On the tidal interaction of a solar-type star with an orbiting companion: Excitation of g-mode oscillation and orbital evolution

We calculate the dynamical tides raised on a nonrotating solar-type star by a close stellar or planetary companion. Dissipation arising from a turbule nt 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 mag nitude of the tidally induced velocity at the stellar photosphere. These ca lculations are compared to the results obtained by assuming that a very sma ll frequency limit can be taken in order to calculate the tidal response (e quilibrium tide). For a standard solar model the latter is found to give a relatively poor approximation at the periods of interest of several days, e ven when the system is far from resonance with a normal mode. This behavior is caused by the small value of the Brunt-Vaisala frequency in the interio r regions of the convection zone. It is shown that although the companion m ay 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 control led 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 simpl y estimated from mixing-length theory for nonrotating stars. We discuss the means by which this enhanced viscosity might be realized. These calculatio ns 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 n ot affected by the possibility of resonance. For this system the stellar ro tation and the orbital motion are expected to be synchronized if the mass o f the companion is as much as 1/10 M..