Angular separations of the lensed QSO images

Abstract

We have analyzed the observed image separations of the gravitationally lensed images of QSOs for a possible correlation with the source redshift. Contrary to the previously noted anti-correlation based on a smaller data set, no correlation is found for the currently available data. We have calculated the average image separations of the lensed QSOs as a function of source redshifts, for isothermal spheres with cores in a flat universe, taking into account the amplification bias caused by lensing. The shape of the distribution of average image separation as a function of redshift is very robust and is insensitive to most model parameters. Observations are found to be roughly consistent with the theoretical results for models which assume the lens distribution to be (i) Schechter luminosity function which, however, can not produce images with large separation and (ii) the mass condensations in a cold dark matter universe, as given by the Press-Schechter theory if an upper limit of 1-7$\times 10^{13}$ M$\odot$ is assumed on the mass of the condensations.