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/B star binary orbit is decaying on a timescale of \P-orb\P-ocb\ = 0.5 Myr, shorter than the characteristic age (tau(c) = 3 Myr) of the pulsar. 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 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,'' yielding an upper limit of 1.4 Myr on the age of the binary system since the neutron star's 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 less than or similar to 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.