How many arcminute-separation lenses are expected in the 2dF QSO survey?

Abstract

Wide separation lensing statistics offer information about the density profile and abundance of dark halos. Recently a possible discovery of six quasar pairs, which may be lensed multiple images, was reported by Miller et al. (2003, astro-ph/0210644). These pairs are selected from a catalog of the 2dF quasar (QSO) survey comprising 22163 quasars. We calculate expected numbers of lensed quasars taking account of the redshift and magnitude distributions of the quasar catalog. Given some of the six pairs are genuine lensed systems, we put interesting constraints on the inner slope of dark halos, \Omega_0, and \sigma_8. We show that the detection of even one lens with separation >30'' is marginally consistent with models that have cuspy inner density profile, \rho \propto r^{-1.5}, and very large \sigma_8, \sigma_8>~1.2 for \Omega_0=0.3. To reconcile with constraints from X-ray clusters or cosmic shear, much lower \Omega_0 and much higher \sigma_8 are needed, although such high \sigma_8 seems too extreme. The shallower inner density profile \rho \propto r^{-1} is hardly acceptable. In particular, the expected number of lenses with separation >200'' is too small to explain the discovery of such anomalously wide separation lens systems. These results imply that we miss some important systematic effects, there is a problem in the cold dark matter scenario, or none of these six quasar pairs is likely to be lensed images.