Ekman Pumping and Tidal Dissipation in Close Binaries: A Refutation of Tassoul's Mechanism
Abstract
We show that the existence of an Ekman boundary layer does not enhance the tidal dissipation in a close binary star because the tides do not exert a stress on the stellar surface. The synchronization timescale is of order (ɛT)-2tadj, where tadj is the (global) viscous damping time and ɛT is the tidal deformation caused by the companion (Darwin 1879; Zahn 1966; Scharlemann 1982; Rieutord & Bonazzola 1987). We thus refute the claim made by Tassoul (1987), who thought to have found a very efficient mechanism for the synchronization and circularization of binary systems. We analyze the paper by Tassoul & Tassoul (1992b) and prove that the alleged magnitude of their Ekman pumping is due to an improper treatment of the surface boundary conditions. Their mechanism would have dramatic, yet unverified consequences, as illustrated by two examples of tidal interaction: between Io and Jupiter, and in the newly discovered planetary system 51 Peg.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- January 1997
- DOI:
- 10.1086/303494
- Bibcode:
- 1997ApJ...474..760R
- Keywords:
-
- Stars: Binaries: Close;
- Hydrodynamics;
- Stars: Interiors;
- Stars: Rotation