Effect of the stellar spin history on the tidal evolution of close-in planets

Context. The spin rate of stars evolves substantially during their lifetime, owing to the evolution of their internal structure and to external torques arising from the interaction of stars with their environments and stellar winds.
Aims: We investigate how the evolution of the stellar spin rate affects, and is affected by, planets in close orbits via star-planet tidal interactions.
Methods: We used a standard equilibrium tidal model to compute the orbital evolution of single planets orbiting both Sun-like stars and very low-mass stars (0.1 M_⊙). We tested two stellar spin evolution profiles, one with fast initial rotation (1.2 day rotation period) and one with slow initial rotation (8 day period). We tested the effect of varying the stellar and planetary dissipations, and the planet's mass and initial orbital radius.
Results: For Sun-like stars, the different tidal evolution between initially rapidly and slowly rotating stars is only evident for extremely close-in gas giants orbiting highly dissipative stars. However, for very low-mass stars the effect of the initial rotation of the star on the planet's evolution is apparent for less massive (1 M_⊕) planets and typical dissipation values. We also find that planetary evolution can have significant effects on the stellar spin history. In particular, when a planet falls onto the star, it can cause the star to spin up.
Conclusions: Tidal evolution allows us to differentiate between the early behaviors of extremely close-in planets orbiting either a rapidly rotating star or a slowly rotating star. The early spin-up of the star allows the close-in planets around fast rotators to survive the early evolution. For planets around M-dwarfs, surviving the early evolution means surviving on Gyr timescales, whereas for Sun-like stars the spin-down brings about late mergers of Jupiter planets. In the light of this study, we can say that differentiating one type of spin evolution from another given the present position of planets can be very tricky. Unless we can observe some markers of former evolution, it is nearly impossible to distinguish the two very different spin profiles, let alone intermediate spin-profiles. Nevertheless, some conclusions can still be drawn about statistical distributions of planets around fully convective M-dwarfs. If tidal evolution brings about a merger late in the stellar history, it can also entail a noticeable acceleration of the star at late ages, so that it is possible to have old stars that spin rapidly. This raises the question of how the age of stars can be more tightly constrained.