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 \sim 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 .