Abstract: We performed a free-form strong lensing analysis of the galaxy cluster MACS J1206.2?0847 in order to estimate and constrain its inner dark matter distribution. The free-form method estimates the cluster total mass distribution without using any prior information about the underlying mass. We used 97 multiple lensed images belonging to 27 background sources and derived several models, which are consistent with the data. Among these models, we focus on those that better reproduce the radial images that are closest to the centre of the cluster. These radial images are the best probes of the dark matter distribution in the central region and constrain the mass distribution down to distances ?7 kpc from the centre. We find that the morphology of the innermost radial arcs is due to the elongated morphology of the dark matter halo. We estimate the stellar mass contribution of the brightest cluster galaxy and subtracted it from the total mass in order to quantify the amount of dark matter in the central region. We fitted the derived dark matter density profile with a gNFW, which is characterised by rs = 167 kpc, ?s = 6.7 × 106?M? kpc?3, and ?gNFW = 0.70. These results are consistent with a dynamically relaxed cluster. This inner slope is smaller than the cannonical ??=?1 predicted by standard CDM models. This slope does not favour self-interacting models for which a shallower slope would be expected.

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