$μ_{\star}$ Masses: Weak Lensing Calibration of the Dark Energy Survey Year 1 redMaPPer Clusters using Stellar Masses
We present the weak lensing mass calibration of the stellar mass based $μ_{\star}$ mass proxy for redMaPPer galaxy clusters in the Dark Energy Survey Year 1. For the first time we are able to perform a calibration of $μ_{\star}$ at high redshifts, $z>0.33$. In a blinded analysis, we use $\sim 6,000$ clusters split into 12 subsets spanning the ranges $0.1 \leqslant z<0.65$ and $μ_{\star}$ up to $\sim 5.5 \times 10^{13} M_{\odot}$, and infer the average masses of these subsets through modelling of their stacked weak lensing signal. In our model we account for the following sources of systematic uncertainty: shear measurement and photometric redshift errors, miscentring, cluster-member contamination of the source sample, deviations from the NFW halo profile, halo triaxiality and projection effects. We use the inferred masses to estimate the joint mass--$μ_{\star}$--$z$ scaling relation given by $\langle M_{200c} | μ_{\star},z \rangle = M_0 (μ_{\star}/5.16\times 10^{12} \mathrm{M_{\odot}})^{F_{μ_{\star}}} ((1+z)/1.35)^{G_z}$. We find $M_0= (1.14 \pm 0.07) \times 10^{14} \mathrm{M_{\odot}}$ with $F_{μ_{\star}}= 0.76 \pm 0.06$ and $G_z= -1.14 \pm 0.37$. We discuss the use of $μ_{\star}$ as a complementary mass proxy to the well-studied richness $λ$ for: $i)$ exploring the regimes of low $z$, $λ<20$ and high $λ$, $z \sim 1$; $ii)$ testing systematics such as projection effects for applications in cluster cosmology.