Frequency analysis of reflex velocities of stars with planets

Since it has become possible to discover planets orbiting nearby solar-type stars through very precise Doppler-shift measurements, the role of methods used to analyze such observations has grown significantly. The widely empl oyed model-dependent approach based on the least-squares fit of the Kepleri an motion to the radial velocity variations can be, as we show, unsatisfact ory. Thus, in this paper, we propose a new method that may be easily and su ccessfully applied to the Doppler-shift measurements. This method allows us to analyze the data without assuming any specific model and yet to extract all significant features of the observations. This very simple idea, based on the subsequent subtraction of all harmonic components from the data, ca n easily be implemented. We show that our method can be used to analyze rea l 16 Cygni B Doppler-shift observations with a surprising but correct resul t that is different from that based on the least-squares fit of a Keplerian orbit. Namely, using frequency analysis, we show that with the current acc uracy of observations of this star it is not possible to determine precisel y the value of the orbital eccentricity, which is claimed to be as high as 0.6.