Dynamical signatures of infall around galaxy clusters: a generalized
  Jeans equation
  We study the internal kinematics of galaxy clusters in the region beyond the
sphere of virialization. Galaxies around a virialized cluster are infalling
towards the cluster centre with a non-zero mean radial velocity. We develop a
new formalism for describing the dynamical state of clusters, by generalizing
the standard Jeans formalism with the inclusion of the peculiar infall motions
of galaxies and the Hubble expansion as well as the contributions due to
background cosmology. Using empirical fits to the radial profiles of density,
mean radial velocity and velocity anisotropy of both a stacked cluster-mass
halo and two isolated halos of a cosmological dark matter only simulation, we
verify that our generalized Jeans equation correctly predicts the radial
velocity dispersion out to 4 virial radii. We find that the radial velocity
dispersion inferred from the standard Jeans equation is accurate up to 2 virial
radii, but overestimated by \approx 20% for the stacked halo and by \approx 40%
for the isolated halos, in the range \approx 2-3 virial radii. Our model
depends on the logarithmic growth rate of the virial radius (function of halo
mass or concentration), which we estimate in 7 different ways, and on the
departure from self-similarity of the evolution of the peculiar velocity
profile in virial units.
