Three-dimensional simulations of internal wave breaking and the fate of planets around solar-type stars

• Published in: Monthly notices of the Royal Astronomical Society 2011-06, Vol.414 (2), p.1365-1378
• Main Author: Barker, Adrian J.
• Format: Article
• Language: English
• Subjects: Astronomy; binaries: close; Earth, ocean, space; Exact sciences and technology; hydrodynamics; instabilities; planetary systems; Planets; Simulation; Stars & galaxies; stars: rotation; Wave power; waves
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2011.18468.x

We study the fate of internal gravity waves approaching the centre of an initially non-rotating solar-type star, by performing three-dimensional numerical simulations using a Boussinesq-type model. These waves are excited at the top of the radiation zone by the tidal forcing of a short-period planet on a circular, coplanar orbit. This extends previous work done in two dimensions by Barker & Ogilvie. We first derive a linear wave solution, which is not exact in three dimensions; however, the reflection of ingoing waves from the centre is close to perfect for moderate amplitude waves. Waves with sufficient amplitude to cause isentropic overturning break, and deposit their angular momentum near the centre. This forms a critical layer, at which the angular velocity of the flow matches the orbital angular frequency of the planet. This efficiently absorbs ingoing waves, and spins up the star from the inside out, while the planet spirals into the star. We also perform numerical integrations to determine the linearized adiabatic tidal response throughout the star, in a wide range of solar-type stellar models with masses in the range 0.5 ≤m ★/M⊙≤ 1.1, throughout their main-sequence lifetimes. The aim is to study the influence of the launching region for these waves at the top of the radiation zone in more detail, and to determine the accuracy of a semi-analytic approximation for the tidal torque on the star, which was derived under the assumption that all ingoing wave angular momentum is absorbed in a critical layer. The main conclusion of this work is that this non-linear mechanism of tidal dissipation could provide an explanation for the survival of all short-period extrasolar planets observed around FGK stars, while it predicts the destruction of more massive planets. This work provides further support for the model outlined in a previous paper by Barker & Ogilvie, and makes predictions that will be tested by ongoing observational studies, such as WASP and Kepler.