On Synchronization in Detached Close Binaries: Reply to Rieutord and Zahn

Abstract

In this paper we discuss the tidally driven meridional currents that spin down (or spin up) a nonsynchronous rotator in a time that is much shorter than the viscous decay time of residual motions. We refute the claim made by Rieutord & Zahn, who have argued that this large-scale meridional flow does not exist, so that the synchronization time should remain larger than the viscous time in a tidally distorted body. To be specific, they describe the internal motion by means of a series in the powers of the small parameter δ/R, which is the relative thickness of the Ekman boundary layer at the free surface. It is shown that their analysis of the second-order terms is inadequate because they have failed to prescribe that these terms, which are intricately coupled to the first-order terms, must satisfy the vorticity equation as well as the boundary conditions on the tensions. Accordingly, because their second-order analysis of the meridional flow in a tidally distorted configuration is incomplete, it is also inconclusive as far as the first-order terms are concerned. In other words, there is no reason to claim that tidally driven currents do not exist in a nonsynchronous rotator. Detailed justification for the existence of these currents, which are proportional to the product of δ/R and the small tidal distortion T, is given in the paper. It is also shown that planetary systems, such as Io-Jupiter or 51 Peg and its planet, do not fulfill the very specific conditions under which we previously derived the characteristic timescale of the hydrodynamical mechanism. Accordingly, planetary systems cannot be used as counterexamples to this process.