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The observation of galaxy and gas distributions, as well as cosmologicalsimulations in a $\Lambda$CDM Universe, suggests that clusters of galaxies arestill accreting mass and are not expected to be in equilibrium. In this work,we investigate the possibility to evaluate the departure from virialequilibrium in order to detect, in that balance, effects from a DarkMatter--Dark Energy interaction. We continue, from previous works, using asimple model of interacting dark sector, the Layzer--Irvine equation fordynamical virial evolution, and employ optical observations in order to obtainthe mass profiles through weak lensing and X-ray observations giving theintracluster gas temperatures. Through a Monte Carlo method, we generate, for aset of clusters, measurements of observed virial ratios, interaction strength,rest virial ratio and departure from equilibrium factors. We found a compoundedinteraction strength of $-1.99^{+2.56}_{-16.00}$, compatible with nointeraction, but also a compounded rest virial ratio of $-0.79 \pm 0.13$, whichwould entail a $2\sigma$ detection. We confirm quantitatively that clusters ofgalaxies are out of equilibrium but further investigation is needed toconstrain a possible interaction in the dark sector.

Non-virialised clusters for detection of Dark Energy-Dark Matter interaction