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tokens: 14 for components A, B, C, and D, respectively. In light of the large core radii of most of the four components (21, 28, 21, and 5 for A, B, C, and D, respectively); however, these offsets are not necessarily significant. Specifically, our analysis does not support the hypothesis advanced by Diego et al. (2015b) that component A is significantly offset from the closest light peak. These authors argued that this offset is probably due to the lack of lensing constraints in that area. Since three of the four components have core radii larger than 15, i.e., larger than 100 kpc at the redshift of MACS J0717, their superposition leads to a relatively flat mass distribution. In the following, this model is referred to as the cored mass model. Various mechanisms that could lead to such large cores have been proposed (see also Diego et al. 2015b , a , for a thorough discussion). Large cores in massive central galaxies are thought to be caused by massive black holes that clear the centre of galaxies of stars (see, e.g. López-Cruz et al. 2014 ). This may affect dark matter as well, but the scales on which this mechanism can be expected to be effective (less than 10 kpc) are smaller than the scale we are interested in here (100 kpc). Actif galactic nucleus feedback can also contribute to the flattening of the central region ( Martizzi et al. 2012 ), but once again this mechanism is efficient only on small scales (up to 10–15 kpc). On scales of 100 kpc, large cores may result from violent interactions related to merging events in this actively evolving cluster, although several studies find that DM profiles are not strongly altered by a collision ( Ricker Sarazin 2001 ; Dekel et al. 2003 ; Molnar et al. 2010 ). Finally, heating of massive galaxies by dynamical friction against the diffuse dark matter distribution of the cluster can flatten the slope of the DM density profile, and sometimes even dominate over adiabatic contraction (see, e.g. El-Zant et al. 2001 , 2004 ). Another explanation might be self-interacting dark matter particles ( Natarajan et al. 2008 ; Rocha et al. 2013 ), known to flatten the cusps of cluster scale haloes on scales up to 100 kpc, or the multi-coupled Dark Energy scenario ( Garaldi et al. 2016 ). Given the implications of a flat mass profile for MACS J0717, we investigate its mass distribution further by testing whether large-core components are really required by the data. To this end, we explore in the next subsection a peaky, non-cored mass model. Table 2 Same as Table 1 for the non-cored mass model. Table 3 NFW parameters inferred for the four large-scale dark matter clumps (A, B, C, D) and the dPIE parameters for the galaxy-scale component (core radius fixed to 0.3 kpc). Notes. These parameters correspond to the NFW mass model. Coordinates are given in arcseconds with respect to . The ellipticity is for the mass distribution. Error bars correspond to confidence level. Concerning the scaling relations, the zero point is set