Abstract
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.
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