  Recent observations of PSR J0045-7319, a radio pulsar in a close eccentric
orbit with a massive main sequence B-star companion, indicate that the system's
orbital period is decreasing on a timescale $\sim 5 x 10^{5}$ years (Kaspi et
al. 1996). Timing observations of PSR J0045-7319 also indicate that the B-star
is rotating rapidly, perhaps close to its breakup rotation rate. For rapid
(super-synchronous) prograde rotation of the B-star, tidal dissipation leads to
an increasing orbital period for the binary system, while for retrograde
rotation of any magnitude, the orbital period decreases with time. We show that
if tidal effects are to account for the observed orbital decay of the PSR
J0045-7319 binary, the B-star must have retrograde rotation. This implies that
the supernova that produced the pulsar in this binary system likely had a
dipole anisotropy.
  For a reasonably wide range of retrograde rotation rates, the energy in the
dynamical tide of the B-star needs to be dissipated in about one orbital period
in order to account for the observed orbital evolution time for the PSR
J0045-7319 binary. We show, however, that the radiative dissipation of the
dynamical tide in a rigidly rotating B-star is too inefficient by a factor of
$\approx$ 10$^3$, regardless of the magnitude of the rotation rate. We describe
how, when the surface of the B-star is rotating nearly synchronously (which is
expected from the work of Goldreich and Nicholson, 1989), the energy in the
dynamical tide is dissipated in less than an orbital period, thus reconciling
the theoretical and observed rates of orbital evolution.
