We present results from strong-lens modelling of 10,000 SDSS clusters , to establish the universal distribution of Einstein radii .
Detailed lensing analyses have shown that the inner mass distribution of clusters can be accurately modelled by assuming light traces mass , successfully uncovering large numbers of multiple-images .
Approximate critical curves and the effective Einstein radius of each cluster can therefore be readily calculated , from the distribution of member galaxies and scaled by their luminosities .
We use a subsample of 10 well-studied clusters covered by both SDSS and HST to calibrate and test this method , and show that an accurate determination of the Einstein radius and mass can be achieved by this approach “ blindly ” , in an automated way , and without requiring multiple images as input .
We present the results of the first 10,000 clusters analysed in the range 0.1 < z < 0.55 , and compare them to theoretical expectations .
We find that for this all-sky representative sample the Einstein radius distribution is log-normal in shape , with \langle Log ( \theta _ { e } \arcsec ) \rangle = 0.73 ^ { +0.02 } _ { -0.03 } , \sigma = 0.316 ^ { +0.004 } _ { -0.002 } , and with higher abundance of large \theta _ { e } clusters than predicted by \Lambda CDM .
We visually inspect each of the clusters with \theta _ { e } > 40 \arcsec ( z _ { s } = 2 ) and find that \sim 20 \% are boosted by various projection effects detailed here , remaining with \sim 40 real giant-lens candidates , with a maximum of \theta _ { e } = 69 \pm 12 \arcsec ( z _ { s } = 2 ) for the most massive candidate , in agreement with semi-analytic calculations .
The results of this work should be verified further when an extended calibration sample is available .