On the Tidal Interaction of a Solar‐Type Star with an Orbiting Companion: Excitation of g‐Mode Oscillation and Orbital Evolution

Abstract

We calculate the dynamical tides raised on a nonrotating solar-type star by a close stellar or planetary companion. Dissipation arising from a turbulent viscosity operating in the convection zone and radiative damping in the radiative core are considered. We compute the torque exerted on the star by a companion in circular orbit and determine the potentially observable magnitude of the tidally induced velocity at the stellar photosphere. These calculations are compared to the results obtained by assuming that a very small frequency limit can be taken in order to calculate the tidal response ( equilibrium tide ). For a standard solar model the latter is found to give a relatively poor approximation at the periods of interest of several days, even when the system is far from resonance with a normal mode. This behavior is caused by the small value of the Brunt-Väisälä frequency in the interior regions of the convection zone. It is shown that although the companion may go through a succession of resonances as it spirals in under the action of the tides, for a fixed spectrum of normal modes its migration is controlled essentially by the nonresonant interaction. We find that the turbulent viscosity that is required to provide the observed circularization rates of main-sequence solar-type binaries is about 50 times larger than that simply estimated from mixing-length theory for nonrotating stars. We discuss the means by which this enhanced viscosity might be realized. These calculations are applied to 51 Pegasi. We show that the perturbed velocity induced by the tides at the stellar surface is too small to be observed. This result is insensitive to the magnitude of the turbulent viscosity assumed and is not affected by the possibility of resonance. For this system the stellar rotation and the orbital motion are expected to be synchronized if the mass of the companion is as much as 1/10 M ☉ .