We measured the radial velocity of 139 stars in the region of NGC 6253, discussing clusters membership and binarity in this sample, complementing our analysis with photometric, proper motion, and radial velocity data available from previous studies of this cluster, and analyzing three planetary transiting candidates we found in the field of NGC 6253. Spectra were obtained with the UVES and GIRAFFE spectrographs at the VLT, during three epochs in August 2008. The mean radial velocity of the cluster is -29.11+/-0.85 km/s. Using both radial velocities and proper motions we found 35 clusters members, among which 12 are likely clusters close binary systems. One star may have a sub-stellar companion, requiring a more intensive follow-up. Our results are in good agreement with past radial velocity and photometric measurements. Furthermore, using our photometry, astrometry and spectroscopy we identified a new sub-giant branch eclipsing binary system, member of the cluster. The clusters close binary frequency at 29% +/- 9% (34% +/-10% once including long period binaries), appears higher than the field binary frequency equal to (22% +/- 5%, though these estimates are still consistent within the uncertainties. Among the three transiting planetary candidates the brightest one (V=15.26) is worth to be more intensively investigated with higher percision spectroscopy. We discussed the possibility to detect sub-stellar companions (brown dwarfs and planets) with the radial velocity technique (both with UVES/GIRAFFE and HARPS) around turn-off stars of old open clusters [abridged].
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