Recent timing observations of PSR J0045-7319 reveal that the neutron star/B star binary orbit is decaying on a time scale of |P _ { orb } / \dot { P } _ { orb } | = 0.5 Myr , shorter than the characteristic age ( \tau _ { c } = 3 Myr ) of the pulsar ( Kaspi et al .
1996a ) .
We study mechanisms for the orbital decay .
The standard weak friction theory based on static tide requires far too short a viscous time to explain the observed \dot { P } _ { orb } .
We show that dynamical tidal excitation of g-modes in the B star can be responsible for the orbital decay .
However , to explain the observed short decay timescale , the B star must have some significant retrograde rotation with respect to the orbit — The retrograde rotation brings lower-order g-modes , which couple much more strongly to the tidal potential , into closer “ resonances ” with the orbital motion , thus significantly enhancing the dynamical tide .
A much less likely possibility is that the g-mode damping time is much shorter than the ordinary radiative damping time .
The observed orbital decay timescale combined with a generic orbital evolution model based on dynamical tide can be used as a “ timer ” , giving an upper limit of 1.4 Myr for the age of the binary system since the neutron star formation .
Thus the characteristic age of the pulsar is not a good age indicator .
Assuming standard magnetic dipole braking for the pulsar and no significant magnetic field decay on a timescale \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } 1 Myr , the upper limit for the age implies that the initial spin of the neutron star at birth was close to its current value .