Influence of stellar structure, evolution, and rotation on the tidal damping of exoplanetary spin-orbit angles

¹ Université Paris-Sud, CNRS, Institut d’Astrophysique Spatiale, UMR8617, 91405 Orsay Cedex, France
² Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
e-mail: damiani@mps.mpg.de
³ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
⁴ Université Paris Diderot, AIM, Sorbonne Paris Cité, CEA, CNRS, 91191 Gif-sur-Yvette, France

Received: 22 December 2017
Accepted: 24 March 2018

Abstract

Context. It is debated whether close-in giant planets can form in-situ and if not, which mechanisms are responsible for their migration. One of the observable tests for migration theories is the current value of the obliquity, that is, the angle between the stellar equatorial plane and the orbital plane. However, after the main migration mechanism has ended, the obliquity and the semi-major axis keep on evolving due to the combined effects of tides and magnetic braking. The observed correlation between effective temperature and measured projected obliquity in well-characterised systems has been taken as evidence of such mechanisms being at play.

Aims. Our aim is to produce an improved model for the tidal evolution of the obliquity, including all the components of the dynamical tide for circular misaligned systems. This model is developed to take into account the strong variations in structure and rotation of stars during their evolution, and their consequences for the efficiency of tidal dissipation.

Methods. Our model uses an analytical formulation for the frequency-averaged dissipation in convective layers for each mode, depending only on global stellar parameters and rotation. It also includes the effect of magnetic braking in the framework of a double zone stellar model.

Results. For the orbital configurations of typical hot Jupiters, the obliquity is generally damped on a much shorter timescale than the semi-major axis. The final outcome of tidal evolution is also very sensitive to the initial conditions, with Jupiter-mass planets being either quickly destroyed or put on more distant orbits, depending on the initial ratio of planetary orbital momentum to stellar spin momentum. However, we find that everything else being the same, the evolution of the obliquity around low-mass stars with a thin convective zone is not slower than around those with a thicker convective zone. On the contrary, we find that more massive stars, which remain faster rotators throughout their main-sequence, produce more efficient dissipation.