Dynamical Tides in Rotating Binary Stars

We study the effect of rotation on the excitation of internal oscillation modes of a star by the external gravitational potential of its companion. Unlike the nonrotating case, there are difficulties with the usual mode decomposition for rotating stars because of the asymmetry between modes propagating in the direction of rotation and those propagating opposite to it. For an eccentric binary system, we derive general expressions for the energy transfer $\Delta E_s$ and the corresponding angular momentum transfer $\Delta J_s$ in a periastron passage when there is no initial oscillation present in the star. Except when a nearly precise orbital resonance occurs (i.e., the mode frequency equals multiple of the orbital frequency), $\Delta E_s$ is very close to the steady-state mode energy in the tide in the presence of dissipation. It is shown that stellar rotation can change the strength of dynamical tide significantly. In particular, retrograde rotation with respect to the orbit increases the energy transfer by bringing lower-order g-modes (or f-mode for convective stars), which couple more strongly to the tidal potential, into closer resonances with the orbital motion of the companion. We apply our general formalism to the problems of tidal capture binary formation and the orbital evolution of PSR J0045-7319/B-star binary. Stellar rotation changes the critical impact parameter for binary capture. Although the enhancement (by retrograde rotation) in the capture cross section is at most $\sim 20%$, the probability that the captured system survives disruption/merging and therefore becomes a binary can be significantly larger. It is found that in order to explain the observed rapid orbital decay of the PSR J0045-7319 binary system, retrograde rotation in the B-star is required.