Effects of Pulsar Rotation on Timing Measurements of the Double Pulsar System J0737−3039

We study the effect of pulsar rotation on timing of binary pulsars, withparticular emphasis on the double pulsar system J0737-3039. Specialrelativistic aberration due to the orbital motion of pulsar changes both thelongitude and colatitude of the emission direction with respect to the pulsarspin axis. The former gives rise to a shift of the arrival time of the pulsecentroid (this is the conventional ``longitudinal'' aberration delay), thelatter results in a distortion (contraction or dilation) of the pulse profileon the orbital timescale. The amplitude of pulse distortion depends inverselyon the variation of polarization position angle across the pulse. For smallangle between the pulsar magnetic and spin axes, as inferred for PSRJ0737-3039A from polarimetric observations, the pulse distortion is significant(\sim 1%) and the associated ``latitudinal'' aberration delay is much largerthan the longitudinal one. By monitoring the arrival time of separate pulsecomponents as a function of pulsar orbital phase, the latitudinal aberrationdelay may be easily measured with the current timing precision, thusconstraining the spin geometry of the system. The latitudinal delay can also bedetected by monitoring system's orbital parameters on the geodetic precessiontimescale. Because of the near edge-on orbital orientation of the PSRJ0737-3039 system, general relativistic bending of pulsar A's radio beam nearits superior conjunction also introduces spin-dependent time delays of similarorder of magnitude as the aberration delays. In addition, light bending splitsthe pulse profile into two variable components, corresponding to twogravitationally lensed images of the source. Detection of lensing effects ischallenging, but may be possible with existing technology.Comment: Minor changes, accepted to Ap