Galaxy Cluster Mass Estimation from Stacked Spectroscopic Analysis

We use simulated galaxy surveys to study: i) how galaxy membership in redMaPPer clusters maps to the underlying halo population, and ii) the accuracy of a mean dynamical cluster mass, $M_\sigma(\lambda)$, derived from stacked pairwise spectroscopy of clusters with richness $\lambda$. Using $\sim\! 130,000$ galaxy pairs patterned after the SDSS redMaPPer cluster sample study of Rozo et al. (2015 RMIV), we show that the pairwise velocity PDF of central--satellite pairs with $m_i < 19$ in the simulation matches the form seen in RMIV. Through joint membership matching, we deconstruct the main Gaussian velocity component into its halo contributions, finding that the top-ranked halo contributes $\sim 60\%$ of the stacked signal. The halo mass scale inferred by applying the virial scaling of Evrard et al. (2008) to the velocity normalization matches, to within a few percent, the log-mean halo mass derived through galaxy membership matching. We apply this approach, along with mis-centering and galaxy velocity bias corrections, to estimate the log-mean matched halo mass at $z=0.2$ of SDSS redMaPPer clusters. Employing the velocity bias constraints of Guo et al. (2015), we find $\langle \ln(M_{200c})|\lambda \rangle = \ln(M_{30}) + \alpha_m \ln(\lambda/30)$ with $M_{30} = 1.56 \pm 0.35 \times 10^{14} M_\odot$ and $\alpha_m = 1.31 \pm 0.06_{stat} \pm 0.13_{sys}$. Systematic uncertainty in the velocity bias of satellite galaxies overwhelmingly dominates the error budget.