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We present the results of a strong‐lensing analysis of a complete sample of 12 very luminous X‐ray clusters at   z  &gt; 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  ≃  28  arcsec (for a source redshift of   z  s ∼ 2 ), 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 × 10 14  M ⊙  . We find that nine clusters cover a very large area ( &gt;  2.5  arcmin  2  ) of high magnification ( μ &gt; 10× ) for a source redshift of   z  s ∼ 8 , providing primary targets for accessing the first stars and galaxies. We compare our results with theoretical predictions of the standard  Λ  cold dark matter ( Λ CDM) model which we show systematically fall short of our measured Einstein radii by a factor of  ≃  1.4 , after accounting for the effect of lensing projection. Nevertheless, a revised analysis, once arc redshifts become available, and similar analyses of larger samples, is needed in order to establish more precisely the level of discrepancy with  Λ CDM predictions.

Strong‐lensing analysis of a complete sample of 12 MACS clusters at z > 0.5: mass models and Einstein radii