arXiv2005
The first extrasolar planets have been detected by the measurement of the wobble of the parent star. This wobble leads to the periodic modulation of three observables: the radial velocity, the position on the sky and the time of arrival of periodic signals. We show that the same wobble, and therefore the same modulation of the three observables, can be due to the presence of a more distant binary stellar companion. Thus, the observation of the wobble does not, by itself, constitute a proof of a planet detection. In particular, astrometric confirmation of a wobble does not necessarily provide a sufficient proof of the existence of a planet candidate detected by radial velocity. Additional conditions, which we discuss here, must be fulfilled. We investigate the observed wobble for the planet candidates already detected and we find that, for each case, a wobble due to a binary stellar companion can be excluded. But for apparent Saturn-like planets in wide orbits, there may be an ambiguity in future detections, especially in spaceborne astrometric missions. We conclude that, in some cases, a definitive proof for the presence of a planet requires further observations such as direct imaging.