Resonant orbital evolution in the putative planetary system of PSR1257 + 12

Periodic variations in the arrival times of pulses from the millisecond pulsar PSR1257+12 are most straightforwardly interpreted as indicating the presence of two planet-like companions orbiting the pulsar¹. Rasio et al.²have proposed that the planetary explanation is amenable to a simple test: the deduced parameters put the planets near an orbital resonance, in which case secular evolution of the orbits should be observable in a matter of years. Detection of such orbital evolution would yield the masses and orbital inclinations of the planets. Here we point out that if the masses of the two planets are more than ∼10 times greater than the minimum values (3.4 and 2.8 Earth masses) allowed by the observations, then their orbits will be in an exact 3:2 resonance. The character of the predicted orbital parameter perturbations is then markedly different from the periodic perturbations that result from only a near-resonance. The amplitude of the perturbations is much greater, and is very sensitive to the planet masses.