Measuring the escape velocity and mass profiles of galaxy clusters
  beyond their virial radius
  The caustic technique uses galaxy redshifts alone to measure the escape
velocity and mass profiles of galaxy clusters to clustrocentric distances well
beyond the virial radius, where dynamical equilibrium does not necessarily
hold. We provide a detailed description of this technique and analyse its
possible systematic errors. We apply the caustic technique to clusters with
mass M_200>=10^{14}h^{-1} M_sun extracted from a cosmological hydrodynamic
simulation of a LambdaCDM universe. With a few tens of redshifts per squared
comoving megaparsec within the cluster, the caustic technique, on average,
recovers the profile of the escape velocity from the cluster with better than
10 percent accuracy up to r~4 r_200. The caustic technique also recovers the
mass profile with better than 10 percent accuracy in the range (0.6-4) r_200,
but it overestimates the mass up to 70 percent at smaller radii. This
overestimate is a consequence of neglecting the radial dependence of the
filling function F_beta(r). The 1-sigma uncertainty on individual escape
velocity profiles increases from ~20 to ~50 percent when the radius increases
from r~0.1 r_200 to ~4 r_200. Individual mass profiles have 1-sigma uncertainty
between 40 and 80 percent within the radial range (0.6-4) r_200. We show that
the amplitude of these uncertainties is completely due to the assumption of
spherical symmetry, which is difficult to drop. Alternatively, we can apply the
technique to synthetic clusters obtained by stacking individual clusters: in
this case, the 1-sigma uncertainty on the escape velocity profile is smaller
than 20 percent out to 4 r_200. The caustic technique thus provides reliable
average profiles which extend to regions difficult or impossible to probe with
other techniques.
