Three-body effects in the PSR 1257+12 planetary system

A detailed theoretical analysis of the three-body effects in the putative planetary system of PSR 1257+12 is presented. Ways in which these effects are manifested in the pattern of pulse arrival times are discussed; the dominant perturbation is described as a modulation of the phases of the near-sinusoidal signals of the two planetary companions. Explicit formulas for the time dependence of the oscillating orbital elements that are needed for an improved timing model for this system are provided. If a timing model with fixed, independent Keplerian orbits continues to be used for the timing analysis, and if two planets are indeed orbiting this pulsar, then the three-body effects should become detectable by means of a growth in the postfit residuals as more observations are accumulated. If the typical error in the pulse arrival time measurements is about 10 microsec, the amplitude of the postfit residuals will increase beyond this level with three to five years of timing observations.