Understanding and improving the timing of PSR J0737−3039B

International audienceThe double pulsar (PSR J0737−3039A/B) provides some of the most stringent tests of general relativity (GR) and its alternatives. The success of this system in tests of GR is largely due to the high-precision, long-term timing of its recycled-pulsar member, pulsar A. On the other hand, pulsar B is a young pulsar that exhibits significant short-term and long-term timing variations due to the electromagnetic-wind interaction with its companion and geodetic precession. Improving pulsar B’s timing precision is a key step towards improving the precision in a number of GR tests with PSR J0737−3039A/B. In this paper, red noise signatures in the timing of pulsar B are investigated using roughly a four-year time span, from 2004 to 2008, beyond which time the pulsar’s radio beam precessed out of view. In particular, we discuss the profile variations seen on timescales ranging from minutes – during the so-called “bright” orbital phases – to hours – during its full 2.5 h orbit – to years, as geodetic precession displaces the pulsar’s beam with respect to our line of sight. Also, we present our efforts to model the orbit-wide, harmonic modulation that has been previously seen in the timing residuals of pulsar B, using simple geometry and the impact of a radial electromagnetic wind originating from pulsar A. Our model successfully accounts for the long-term precessional changes in the amplitude of the timing residuals but does not attempt to describe the fast profile changes observed during each of the bright phases, nor is it able to reproduce the lack of observable emission between phases. Using a nested sampling analysis, our simple analytical model allowed us to extract information about the general properties of pulsar B’s emission beam, such as its approximate shape and intensity, as well as the magnitude of the deflection of that beam, caused by pulsar A’s wind. We also determined for the first time that the most likely sense of rotation of pulsar B, consistent with our model, is prograde with respect to its orbital motion. Finally, we discuss the potential of combining our model with future timing of pulsar B, when it becomes visible again, towards improving the precision of tests of GR with the double pulsar. The timing of pulsar B presented in this paper depends on the size of the pulsar’s orbit, which was calculated from GR, in order to precisely account for orbital timing delays. Consequently, our timing cannot directly be used to test theories of gravity. However, our modelling of the beam shape and radial wind of pulsar B can indirectly aid future efforts to time this pulsar by constraining part of the additional red noise observed on top of the orbital delays. As such, we conclude that, in the idealised case of zero covariance between our model’s parameters and those of the timing model, our model can bring about a factor 2.6 improvement on the measurement precision of the mass ratio, $R$ = $m_A/m_B$, between the two pulsars: a theory-independent parameter, which is pivotal in tests of GR