Constraining cluster masses from the stacked phase space distribution at large radii

Velocity dispersions have been employed as a method to measure masses of clusters. To complement this conventional method, we explore the possibility of constraining cluster masses from the stacked phase space distribution of galaxies at larger radii, where infall velocities are expected to have a sensitivity to cluster masses. First, we construct a two component model of the three-dimensional phase space distribution of haloes surrounding clusters up to 50 $h^{-1}$Mpc from cluster centres based on $N$-body simulations. We find that the three-dimensional phase space distribution shows a clear cluster mass dependence up to the largest scale examined. We then calculate the probability distribution function of pairwise line-of-sight velocities between clusters and haloes by projecting the three-dimensional phase space distribution along the line-of-sight with the effect of the Hubble flow. We find that this projected phase space distribution, which can directly be compared with observations, shows a complex mass dependence due to the interplay between infall velocities and the Hubble flow. Using this model, we estimate the accuracy of dynamical mass measurements from the projected phase space distribution at the transverse distance from cluster centres larger than $2h^{-1}$Mpc. We estimate that, by using $1.5\times 10^5$ spectroscopic galaxies, we can constrain the mean cluster masses with an accuracy of 14.5\% if we fully take account of the systematic error coming from the inaccuracy of our model. This can be improved down to 5.7\% by improving the accuracy of the model.