Dissipation of a tide in a differentially rotating star

The orbital period of the binary pulsar PSR J0045-7319, which is located in our neighboring galaxy, the Small Magellanic Cloud (SMC), appears to be de creasing on a timescale of similar to 5 x 10(5) yr. This timescale is more than 2 orders of magnitude smaller than what is expected from the standard theory of tidal dissipation. Kumar & Quataert proposed that this rapid evol ution could be understood provided that the neutron star's companion, a mai n-sequence B star, has set up significant differential rotation. The goal o f this paper is to evaluate the redistribution of angular momentum in the B star due to meridional circulation and shear stresses and to calculate the evolution of the rotation profile when these two processes act in competit ion with the deposition of momentum by the tidal wave. We find that althoug h angular momentum redistribution is important, the B star may continue to have sufficient differential rotation sb that tidal waves are entirely abso rbed as they arrive at the surface. The mechanism proposed by Kumar & Quata ert to speed up the orbital evolution of the SMC binary pulsar should there fore work as suggested.