We use high-resolution N -body numerical simulations to study the number of predicted large-separation multiply-imaged systems produced by clusters of galaxies in the SDSS photometric and spectroscopic quasar samples .
We incorporate the condensation of baryons at the centre of clusters by ( artificially ) adding a brightest central galaxy ( BCG ) as a truncated isothermal sphere .
We make predictions in two flat cosmological models : a \Lambda { CDM } model with a matter density \Omega _ { m, 0 } = 0.3 , and \sigma _ { 8 } = 0.9 ( \Lambda { CDM } 0 ) , and a model favoured by the WMAP three-year data with \Omega _ { m, 0 } = 0.238 , and \sigma _ { 8 } = 0.74 ( WMAP3 ) .
We found that the predicted multiply-imaged quasars with separation > 10 \arcsec is about 6.2 and 2.6 for the SDSS photometric ( with an effective area 8000 deg ^ { 2 } ) and spectroscopic ( with an effective area 5000 deg ^ { 2 } ) quasar samples respectively in the \Lambda { CDM } 0 model ; the predicted numbers of large-separation lensed quasars agree well with the observations .
These numbers are reduced by a factor of 7 or more in the WMAP3 model , and are consistent with data at \la 8 \% level .
The predicted cluster lens redshift peaks around redshift 0.5 , and 90 % are between 0.2 and 1 .
The ratio of systems with at least four image systems ( { N _ { img } } \geq 4 ) and those with { N _ { img } } \geq 2 is about 1/3.5 for both the \Lambda { CDM } 0 and WMAP3 models , and for both the photometric and spectroscopic quasar samples .
We find that the BCG creates a central circular region , comparable to the Einstein ring of the BCG , where the central image disappears in the usual three-image and five-image configurations .
If we include four image systems as an extreme case of five-image systems ( with an infinitely demagnified central image ) , we find that 68 % of the central images are fainter by a factor of 100 than the brightest image , and about 80 % are within 1.5 \arcsec of the BCG .