On the detection of other planetary systems by astrometric techniques

A quantitative method for astrometrically detecting perturbations induced in a star's motion by the presence of a planetary object is described. A periodogram is defined, wherein signals observed from a star show exactly periodic variations, which can be extracted from observational data using purely statistical methods. A detection threshold is defined for the frequency of occurrence of some detectable signal, e.g., the Nyquist frequency. Possible effects of a stellar orbital eccentricity and multiple companions are discussed, noting that assumption of a circular orbit assures the spectral purity of the signal described. The periodogram technique was applied to 12 yr of astrometric data from the U.S. Naval Observatory for three stars with low mass stellar companions. Periodic perturbations were confirmed. A comparison of the accuracy of different astrometric systems shows that the detection accuracy of a system is determined by the measurement accuracy and the number of observations, although the detection efficiency can be maximized by minimizing the number of data points for the case when observational errors are proportional to the square root of the number of data points. It is suggested that a space-based astrometric telescope is best suited to take advantage of the method.