Weak-lensing calibration of a stellar mass-based mass proxy for redMaPPer and Voronoi Tessellation clusters in SDSS Stripe 82

We present the first weak lensing calibration of $\mu_{\star}$, a new galaxy cluster mass proxy corresponding to the total stellar mass of red and blue members, in two cluster samples selected from the SDSS Stripe 82 data: 230 redMaPPer clusters at redshift $0.1\leq z<0.33$ and 136 Voronoi Tessellation (VT) clusters at $0.1 \leq z < 0.6$. We use the CS82 shear catalog and stack the clusters in $\mu_{\star}$ bins to measure a mass-observable power law relation. For redMaPPer clusters we obtain $M_0 = (1.77 \pm 0.36) \times 10^{14}h^{-1} M_{\odot}$, $\alpha = 1.74 \pm 0.62$. For VT clusters, we find $M_0 = (4.31 \pm 0.89) \times 10^{14}h^{-1} M_{\odot}$, $\alpha = 0.59 \pm 0.54$ and $M_0 = (3.67 \pm 0.56) \times 10^{14}h^{-1} M_{\odot}$, $\alpha = 0.68 \pm 0.49$ for a low and a high redshift bin, respectively. Our results are consistent, internally and with the literature, indicating that our method can be applied to any cluster finding algorithm. In particular, we recommend that $\mu_{\star}$ be used as the mass proxy for VT clusters. Catalogs including $\mu_{\star}$ measurements will enable its use in studies of galaxy evolution in clusters and cluster cosmology.