V. Dynamical and equilibrium tides in convective zones
Geneva Observatory, University of Geneva,
2 Indian Institute of Technology, Kharagpur, India
3 Physikalisches Institut, University of Bern, 3012 Bern, Switzerland
Accepted: 28 June 2018
Context. When planets are formed from the protoplanetary disk and after the disk has dissipated, the evolution of their orbits is governed by tidal interactions, friction, and gravitational drag, and also by changes in the mass of the star and planet. These interactions may change the initial distribution of the distances between the planets and their host star by expanding the original orbit, by contracting it (which may cause an engulfment of the planet by the star), or by destroying the planet.
Aims. We study the evolution of the orbit of a planet orbiting its host star under the effects of equilibrium tides, dynamical tides, drag (frictional and gravitational), and stellar mass loss.
Methods. We used the Geneva stellar evolution code to compute the evolution of stars with initial masses of 1 and 1.5 M⊙ with different rotation rates at solar metallicity. The star is evolved from the pre-main-sequence (PMS) up to the tip of the red giant branch. We used these models as input for computing the evolution of the planetary orbits. We explored the effects of changing the planet masses (of 1 Earth mass up to 20 Jupiter masses), the distance between the planet and the star (of 0.015 and more than 3 au), the mass, and the spin of the star. We present results when only the equilibrium tide was accounted for and when both equilibrium and dynamical tides were accounted for. The expression for the dynamical tide is a frequency-averaged dissipation of tidally excited inertial waves, obtained from a piecewise homogeneous two-layer stellar model. Gravity wave damping was neglected.
Results. Dynamical tides in convective zones have a significant effect on planetary orbits only during the PMS phase and only for fast-rotating stars. They have no significant effects during the PMS phase for initially slow-rotating stars and during the red giant branch phase, regardless of the initial rotation. In the plots of initial orbital distance versus planetary mass, we show the regions that lead to engulfment or any significant changes in the orbit. As a result of orbital evolution, a region near the star can become devoid of planets after the PMS phase. We call this zone the planet desert, and its extent depends sensitively on stellar rotation. An examination of the planet distribution as a function of distance to the host star and mass can provide constraints on current computations.
Key words: planetary systems / planet–star interactions
© ESO 2018