## 6. SummaryUsing the redshift and magnitude, or flux, distribution observed towards the HDF to describe background sources and Press-Schechter theory and singular isothermal sphere models to describe the foreground lensing clusters, we have calculated the expected number of lensed arcs towards galaxy clusters. We have improved previous calculations on arc statistics by including redshift information for background galaxies and accounting for the redshift evolution of foreground lensing clusters in different cosmological models. We have also accounted for the magnification bias in magnitude-limited search programs based on the HDF luminosity function. Our predicted numbers are in agreement with an extrapolation of the observed number of arcs towards a sample of bright EMSS clusters to the whole sky when in a flat universe with . Given the large systematic effects involved with both the predicted and observed number of arcs, more reliable constraints on the cosmological parameters are not currently possible. Using the redshift and flux information for HDF radio sources, and
the same lens population, we have extended the calculation to predict
the expected number of lensed At sub-mm wavelengths, we predict lensed sources towards clusters for same cosmology as above. We have compared our predicted numbers to the observed number of lensed sub-mm sources towards a sample of galaxy clusters. However, various biases in this observed sample and possible source contamination, do not allow us to constrain cosmological parameters based on current statistics. We have briefly studied the possibility of using the Planck surveyor and the South Pole 10-m telescope data to perform this task. A catalog of 100 lensed sources towards clusters is likely to be a useful by-product of Planck. © European Southern Observatory (ESO) 1999 Online publication: December 16, 1998 |