 37: 127-189
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7.2. Statistics of Arc(let)s

Up to now, several tens of multiply imaged distant galaxies have already been detected in clusters of galaxies, and this number will probably increase by a large factor within the next few years. Since the fraction of rich clusters (and therefore lensing-clusters) strongly depends on the cosmological scenario, we expect the number of arc(let)s to depend on cosmological parameters (Wilson et al 1996b).

It is well known that present-day statistical studies of clusters of galaxies are limited by the few samples of cluster catalogs with well understood selection function. Wu & Mao (1996) analyzed the statistics of arcs in the EMSS cluster sample (Gioia et al 1990) and show that the fraction is twice the one expected for an EdS Universe, but compatible with a flat lambda = 0.7 model (see also Cooray 1999). Unfortunately, the geometry of the mass distribution and the substructures present in the lensing cluster increase the shear contribution to the magnification and change dramatically the expected number of arcs (Bartelmann et al 1995, Bartelmann 1995b, Hattori et al 1997, Bartelmann et al 1998). The importance of accurate simulations of clusters is clearly obvious from the recent studies. Bartelmann et al (1998) find a totally opposite result to that of Wu & Mao, and conclude that an open model (Omega = 0.3 and lambda = 0) is preferred to any flat models to reproduce the number of arcs observed. The other models, including the lambda = 0.7 model, fail by about of factor of ten. This is a clear demonstration that the use of statistics of arc(let)s to constrain the cosmological scenario is very sensitive to the assumptions. The constraint on lambda from the fraction of arc(let)s is therefore rather weak and hopeless for the moment.

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