The Hubble Frontier Fields (HFFs) are six clusters of galaxies, all showing indications of recent mergers, which have recently been observed for lensed images. As such they are the natural laboratories to study the merging history of galaxy clusters. In this work, we explore the 2D power spectrum of the mass distribution PM(k) as a measure of substructure. We compare PM(k) of these clusters (obtained using strong gravitational lensing) to that of Λ cold dark matter simulated clusters of similar mass. To compute lensing PM(k), we produced free-form lensing mass reconstructions of HFF clusters, without any light traces mass (LTM) assumption. The inferred power at small scales tends to be larger if (i) the cluster is at lower redshift, and/or (ii) there are deeper observations and hence more lensed images. In contrast, lens reconstructions assuming LTMshow higher power at small scales even with fewer lensed images; it appears the small-scale power in the LTM reconstructions is dominated by light information, rather than the lensing data. The average lensing derived PM(k) shows lower power at small scales as compared to that of simulated clusters at redshift zero, both dark matter only and hydrodynamical. The possible reasons are (i) the available strong lensing data are limited in their effective spatial resolution on the mass distribution; (ii) HFF clusters have yet to build the small-scale power they would have at z ~ 0 or (iii) simulations are somehow overestimating the small-scale power.
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