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.
