A MeerKAT view of the double pulsar eclipses. Geodetic precession of pulsar B and system geometry

The double pulsar system, PSR J0737$-$3039A/B, consists of two neutron stars bound together in a highly relativistic orbit that is viewed nearly edge-on from the Earth. This alignment results in brief radio eclipses of the fast-rotating pulsar A when it passes behind the toroidal magnetosphere of the slow-rotating pulsar B. The morphology of these eclipses is strongly dependent on the geometric orientation and rotation phase of pulsar B, and their time evolution can be used to constrain the geodetic precession rate of the pulsar. We demonstrate a Bayesian inference framework for modelling high-sensitivity eclipse light curves obtained with MeerKAT between 2019 and 2023. Using a hierarchical inference approach, we obtained a precession rate of $ SO B circ circ circ $ (68 confidence intervals) for pulsar B, consistent with predictions from general relativity to a relative uncertainty of 6.5. This updated measurement provides a 6.1 test of relativistic spin-orbit coupling in the strong-field regime. We show that a simultaneous fit to all of our observed eclipses can in principle return a sim 1.5 test of spin-orbit coupling. However, systematic effects introduced by the current geometric orientation of pulsar B along with inconsistencies between the observed and predicted eclipse light curves result in difficult to quantify uncertainties when using this approach. Assuming the validity of general relativity, we definitively show that the spin axis of pulsar B is misaligned from the total angular momentum vector by $40.6^ circ circ $ and that the orbit of the system is inclined by approximately $90.5^ circ $ from the direction of our line of sight. Our measured geometry for pulsar B suggests the largely empty emission cone contains an elongated horseshoe-shaped beam centred on the magnetic axis, and that it may not be re-detected as a radio pulsar until early 2035.