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_σ(λ), derived from stacked pairwise spectroscopy of clusters with richness λ. Using ~130 000 galaxy pairs patterned after the Sloan Digital Sky Survey (SDSS) redMaPPer cluster sample study of Rozo et al., we show that the pairwise velocity probability density function of central-satellite pairs with m_i < 19 in the simulation matches the form seen in Rozo et al. Through joint membership matching, we deconstruct the main Gaussian velocity component into its halo contributions, finding that the top-ranked halo contributes ~60 per cent of the stacked signal. The halo mass scale inferred by applying the virial scaling of Evrard et al. to the velocity normalization matches, to within a few per cent, the log-mean halo mass derived through galaxy membership matching. We apply this approach, along with miscentring 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., we find 〈ln (M_200c)|λ〉 = ln (M₃₀) + α_m ln (λ/30) with M₃₀ = 1.56 ± 0.35 × 10¹⁴ M_⊙ and α_m = 1.31 ± 0.06_stat ± 0.13_sys. Systematic uncertainty in the velocity bias of satellite galaxies overwhelmingly dominates the error budget.