We study shapes and alignments of 45 dark matter (DM) haloes and their brightest cluster galaxies (BCGs) using a sample of 39 massive clusters from Hubble Frontier Field (HFF), Cluster Lensing And Supernova survey with Hubble (CLASH), and Reionization Lensing Cluster Survey (RELICS). We measure shapes of the DM haloes by strong gravitational lensing, whereas BCG shapes are derived from their light profiles in Hubble Space Telescope images. Our measurements from a large sample of massive clusters presented here provide new constraints on dark matter and cluster astrophysics. We find that DM haloes are on average highly elongated with the mean ellipticity of $0.482pm 0.028$, and position angles of major axes of DM haloes and their BCGs tend to be aligned well with the mean value of alignment angles of $22.2pm 3.9$ deg. We find that DM haloes in our sample are on average more elongated than their BCGs with the mean difference of their ellipticities of $0.11pm 0.03$. In contrast, the Horizon-AGN cosmological hydrodynamical simulation predicts on average similar ellipticities between DM haloes and their central galaxies. While such a difference between the observations and the simulation may well be explained by the difference of their halo mass scales, other possibilities include the bias inherent to strong lensing measurements, limited knowledge of baryon physics, or a limitation of cold dark matter.
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