Dark Energy Surveyed Year 1 results: calibration of cluster mis-centring in the redMaPPer catalogues

 The centre determination of a galaxy cluster from an optical cluster finding algorithm can be offset from theoretical prescriptions or N-body definitions of its host halo centre. These offsets impact the recovered cluster statistics, affecting both richness measurements and the weak lensing shear profile around the clusters. This paper models the centring performance of the redMaPPer cluster finding algorithm using archival X-ray observations of redMaPPer-selected clusters. Assuming the X-ray emission peaks as the fiducial halo centres, and through analysing their offsets to the redMaPPer centres, we find that ${\sim } 75\pm 8 {{\ \rm per\ cent}}$ of the redMaPPer clusters are well centred and the mis-centred offset follows a Gamma distribution in normalized, projected distance. These mis-centring offsets cause a systematic underestimation of cluster richness relative to the well-centred clusters, for which we propose a descriptive model. Our results enable the DES Y1 cluster cosmology analysis by characterizing the necessary corrections to both the weak lensing and richness abundance functions of the DES Y1 redMaPPer cluster catalogue.