Title: Intrinsic alignment of redMaPPer clusters: cluster shape - matter density correlation,
Abstract: 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.