We measure the alignment of the shapes of galaxy clusters, as traced by their satellite distributions, with the matter density field using the public redMaPPer catalogue based on SDSS-DR8, which contains 26 111 clusters up to z~0.6. The clusters are split into nine redshift and richness samples; in each of them we detect a positive alignment, showing that clusters point towards density peaks. We interpret the measurements within the tidal alignment paradigm, allowing for a richness and redshift dependence. The intrinsic alignment (IA) amplitude at the pivot redshift z=0.3 and pivot richness lambda=30 is A_{IA}^{gen}=12.6_{-1.2}^{+1.5}. We obtain tentative evidence that the signal increases towards higher richness and lower redshift. Our measurements agree well with results of maxBCG clusters and with dark-matter-only simulations. Comparing our results to IA measurements of luminous red galaxies, we find that the IA amplitude of galaxy clusters forms a smooth extension towards higher mass. This suggests that these systems share a common alignment mechanism, which can be exploited to improve our physical understanding of IA.
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