Non-virialised clusters for detection of Dark Energy-Dark Matter
  interaction
  The observation of galaxy and gas distributions, as well as cosmological
simulations in a $\Lambda$CDM Universe, suggests that clusters of galaxies are
still accreting mass and are not expected to be in equilibrium. In this work,
we investigate the possibility to evaluate the departure from virial
equilibrium in order to detect, in that balance, effects from a Dark
Matter--Dark Energy interaction. We continue, from previous works, using a
simple model of interacting dark sector, the Layzer--Irvine equation for
dynamical virial evolution, and employ optical observations in order to obtain
the mass profiles through weak lensing and X-ray observations giving the
intracluster gas temperatures. Through a Monte Carlo method, we generate, for a
set of clusters, measurements of observed virial ratios, interaction strength,
rest virial ratio and departure from equilibrium factors. We found a compounded
interaction strength of $-1.99^{+2.56}_{-16.00}$, compatible with no
interaction, but also a compounded rest virial ratio of $-0.79 \pm 0.13$, which
would entail a $2\sigma$ detection. We confirm quantitatively that clusters of
galaxies are out of equilibrium but further investigation is needed to
constrain a possible interaction in the dark sector.
