2006ApJ...641..438R

We study the effect of pulsar rotation on the timing of binary pulsars, with particular emphasis on the double pulsar system J0737-3039. Special relativistic aberration due to the orbital motion of a pulsar changes both the longitude and latitude of the emission direction with respect to the pulsar spin axis. The former gives rise to a shift of the arrival time of the pulse centroid (this is the conventional ``longitudinal'' aberration delay), and the latter results in a distortion (contraction or dilation) of the pulse profile on the orbital timescale. In the framework of the rotating vector model of pulsar emission, the amplitude of pulse distortion depends inversely on the variation of the polarization position angle across the pulse. For a small angle between the pulsar magnetic and spin axes, as has been inferred for PSR J0737-3039A from polarimetric observations, the pulse distortion is significant (∼1%) and the associated ``latitudinal'' aberration delay is much larger than the longitudinal one. We show that by monitoring the arrival time of separate pulse components as a function of pulsar orbital phase, the latitudinal aberration delay may be easily measured with the current timing precision. Such a measurement would constrain the spin geometry of the system. The latitudinal delay can also be detected by monitoring the system's orbital parameters on the geodetic precession timescale. Because of the near-edge-on orbital orientation of the PSR J0737-3039 system, general relativistic bending of pulsar A's radio beam near its superior conjunction also introduces spin-dependent time delays of similar orders of magnitude as the aberration delays. In addition, light bending splits the pulse profile into two variable components, corresponding to two gravitationally lensed images of the source. Detection of lensing effects is challenging, but it may be possible with existing technology.