On internal wave breaking and tidal dissipation near the centre of a solar-type star

TL;DR

This paper investigates how internal gravity waves in solar-type stars break and dissipate energy, affecting tidal interactions and planetary orbital evolution, with implications for the survival of close-in giant planets.

Contribution

It introduces a model for wave breaking and dissipation near the star's center, linking wave amplitude to tidal quality factor and planetary orbital outcomes.

Findings

Wave breaking occurs above a critical amplitude, leading to efficient dissipation.

The tidal quality factor Q' depends on wave amplitude and stellar type.

Fewer close-in giant planets are expected around stars where wave breaking is efficient.

Abstract

We study the fate of internal gravity waves, which are excited by tidal forcing by a short-period planet at the interface of convection and radiation zones, approaching the centre of a solar-type star. We study at what amplitude these wave are subject to instabilities. These instabilities lead to wave breaking whenever the amplitude exceeds a critical value. Below this value, the wave reflects perfectly from the centre of the star. Wave breaking results in spinning up the central regions of the star, and the formation of a critical layer, which acts as an absorbing barrier for ingoing waves. As these waves are absorbed, the star is spun up from the inside out. This results in an important amplitude dependence of the tidal quality factor Q'. If the tidal forcing amplitude exceeds the value required for wave breaking, efficient dissipation results over a continuous range of tidal frequencies, leading to Q' \approx 10^5 (P/1day)^(8/3), for the current Sun. This varies by less than a factor of 5 throughout the range of G and K type main sequence stars, for a given orbit. We predict fewer giant planets with orbital periods of less than about 2 days around such stars, if they cause breaking at the centre, due to the efficiency of this process. This mechanism would, however, be ineffective in stars with a convective core, such as WASP-18, WASP-12 and OGLE-TR-56, perhaps partly explaining the survival of their close planetary companions.