The mass accretion rate of galaxy clusters: a measurable quantity
  We explore the possibility of measuring the mass accretion rate (MAR) of
galaxy clusters from their mass profiles beyond the virial radius $R_{200}$. We
derive the accretion rate from the mass of a spherical shell whose inner radius
is $2R_{200}$, whose thickness changes with redshift, and whose infall velocity
is assumed to be equal to the mean infall velocity of the spherical shells of
dark matter halos extracted from $N$-body simulations. This approximation is
rather crude in hierarchical clustering scenarios where both smooth accretion
and aggregation of smaller dark matter halos contribute to the mass accretion
of clusters.Nevertheless, in the redshift range $z=[0,2]$, our prescription
returns an average MAR within $20-40 \%$ of the average rate derived from the
merger trees of dark matter halos extracted from $N$-body simulations. The MAR
of galaxy clusters has been the topic of numerous detailed numerical and
theoretical investigations, but so far it has remained inaccessible to
measurements in the real universe. Since the measurement of the mass profile of
clusters beyond their virial radius can be performed with the caustic technique
applied to dense redshift surveys of the cluster outer regions, our result
suggests that measuring the mean MAR of a sample of galaxy clusters is actually
feasible. We thus provide a new potential observational test of the
cosmological and structure formation models.
