Non-adiabatic tidal oscillations induced by a planetary companion

TL;DR

This paper calculates non-adiabatic tidal oscillations caused by a planetary companion on stars, revealing large horizontal displacements and significant flux perturbations that could enhance observational detection.

Contribution

It provides the first fully non-adiabatic calculations of dynamical tides in stars with planetary companions, highlighting the importance of non-adiabatic effects near the surface.

Findings

Horizontal displacements are 10 to 100 times larger than equilibrium tide predictions.

Surface flux perturbations can reach about 0.1%, affecting observability.

Non-adiabatic effects dominate in the outer stellar layers, invalidating the equilibrium tide approximation.

Abstract

We calculate the dynamical tides raised by a close planetary companion on non-rotating stars of $1$ $\text{M}_{\odot}$ and $1.4$ $\text{M}_{\odot}$. Using the Henyey method, we solve the fully non-adiabatic equations throughout the star. The horizontal Lagrangian displacement is found to be 10 to 100 times larger than the equilibrium tide value in a thin region near the surface of the star. This is because non--adiabatic effects dominate in a region that extends from below the outer edge of the convection zone up to the stellar surface, and the equilibrium tide approximation is inconsistent with non--adiabaticity. Although this approximation generally applies in the low frequency limit, it also fails in the parts of the convection zone where the forcing frequency is small but larger than the Brunt-V\"ais\"al\"a frequency. We derive analytical estimates which give a good approximation to the numerical values of the magnitude of the ratio of the horizontal and radial displacements at the surface. The relative surface flux perturbation is also significant, on the order of 0.1 % for a system modelled on 51 Pegasi b. Observations affected by the horizontal displacement may therefore be more achievable than previously thought, and brightness perturbations may be the result of flux perturbations rather than due to the radial displacement. We discuss the implication of this on the possibility of detecting such tidally excited oscillations, including the prospect of utilising the large horizontal motion for observations of systems such as 51 Pegasi.