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 ≈28 arcsec (for a source redshift of zs ~ 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 × 10¹⁴M⊙. We find that nine clusters cover a very large area (>2.5 arcmin²) of high magnification (μ > 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 (ΛCDM) 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 ΛCDM predictions.