Intrinsic alignment of redMaPPer clusters: cluster shape - matter density correlation

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.