Studies of transiting extrasolar planets are of key importance for understanding the nature of planets outside our solar system because their masses, diameters, and bulk densities can be measured. An important part of transit-search programmes is the removal of false-positives. The critical question is how many of the candidates that passed all previous tests are false positives. For our study we selected 25 CoRoT candidates that have already been screened against false-positives using detailed analysis of the light curves and seeing-limited imaging, which has transits that are between 0.7 and 0.05% deep. We observed 20 candidates with the adaptive optics imager NaCo and 18 with the high-resolution infrared spectrograph CRIRES. We found previously unknown stars within 2 arcsec of the targets in seven of the candidates. All of these are too faint and too close to the targets to have been previously detected with seeing-limited telescopes in the optical. Our study thus leads to the surprising results that if we remove all candidates excluded by the sophisticated analysis of the light-curve, as well as carrying out deep imaging with seeing-limited telescopes, still 28-35% of the remaining candidates are found to possess companions that are bright enough to be false-positives. Given that the companion-candidates cluster around the targets and that the J-K colours are consistent with physical companions, we conclude that the companion-candidates are more likely to be physical companions rather than unrelated field stars.
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