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.

Context. Fast rotating red giants in the upper part of the red giant branch have surface velocities that cannot be explained by single star evolution. Aims. We check whether tides between a star and a planet followed by planet engulfment can indeed accelerate the surface rotation of red giants for a sufficiently long time to produce these fast rotating red giants. Methods. We studied how the surface rotation velocity at the stellar surface evolves using rotating stellar models, accounting for the redistribution of the angular momentum inside the star by different transport mechanisms, the exchanges of angular momentum between the planet orbit and the star before the engulfment, and for the deposition of angular momentum inside the star at the engulfment. We considered different situations with masses of stars in the range between 1.5 and 2.5 M , masses of the planets between 1 and 15 M J (Jupiter mass), and initial semimajor axis between 0.5 and 1.5 au. The metallicity Z for our stellar models is 0.02. Results. We show that the surface velocities reached at the end of the orbital decay due to tidal forces and planet engulfment can be similar to values observed for fast rotating red giants. This surface velocity then decreases when the star evolves along the red giant branch but at a sufficiently slow pace to allowing stars to be detected with such a high velocity. More quantitatively, star-planet interaction can produce a rapid acceleration of the surface of the star, above values equal to 8 km s −1 , for periods lasting up to more than 30% the red giant branch phase. As found already by previous works, the changes of the surface carbon isotopic ratios produced by the dilution of the planetary material into the convective envelope is modest. The increase of the lithium abundance due to this effect might be much more important, however lithium may be affected by many different, still uncertain, processes. Thus any lithium measurement can hardly be taken as a support or argument against any star-planet interaction. Conclusions. The acceleration of the stellar surface to rotation velocities above limits that depend on the surface gravity does appear at the moment to be the clearest signature of a star-planet interaction.

Context. As a star evolves, planet orbits change over time owing to tidal interactions, stellar mass losses, friction and gravitational drag forces, mass accretion, and evaporation on/by the planet. Stellar rotation modifies the structure of the star and therefore the way these different processes occur. Changes in orbits, subsequently, have an impact on the rotation of the star. Aims. Models that account in a consistent way for these interactions between the orbital evolution of the planet and the evolution of the rotation of the star are still missing. The present work is a first attempt to fill this gap. Methods. We compute the evolution of stellar models including a comprehensive treatment of rotational effects, together with the evolution of planetary orbits, so that the exchanges of angular momentum between the star and the planetary orbit are treated in a self-consistent way. The evolution of the rotation of the star accounts for the angular momentum exchange with the planet and also follows the effects of the internal transport of angular momentum and chemicals. These rotating models are computed for initial masses of the host star between 1.5 and 2.5 M , with initial surface angular velocities equal to 10 and 50% of the critical velocity on the zero age main sequence (ZAMS), for a metallicity Z = 0.02, with and without tidal interactions with a planet. We consider planets with masses between 1 and 15 Jupiter masses (M J ), which are beginning their evolution at various distances between 0.35 and 4.5 au. Results. We demonstrate that rotating stellar models without tidal interactions and without any wind magnetic braking during the red giant phase can well reproduce the surface rotations of the bulk of red giants. However, models without any interactions cannot account for fast rotating red giants in the upper part of the red giant branch, where these models, whatever the initial rotation considered on the ZAMS, always predict very low velocities. For these stars, some interaction with a companion is highly probable and the present rotating stellar models with planets confirm that tidal interaction can reproduce their high surface velocities. We also show that the minimum distance between the planet and the star on the ZAMS, which enables the planet to avoid engulfment and survive (i.e. the survival limit) is decreased around faster rotating stars.