We present a strong-lensing analysis of the galaxy cluster MACS J1206.2-0847 (z = 0.44) using UV, Optical, and IR, HST/ACS/WFC3 data taken as part of the CLASH multi-cycle treasury program, with VLT/VIMOS spectroscopy for some of the multiply lensed arcs. The CLASH observations, combined with our mass model, allow us to identify 47 new multiply lensed images of 12 distant sources. These images, along with the previously known arc, span the redshift range 1 less than or similar to z less than or similar to 5.5, and thus enable us to derive a detailed mass distribution and to accurately constrain, for the first time, the inner mass profile of this cluster. We find an inner profile slope of d log Sigma/d log theta similar or equal to -0.55 +/- 0.1 (in the range [1 '', 53 ''], or 5 kpc less than or similar to r less than or similar to 300 kpc), as commonly found for relaxed and well-concentrated clusters. Using the many systems uncovered here we derive credible critical curves and Einstein radii for different source redshifts. For a source at z(s) similar or equal to 2.5, the critical curve encloses a large area with an effective Einstein radius of theta(E) = 28 '' +/- 3 '', and a projected mass of (1.34 +/- 0.15) x 10(14) M-circle dot. From the current understanding of structure formation in concordance cosmology, these values are relatively high for clusters at z similar to 0.5, so that detailed studies of the inner mass distribution of clusters such as MACS J1206.2-0847 can provide stringent tests of the Lambda CDM paradigm.
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