Prospects for measuring the moment of inertia of pulsar J0737-3039A

Abstract

Here we consider the possibility-envisaged by many authors as feasible in the near future-of measuring at 10% or better the moment of inertia I of the pulsar J0737-3039A via the gravitomagnetic spin–orbit periastron precession (analogous to the Lense–Thirring pericentre precession in the case of a test-particle orbiting a central spinning mass). Such a gravitomagnetic effect is expected to be of the order of 10 - 4 deg yr - 1 and the present-day precision in measuring the periastron precession of J0737-3039A via pulsar timing is 6.8 × 10 - 4 deg yr - 1 . However the systematic uncertainty in the much larger first-order post-Newtonian (1PN) gravitoelectric precession (analogous to the Einstein Mercury’s perihelion precession in the weak-field and slow-motion approximation), which should be subtracted from the measured one in order to pick up the gravitomagnetic rate, is of primary importance. Indeed, by determining the sum of the masses by means of the third Kepler law, such a bias amounts to 0.03165 deg yr −1, according to the current level of accuracy in knowing the parameters of the J0737-3039 system. The major sources of uncertainty are the Keplerian projected semimajor axis x B of the component B and the post-Keplerian parameter s, identified with sin i ; their knowledge should be improved by three orders of magnitude at least; the bias due to the Keplerian projected semimajor axis x A of the component A amounts to ≈ 10 % today. The present-day level of accuracy in the eccentricity e would affect the investigated measurement at a percent level, while the impact of the orbital period P b is completely negligible. If, instead, the sum of the masses is measured by means of the post-Keplerian parameters r and s, it turns out that r should be measured five orders of magnitude better than now: according to the present-day level of accuracy, the total uncertainty in the 1PN periastron rate is, in this case, 2.11819 deg yr −1. In conclusion, the prospect of measuring the moment of inertia of PSR J0737-3039A at 10% accuracy or better seems unlikely given the limitations to the precision with which the system’s basic binary and post-Keplerian parameters can be measured via radio timing.