Frequency Analysis of Reflex Velocities of Stars with Planets

Since the discovery of planets orbiting nearby solar-type stars through very precise Doppler-shift measurements has become possible, the role of methods used to analyze such observations has grown significantly. The widely employed model-dependent approach based on the least-squares fit of the Keplerian motion to the radial-velocity variations can be, as we show, unsatisfactory. Thus, in this paper, we propose a new method that may be easily and successfully 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 subsequent subtraction of all harmonic components from the data, leads to a numerical implementation involving only the computation of Lomb-Scargle periodograms and least-squares fits of sine and cosine functions. This method has given an independent proof of the existence of the PSR1257+12 planetary system, and, as we show, it is a good tool for analyzing Doppler-shift measurements. We show that our method can be used to analyze real 16 Cygni B Doppler-shift observations with a surprising but correct result which is substantially different than that based on the least-squares fit of a Keplerian orbit. Namely, using frequency analysis we show that with the current accuracy of this star's observations it is not possible to determine the value of the orbital eccentricity which is claimed to be as high as 0.6.