A PULSE-TIMING MODEL FOR PULSARS IN MASSIVE ECLIPSING BINARIES - DELAYS CAUSED BY HIGH RATIOS BETWEEN THE PULSAR PERIOD AND ORBITAL LENGTH

We study the delay induced by gravitational light bending in the arriv al times of signals emitted by an anisotropic source in rotation (puls ar). The shift of the direction of the allowed pulsar beam (a vector d efined by the null geodesic connecting the pulsar to the observer) wit h orbital phase induces a delay arising from the movement of the pulsa r in its orbit (orbital aberration) and another of gravitational origi n (gravitational shift delay). The delay due to the orbital aberration has the same dependence on orbital phase as the purely geometric orbi tal delay and is therefore unobservable. We derive a pulse-timing mode l for pulsars in massive binaries with high inclination (i = pi/2) and negligible eccentricity, adding to the well-known contributions (orbi tal, Shapiro and non-observable orbital aberration) an extra delay pro duced by the gravitational shift of the allowed pulsar beam and by an additional (and measurable) term of aberration which appears when the number of pulses is used to define the coordinate time of emission in the pulse-timing model. From the ratio of the pulsar period P to the o rbital length L (in c = 1 units), the extra and the Shapiro delays are compared. If P/L greater than or equal to 1, the extra delay is the d ominant one. Some high-mass X-ray binaries (e.g. Vela X-1) may be idea l scenarios for measuring the extra delay and testing whether pulsars are indeed rotating beacons. However, for X-ray binaries with long pul sar periods, the arrival times are poorly determined and this effect c annot be observed. For high-mass radio binaries, the uncertainties in the determination of the pulse arrival time are small, but the amplitu de of the extra delay is also small. The possible discovery of binary pulsars with short periods and significant values of P/L (or the impro vement in the measure of arrival times) should allow the observation o f this interesting effect involving gravitation and aberration.