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We use hydrodynamical simulations of different dark energy cosmologies toinvestigate the concentration-mass (c-M) relation in galaxy clusters. Inparticular, we consider a reference \Lambda CDM model, two quintessence modelswith inverse power-law potentials (RP and SUGRA), and two extended quintessencemodels, one with positive and one with negative coupling with gravity (EQp andEQn respectively). All the models are normalized in order to match CMB datafrom WMAP3. We fit both the dark matter only and the total mass profile with aNFW profile, and recover the concentration of each halo from the fit usingdifferent definition. We consider both the complete catalog of clusters andgroups and subsamples of objects at different level of relaxation. We find thatthe definition itself of the concentration can lead to differences up to 20% inits value and that these differences are smaller when more relaxed objects areconsidered. The c-M relation of our reference \Lambda CDM model is in goodagreement with the results in literature, and relaxed objects have a highernormalization and a shallower slope with respect to the complete sample. Theinclusion of baryon physics is found to influence more high-mass systems thanlow-mass ones, due to a higher concentration of baryons in the inner regions ofmassive halos. For the different dark energy models, we find that for \LambdaCDM, RP and SUGRA the normalization of the c-M relation is linked to the growthfactor, with models having a higher value of \sigma 8 D+ having also a highernormalization. This simple scheme is no longer valid for EQp and EQn because inthese models a time dependent effective gravitational interaction, whoseredshift evolution depends on the sign of the coupling, is present. This leadsto a decrease (increase) of the expected normalization in the EQp (EQn) model.[Abridged]

Hydrodynamical simulations of galaxy clusters in dark energy cosmologies: II. c-M relation