Orbital Decay of the PSR J0045−7319 Binary System: Age of Radio Pulsar and Initial Spin of Neutron Star

Recent timing observations of PSR J0045-7319 reveal that the neutron star/Bstar binary orbit is decaying on a time scale of $|\Porb/\dot\Porb|=0.5$ Myr,shorter than the characteristic age ($\tau_c=3$ Myr) of the pulsar (Kaspi etal.~1996a). We study mechanisms for the orbital decay. The standard weakfriction theory based on static tide requires far too short a viscous time toexplain the observed $\dot\Porb$. We show that dynamical tidal excitation ofg-modes in the B star can be responsible for the orbital decay. However, toexplain the observed short decay timescale, the B star must have somesignificant retrograde rotation with respect to the orbit --- The retrograderotation brings lower-order g-modes, which couple much more strongly to thetidal potential, into closer ``resonances'' with the orbital motion, thussignificantly enhancing the dynamical tide. A much less likely possibility isthat the g-mode damping time is much shorter than the ordinary radiativedamping time. The observed orbital decay timescale combined with a genericorbital 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 theneutron star formation. Thus the characteristic age of the pulsar is not a goodage indicator. Assuming standard magnetic dipole braking for the pulsar and nosignificant magnetic field decay on a timescale $\lo 1$ Myr, the upper limitfor the age implies that the initial spin of the neutron star at birth wasclose to its current value.Comment: AASTeX, 9 pages, 3 ps figures. ApJ Letters, in pres