The strongest gravitational lenses: III. The order statistics of the
  largest Einstein radii
  The Einstein radius (ER) of a gravitational lens encodes information about
decisive quantities such as halo mass, concentration, triaxiality, and
orientation with respect to the observer. Thus, the largest Einstein radii can
potentially be utilised to test the predictions of the LCDM model. Hitherto,
studies have focussed on the single largest observed ER. We extend those
studies by employing order statistics to formulate exclusion criteria based on
the n largest Einstein radii and apply these criteria to the strong lensing
analysis of 12 MACS clusters at z>0.5. We obtain the order statistics of
Einstein radii by a MC approach, based on the semi-analytic modelling of the
halo population on the past lightcone. After sampling the order statistics, we
fit a GEV distribution to the first-order distribution, which allows us to
derive analytic relations for the order statistics of the Einstein radii. We
find that the Einstein radii of the 12 MACS clusters are not in conflict with
the LCDM expectations. Our exclusion criteria indicate that, in order to
exhibit tension with the concordance model, one would need to observe
approximately twenty Einstein radii >30", ten >35" or five >42" in the range of
0.5<z<1.0 on the full sky. Furthermore, we find that, with increasing order,
the haloes with the largest Einstein radii are on average less aligned along
the line-of-sight and less triaxial. In general, the cumulative distribution
functions steepen for higher orders, giving them better constraining power.
(abridged)
