Using the outskirts of galaxy clusters to determine their mass accretion
  rate
  We explore the possibility of using the external regions of galaxy clusters
to measure their mass accretion rate (MAR). The main goal is to provide a
method to observationally investigate the growth of structures on the nonlinear
scales of galaxy clusters. We derive the MAR by using the mass profile beyond
the splashback radius, evaluating the mass of a spherical shell and the time it
takes to fall in. The infall velocity of the shell is extracted from $N$-body
simulations. The average MAR returned by our prescription in the redshift range
$z=[0, 2]$ is within $20-40 \%$ of the average MAR derived from the merger
trees of dark matter haloes in the reference $N$-body simulations. Our result
suggests that the external regions of galaxy clusters can be used to measure
the mean MAR of a sample of clusters.
