Timing the last major merger of galaxy clusters with large halo sparsity
  Numerical simulations have shown that massive dark matter haloes, which today
host galaxy clusters, assemble their mass over time alternating periods of
quiescent accretion and phases of rapid growth associated with major merger
episodes. Observations of such events in clusters can provide insights on the
astrophysical processes that characterise the properties of the intra-cluster
medium, as well as the gravitational processes that contribute to their
assembly. It is therefore of prime interest to devise a fast and reliable way
of detecting such perturbed systems. We present a novel approach to identifying
and timing major mergers in clusters characterised by large values of halo
sparsity. Using halo catalogues from the MultiDark-Planck2 simulation, we show
that major merger events disrupt the radial mass distribution of haloes, thus
leaving a distinct universal imprint on the evolution of halo sparsity over a
period not exceeding two dynamical times. We exploit this feature using
numerically calibrated distributions to test whether an observed galaxy cluster
with given sparsity measurements has undergone a recent major merger and to
eventually estimate when such an event occurred. We implement these statistical
tools in a specifically developed public python library \textsc{lammas}, which
we apply to the analysis of Abell 383 and Abell 2345 as test cases. Finding
that, for example, Abell 2345 had a major merger about $2.1\pm 0.2$ Gyr ago.
This work opens the way to detecting and timing major mergers in galaxy
clusters solely through measurements of their mass at different radii.
