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 similar or equal to 28 arcsec (for a source redshift of z(s) similar to 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 x 1014 M-circle dot. We find that nine clusters cover a very large area (> 2.5 arcmin2) of high magnification (mu > 10x) for a source redshift of z(s) similar to 8, providing primary targets for accessing the first stars and galaxies. We compare our results with theoretical predictions of the standard Lambda cold dark matter (Lambda CDM) model which we show systematically fall short of our measured Einstein radii by a factor of similar or equal to 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 Lambda CDM predictions.