Weak Lensing Measurement of the Mass--Richness Relation of SDSS redMaPPer Clusters

We perform a measurement of the mass--richness relation of the redMaPPer galaxy cluster catalogue using weak lensing data from the Sloan Digital Sky Survey. We have carefully characterized a broad range of systematic uncertainties, including shear calibration errors, photo-$z$ biases, dilution by member galaxies, source obscuration, magnification bias, incorrect assumptions about cluster mass profiles, cluster centering, halo triaxiality, and projection effects. We also compare measurements of the lensing signal from two independently-produced shear and photometric redshift catalogues to characterize systematic errors in the lensing signal itself. Using a sample of 5,570 clusters from $0.1\le z\le 0.33$, the normalization of our power-law mass vs.\ $\lambda$ relation is $\log_{10}[M_{200m}/h^{-1}\ M_{\odot}]$ = $14.344 \pm 0.021$ (statistical) $\pm 0.023$ (systematic) at a richness $\lambda=40$, a 7 per cent calibration uncertainty, with a power-law index of $1.33^{+0.09}_{-0.10}$ ($1\sigma$). The detailed systematics characterization in this work renders it the definitive weak lensing mass calibration for SDSS redMaPPer clusters at this time.