Differential rotation enhanced dissipation of tides in the PSR J0045-7319 binary

Recent observations of PSR J0045-7319, a radio pulsar in a close eccentric orbit with a massive B star companion, indicate that the system's orbital period is decreasing on a timescale of approximate to 5 x 10(5) yr. This is much shorter than the timescale of approximate to 10(9) yr given by the standard theory of tidal dissipation in radiative stars. Observations also suggest that the B star is rotating rapidly, perhaps at nearly its breakup speed. We show that the dissipation of the dynamical tide in a star rotating in the same direction as the orbital motion of its companion (prograde rotation) with a speed greater than the orbital angular speed of the star at periastron (supersynchronous rotation) results in an increase in the orbital period of the binary system with time. Thus, if the magnitude of the rotation speed of the B star is supersynchronous, then the observed decrease in the orbital period requires the direction of the rotation of the B star to be retrograde. For subsynchronous prograde rotation of the B star, the energy in the dynamical tide, even if it is dissipated in one orbital period, is too small to account for the observed orbital evolution, unless the rotation speed is close to zero. Slow rotation of the B star is, however, ruled out by the observed apsidal motion of the system (Lai et al., Kaspi et al.). Thus, in order to explain both the observed apsidal motion and the orbital evolution of the PSR J0045-7319 binary, the B star must have retrograde rotation. If the rotation in the interior of the B star is not synchronized, which we show is the case, then the work of Goldreich & Nicholson suggests that the B star should be rotating differentially, with the rotation speed of the outer layers close to the synchronous value. We show that the dissipation of the dynamical tide in such a differentially rotating B star is enhanced by almost 3 orders of magnitude, leading to an orbital evolution time for the PSR J0045-7319 binary that is consistent with the observations.