A survey for large-separation lensed FIRST quasars - II. Magnification bias and redshift distribution

The statistics of large-separation gravitational lensing are a powerful tool for probing mass distributions on the scale of galaxy clusters. In this paper we refine the analysis of our survey for large-separation (>5 arcsec) lensed FIRST quasars by estimating the magnification bias and the source redshift distribution. Finding no large-separation lens among 8000 probable quasars in that sample, implies an upper bound on the lensed fraction of 3.7 × 10-4 at 95 per cent confidence level. From a published deep 1.4-GHz radio survey of the Hubble Deep Field, and corresponding optical searches for faint quasars, we calculate a lower limit to the `double-flux magnification bias' affecting our radio-optically selected sample, of B>= 1.1. From the four-colour information in the SDSS Early Data Release, we calculate the photometric-redshift distribution of a sample of FIRST quasar candidates and compare it with the redshift distribution from the FIRST Bright Quasar Survey. We find that the median redshift of the quasars in our sample is approximately 1.4. With these new results, we find that for all plausible cosmologies, the absence of lensed quasars in our survey is consistent with a model based on an empirical, non-evolving, cluster mass function, where clusters are represented by singular isothermal spheres. On the other hand, comparison of our results with the lensing predictions of published N-body ray-tracing simulations rejects the COBE normalized Ω0= 1 cold dark matter model at 99.9 per cent confidence