Attempts to dynamically constrain the quadrupole mass moment of millisecond pulsars

In this paper we try to dynamically constrain the quadrupole mass moment Q of the millisecond PSR B1257+12 pulsar from the orbital periods of its three planets, assumed to be in equatorial and circular orbits. Given the present-day accuracy in knowing their ephemerides, no post-Newtonian corrections to their motions are required. By conservatively assuming 1% and 10% uncertainties in the pulsar’s mass and planets’ semimajor axes, respectively, our determination of the adimensional parameter q = cQ/GM is q = (−0.90± 67.45)× 10, so that Q = (−1.08 ± 80.22)× 10 kg m. As an independent check of such a result, we apply the same method to the binary system composed by the millisecond PSR J1909-3744 pulsar and a white dwarf in circular orbit. We find for such a pulsar q = (−0.76 ± 21.18) × 10 and Q = (−0.98± 27.26)× 10 kg m, which are consistent with the estimates for PSR B1257+12.