Evolution of star–planet systems under magnetic braking and tidal interaction

M Benbakoura,C Le Poncin-Lafitte,S Mathis,V Réville,A S Brun

doi:10.1051/0004-6361/201833314

Abstract

Context.With the discovery over the last two decades of a large diversity of exoplanetary systems, it is now of prime importance to characterize star–planet interactions and how such systems evolve.Aims.We address this question by studying systems formed by a solar-like star and a close-in planet. We focus on the stellar wind spinning down the star along its main-sequence phase and tidal interaction causing orbital evolution of the systems. Despite recent significant advances in these fields, all current models use parametric descriptions to study at least one of these effects. Our objective is to introduce ab initio prescriptions of the tidal and braking torques simultaneously, so as to improve our understanding of the underlying physics.Methods.We develop a one-dimensional (1D) numerical model of coplanar circular star–planet systems taking into account stellar structural changes, wind braking, and tidal interaction and implement it in a code called ESPEM. We follow the secular evolution of the stellar rotation and of the semi-major axis of the orbit, assuming a bilayer internal structure for the former. After comparing our predictions to recent observations and models, we perform tests to emphasize the contribution of ab initio prescriptions. Finally, we isolate four significant characteristics of star–planet systems: stellar mass, initial stellar rotation period, planetary mass and initial semi-major axis; and browse the parameter space to investigate the influence of each of them on the fate of the system.Results.Our secular model of stellar wind braking accurately reproduces the recent observations of stellar rotation in open clusters. Our results show that a planet can affect the rotation of its host star and that the resulting spin-up or spin-down depends on the orbital semi-major axis and on the joint influence of magnetic and tidal effects. The ab initio prescription for tidal dissipation that we used predicts fast outward migration of massive planets orbiting fast-rotating young stars. Finally, we provide the reader with a criterion based on the characteristics of the system that allows us to assess whether or not the planet will undergo orbital decay due to tidal interaction.

Highlights

The planetary systems discovered during the last two decades show a wide and unexpected diversity
We computed the secular evolution of a star–planet system composed of a solarmass star and a Jupiter-mass planet with an initial semi-major axis equal to 0.025 AU
We presented ESPEM, a code implementing a model of secular evolution of star–planet systems under magnetic braking and tidal interaction

Summary

Introduction

The planetary systems discovered during the last two decades show a wide and unexpected diversity. Tidal interactions play a key role in the orbital configuration of these very compact systems since they are likely to circularize orbits, align spins, and synchronize periods (Zahn 1977; Mathis & Remus 2013; Ogilvie 2014) These interactions consists in an exchange of angular momentum between the orbit and the spins of the celestial bodies. The equilibrium tide is the large-scale velocity field associated with tidal deformation, the so-called tidal bulge This nonwave-like entity corresponds to the hydrostatic adjustment of the star to the gravitational perturbation (Zahn 1966; Remus et al 2012). The friction applied by convective motions delays the response of the star to the perturbation (e.g., Zahn 1989; Ogilvie & Lesur 2012; Mathis et al 2016) This results in a lag angle between the axes of the tidal bulge and the line of centers. Since lower-mass stars have deeper convective envelopes, they dissipate more energy than

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Results

Conclusion