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

We present a detailed theoretical analysis of the three-body effects in the putative planetary system of PSR 1257+12. We discuss how these effects are manifested in the pattern of pulse arrival times; the dominant perturbation can be described as a modulation of the phases of the near-sinusoidal signals of the two planetary companions. We provide explicit formulas for the time dependence of the osculating orbital elements that are needed for an improved timing model for this system. 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 ∼ 10 μs, the amplitude of the postfit residuals will increase beyond this level with three to five years of timing observations. Their detection will place the planetary interpretation on firmer ground, and the improved timing model will yield the orbital inclinations and the masses of the planets relative to the mass of the pulsar. An absence of this signal will make the presence of these planets highly unlikely.