XO-2 is the first confirmed wide stellar binary system where the almost twin components XO-2N and XO-2S have planets. This stimulated a detailed characterization study of the stellar and planetary components based on new observations. We collected high-resolution spectra with the HARPS-N spectrograph and multi-band light curves. Spectral analysis led to an accurate determination of the stellar atmospheric parameters and characterization of the stellar activity. We collected 14 transit light curves of XO-2Nb used to improve the transit parameters. Photometry provided accurate magnitude differences between the stars and a measure of their rotation periods. The iron abundance of XO-2N was found to be +0.054 dex greater, within more than 3-sigma, than that of XO-2S. We confirm a long-term variation in the radial velocities of XO-2N, and we detected a turn-over with respect to previous measurements. We suggest the presence of a second massive companion in an outer orbit or the stellar activity cycle as possible causes of the observed acceleration. The latter explanation seems more plausible with the present dataset. We obtained an accurate value of the projected spin-orbit angle for the XO-2N system (lambda=7+/-11 degrees), and estimated the real 3-D spin-orbit angle (psi=27 +12/-27 degrees). We measured the XO-2 rotation periods, and found a value of P=41.6 days in the case of XO-2N, in excellent agreement with the predictions. The period of XO-2S appears shorter, with an ambiguity between 26 and 34.5 days that we cannot solve with the present dataset alone. XO-2N appears to be more active than the companion, and this could be due to the fact that we sampled different phases of their activity cycle, or to an interaction between XO-2N and its hot Jupiter that we could not confirm.
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