Non-adiabatic tidal oscillations induced by a planetary companion

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-Väisälä 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.

References in corpus (7)

• Characteristics of planetary candidates observed by Kepler, II: Analysis of the first four months of data
• The Occurrence and Architecture of Exoplanetary Systems
• On the tidal interaction of a solar-type star with an orbiting companion: Excitation of g mode oscillation and orbital evolution
• Heartbeat Stars, Tidally Excited Oscillations, and Resonance Locking
• Tidal asteroseismology: Kepler's KOI-54
• Ellipsoidal Oscillations Induced by Substellar Companions: A Prospect for the Kepler Mission
• The Radial Velocity Signature of Tides Raised in Stars Hosting Exoplanets

Cited by in corpus (7)

• Tidal dissipation in evolving low-mass and solar-type stars with predictions for planetary orbital decay
• On a new formulation for energy transfer between convection and fast tides with application to giant planets and solar type stars
• On the interaction between fast tides and convection
• On the energetics of a tidally oscillating convective flow
• On the evolution of a binary system with arbitrarily misaligned orbital and stellar angular momenta due to quasi-stationary tides
• The tidal excitation of r modes in a solar type star orbited by a giant planet companion and the effect on orbital evolution I: The aligned case
• Tidally induced stellar oscillations: converting modelled oscillations excited by hot Jupiters into observables