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

Abstract

A detailed theoretical analysis of the three-body effects inthe putative planetary system of PSR 1257+12 is presented. Ways inwhich these effects are manifested in the pattern of pulse arrivaltimes are discussed; the dominant perturbation is described as amodulation of the phases of the near-sinusoidal signals of the twoplanetary companions. Explicit formulas for the time dependence of theoscillating orbital elements that are needed for an improved timingmodel for this system are provided. If a timing model with fixed,independent Keplerian orbits continues to be used for the timinganalysis, and if two planets are indeed orbiting this pulsar, then thethree-body effects should become detectable by means of a growthin the postfit residuals as more observations are accumulated. Ifthe typical error in the pulse arrival time measurements is about10 microsec, the amplitude of the postfit residuals will increasebeyond this level with three to five years of timing observations.