Strong-Lensing Analysis of a Complete Sample of 12 MACS Clusters at
  z>0.5: Mass Models and Einstein Radii
  We present the results of a strong-lensing analysis of a complete sample of
12 very luminous X-ray clusters at $z>0.5$ using HST/ACS images. Our modelling
technique has uncovered some of the largest known critical curves outlined by
many accurately-predicted sets of multiple images. The distribution of Einstein
radii has a median value of $\simeq28\arcsec$ (for a source redshift of
$z_{s}\sim2$), twice as large as other lower-$z$ samples, and extends to
$55\arcsec$ for MACS J0717.5+3745, with an impressive enclosed Einstein mass of
$7.4\times10^{14} M_{\odot}$. We find that 9 clusters cover a very large area
($>2.5 \sq \arcmin$) of high magnification ($\mu > \times10$) for a source
redshift of $z_{s}\sim8$, providing primary targets for accessing the first
stars and galaxies. We compare our results with theoretical predictions of the
standard $\Lambda$CDM model which we show systematically fall short of our
measured Einstein radii by a factor of $\simeq1.4$, after accounting for the
effect of lensing projection. Nevertheless, a revised analysis once arc
redshifts become available, and similar analyses of larger samples, are needed
in order to establish more precisely the level of discrepancy with $\Lambda$CDM
predictions.
